include('Axioms/errorStateMonad+2.ax').
fof(mem_c_2EquantHeuristics_2EGUESS__EXISTS,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) )).
fof(mem_c_2EquantHeuristics_2EGUESS__EXISTS__GAP,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) )).
fof(mem_c_2EquantHeuristics_2EGUESS__EXISTS__POINT,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) )).
fof(mem_c_2EquantHeuristics_2EGUESS__FORALL,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) )).
fof(mem_c_2EquantHeuristics_2EGUESS__FORALL__GAP,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) )).
fof(mem_c_2EquantHeuristics_2EGUESS__FORALL__POINT,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) )).
fof(mem_c_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)) ) ) )).
fof(mem_c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),arr(A_27a,arr(A_27a,arr(bool,bool)))) ) )).
fof(mem_c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),arr(A_27a,arr(A_27a,arr(bool,bool)))) ) )).
fof(ax_thm_2EquantHeuristics_2EGUESS__EXISTS__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) <=> ( ( ? [V2v] : ( mem(V2v,A_27b) & p(ap(V1P,V2v)) ) ) <=> ? [V3fv] : ( mem(V3fv,A_27a) & p(ap(V1P,ap(V0i,V3fv))) ) ) ) ) ) ) ) )).
fof(ax_thm_2EquantHeuristics_2EGUESS__FORALL__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P)) <=> ( ( ! [V2v] : ( mem(V2v,A_27b) => p(ap(V1P,V2v)) ) ) <=> ! [V3fv] : ( mem(V3fv,A_27a) => p(ap(V1P,ap(V0i,V3fv))) ) ) ) ) ) ) ) )).
fof(conj_thm_2EquantHeuristics_2EGUESS__EXISTS__FORALL__REWRITES,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) <=> ! [V2v] : ( mem(V2v,A_27b) => ( p(ap(V1P,V2v)) => ? [V3fv] : ( mem(V3fv,A_27a) & p(ap(V1P,ap(V0i,V3fv))) ) ) ) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P)) <=> ! [V4v] : ( mem(V4v,A_27b) => ( ( ~~ p(ap(V1P,V4v)) ) => ? [V5fv] : ( mem(V5fv,A_27a) & ( ~~ p(ap(V1P,ap(V0i,V5fv))) ) ) ) ) ) ) ) ))))).
fof(ax_thm_2EquantHeuristics_2EGUESS__EXISTS__POINT__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P)) <=> ! [V2fv] : ( mem(V2fv,A_27a) => p(ap(V1P,ap(V0i,V2fv))) ) ) ) ) ) ) )).
fof(ax_thm_2EquantHeuristics_2EGUESS__FORALL__POINT__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P)) <=> ! [V2fv] : ( mem(V2fv,A_27a) => ( ~~ p(ap(V1P,ap(V0i,V2fv))) ) ) ) ) ) ) ) )).
fof(conj_thm_2EquantHeuristics_2EGUESS__POINT__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P)) => ( ( ? [V2v] : ( mem(V2v,A_27b) & p(ap(V1P,V2v)) ) ) <=> $true ) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P)) => ( ( ! [V3v] : ( mem(V3v,A_27b) => p(ap(V1P,V3v)) ) ) <=> $false ) ) ) ) ))))).
fof(ax_thm_2EquantHeuristics_2EGUESS__EXISTS__GAP__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),V1P)) <=> ! [V2v] : ( mem(V2v,A_27b) => ( p(ap(V1P,V2v)) => ? [V3fv] : ( mem(V3fv,A_27a) & ( V2v = ap(V0i,V3fv) ) ) ) ) ) ) ) ) ) )).
fof(ax_thm_2EquantHeuristics_2EGUESS__FORALL__GAP__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),V1P)) <=> ! [V2v] : ( mem(V2v,A_27b) => ( ( ~~ p(ap(V1P,V2v)) ) => ? [V3fv] : ( mem(V3fv,A_27a) & ( V2v = ap(V0i,V3fv) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2EquantHeuristics_2EGUESS__REWRITES,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) <=> ! [V2v] : ( mem(V2v,A_27b) => ( p(ap(V1P,V2v)) => ? [V3fv] : ( mem(V3fv,A_27a) & p(ap(V1P,ap(V0i,V3fv))) ) ) ) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P)) <=> ! [V4v] : ( mem(V4v,A_27b) => ( ( ~~ p(ap(V1P,V4v)) ) => ? [V5fv] : ( mem(V5fv,A_27a) & ( ~~ p(ap(V1P,ap(V0i,V5fv))) ) ) ) ) ) ) & ( ( ! [V6i] : ( mem(V6i,arr(A_27a,A_27b)) => ! [V7P] : ( mem(V7P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V6i),V7P)) <=> ! [V8fv] : ( mem(V8fv,A_27a) => p(ap(V7P,ap(V6i,V8fv))) ) ) ) ) ) & ( ( ! [V9i] : ( mem(V9i,arr(A_27a,A_27b)) => ! [V10P] : ( mem(V10P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V9i),V10P)) <=> ! [V11fv] : ( mem(V11fv,A_27a) => ( ~~ p(ap(V10P,ap(V9i,V11fv))) ) ) ) ) ) ) & ( ( ! [V12i] : ( mem(V12i,arr(A_27a,A_27b)) => ! [V13P] : ( mem(V13P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V12i),V13P)) <=> ! [V14v] : ( mem(V14v,A_27b) => ( p(ap(V13P,V14v)) => ? [V15fv] : ( mem(V15fv,A_27a) & ( V14v = ap(V12i,V15fv) ) ) ) ) ) ) ) ) & ! [V16i] : ( mem(V16i,arr(A_27a,A_27b)) => ! [V17P] : ( mem(V17P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V16i),V17P)) <=> ! [V18v] : ( mem(V18v,A_27b) => ( ( ~~ p(ap(V17P,V18v)) ) => ? [V19fv] : ( mem(V19fv,A_27a) & ( V18v = ap(V16i,V19fv) ) ) ) ) ) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__EXISTS__POINT__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P)) => ( p(ap(c_2Ebool_2E_3F(A_27b),V1P)) <=> $true ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__FORALL__POINT__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P)) => ( p(ap(c_2Ebool_2E_21(A_27b),V1P)) <=> $false ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__EXISTS__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) => ( p(ap(c_2Ebool_2E_3F(A_27b),V1P)) <=> ? [V2fv] : ( mem(V2fv,A_27a) & p(ap(V1P,ap(V0i,V2fv))) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__FORALL__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P)) => ( p(ap(c_2Ebool_2E_21(A_27b),V1P)) <=> ! [V2fv] : ( mem(V2fv,A_27a) => p(ap(V1P,ap(V0i,V2fv))) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESSES__UEXISTS__THM1,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b,A_27a),k(A_27b,V0i)),V1P)) => ( p(ap(c_2Ebool_2E_3F_21(A_27a),V1P)) <=> ( p(ap(V1P,V0i)) & ! [V3v] : ( mem(V3v,A_27a) => ( p(ap(V1P,V3v)) => ( V3v = V0i ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESSES__UEXISTS__THM2,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27a),k(A_27b,V0i)),V1P)) => ( p(ap(c_2Ebool_2E_3F_21(A_27a),V1P)) <=> p(ap(V1P,V0i)) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESSES__UEXISTS__THM3,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27a),k(A_27b,V0i)),V1P)) => ( p(ap(c_2Ebool_2E_3F_21(A_27a),V1P)) <=> ! [V3v] : ( mem(V3v,A_27a) => ( p(ap(V1P,V3v)) => ( V3v = V0i ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESSES__UEXISTS__THM4,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27a),k(A_27b,V0i)),V1P)) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27c,A_27a),k(A_27c,V0i)),V1P)) => ( p(ap(c_2Ebool_2E_3F_21(A_27a),V1P)) <=> $true ) ) ) ) )))))).
fof(conj_thm_2EquantHeuristics_2EGUESSES__NEG__DUALITY,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),V1P)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),V1P)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P)) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P)) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESSES__NEG__REWRITE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f581(A_27b,V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f582(A_27b,V1P))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f583(A_27b,V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f584(A_27b,V1P))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f585(A_27b,V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f586(A_27b,V1P))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f587(A_27b,V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f588(A_27b,V1P))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f589(A_27b,V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f590(A_27b,V1P))) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f591(A_27b,V1P))) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f592(A_27b,V1P))) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESSES__WEAKEN__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__EQUATION__EXISTS__POINT,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,A_27b)) => ! [V2Q] : ( mem(V2Q,arr(A_27a,A_27b)) => ( ( ap(V1P,V0i) = ap(V2Q,V0i) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Eone_2Eone,A_27a),k(ty_2Eone_2Eone,V0i)),f593(A_27b,A_27a,V1P,V2Q))) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__EQUATION__FORALL__POINT,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,A_27c)) => ! [V2Q] : ( mem(V2Q,arr(A_27b,A_27c)) => ( ( ! [V3fv] : ( mem(V3fv,A_27a) => ( ~~ ( ap(V1P,ap(V0i,V3fv)) = ap(V2Q,ap(V0i,V3fv)) ) ) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f594(A_27c,A_27b,V1P,V2Q))) ) ) ) )))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__EQUATION__EXISTS__GAP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Eone_2Eone,A_27a),k(ty_2Eone_2Eone,V0i)),f595(A_27a,V0i))) )))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__TRIVIAL__EXISTS__POINT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( p(ap(V1P,V0i)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Eone_2Eone,A_27a),k(ty_2Eone_2Eone,V0i)),V1P)) ) ) )))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__TRIVIAL__FORALL__POINT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ~~ p(ap(V1P,V0i)) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(ty_2Eone_2Eone,A_27a),k(ty_2Eone_2Eone,V0i)),V1P)) ) ) )))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__BOOL,lemma,(( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Eone_2Eone,bool),k(ty_2Eone_2Eone,c_2Ebool_2ET)),i(bool))) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(ty_2Eone_2Eone,bool),k(ty_2Eone_2Eone,c_2Ebool_2EF)),i(bool))) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Eone_2Eone,bool),k(ty_2Eone_2Eone,c_2Ebool_2ET)),i(bool))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Eone_2Eone,bool),k(ty_2Eone_2Eone,c_2Ebool_2EF)),i(bool))) ) ) ))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__TWO__CASES,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0y] : ( mem(V0y,A_27a) => ! [V1Q] : ( mem(V1Q,arr(A_27b,A_27a)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( ( V2x = V0y ) | ? [V3fv] : ( mem(V3fv,A_27b) & ( V2x = ap(V1Q,V3fv) ) ) ) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27a),V1Q),f596(A_27a,V0y))) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__ONE__CASE______FORALL__GAP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27b,A_27a)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ? [V3fv] : ( mem(V3fv,A_27b) & ( V2x = ap(V1Q,V3fv) ) ) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27a),V1Q),V0P)) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__ONE__CASE______EXISTS__GAP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27b,A_27a)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ? [V3fv] : ( mem(V3fv,A_27b) & ( V2x = ap(V1Q,V3fv) ) ) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27a),V1Q),V0P)) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__NEG,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f597(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f598(A_27b,V1P))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f599(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f600(A_27b,V1P))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f601(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f602(A_27b,V1P))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f603(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f604(A_27b,V1P))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f605(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f606(A_27b,V1P))) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f607(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f608(A_27b,V1P))) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__CONSTANT__EXISTS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1p] : ( mem(V1p,bool) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),k(A_27b,V1p))) <=> $true ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__CONSTANT__FORALL,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1p] : ( mem(V1p,bool) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),k(A_27b,V1p))) <=> $true ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__DISJ,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27b,bool)) => ! [V3iK] : ( mem(V3iK,A_27b) => ! [V4q] : ( mem(V4q,bool) => ! [V5p] : ( mem(V5p,bool) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f601(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f609(A_27b,V1P,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f610(A_27b,V2Q))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f611(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f605(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f612(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f613(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f592(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f614(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f615(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f616(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f617(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f618(A_27b,V1P,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f619(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f620(A_27b,V1P,V4q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f621(A_27b,V2Q))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f622(A_27b,V2Q,V5p))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f623(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f624(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f625(A_27b,V1P,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f626(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f627(A_27b,V1P,V2Q))) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f628(A_27b,V2Q))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f629(A_27b,V1P,V2Q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__CONJ,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27b,bool)) => ! [V3iK] : ( mem(V3iK,A_27b) => ! [V4q] : ( mem(V4q,bool) => ! [V5p] : ( mem(V5p,bool) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f601(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f630(A_27b,V1P,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f610(A_27b,V2Q))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f631(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f605(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f612(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f632(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f592(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f614(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f633(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f616(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f617(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f634(A_27b,V1P,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f619(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f635(A_27b,V1P,V4q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f621(A_27b,V2Q))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f636(A_27b,V2Q,V5p))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f623(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f624(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f637(A_27b,V1P,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f626(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f638(A_27b,V1P,V2Q))) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f628(A_27b,V2Q))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f639(A_27b,V1P,V2Q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__IMP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27b,bool)) => ! [V3iK] : ( mem(V3iK,A_27b) => ! [V4q] : ( mem(V4q,bool) => ! [V5p] : ( mem(V5p,bool) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f601(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f640(A_27b,V1P,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f610(A_27b,V2Q))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f641(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f605(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f612(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f642(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f592(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f614(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f643(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f616(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f617(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f644(A_27b,V1P,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f619(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f645(A_27b,V1P,V4q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f621(A_27b,V2Q))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f646(A_27b,V2Q,V5p))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f623(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f624(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f647(A_27b,V1P,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f626(A_27b,V1P))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f648(A_27b,V1P,V2Q))) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f628(A_27b,V2Q))) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f649(A_27b,V1P,V2Q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__EQUIV,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27b,bool)) => ! [V3P1] : ( mem(V3P1,arr(A_27b,bool)) => ! [V4P2] : ( mem(V4P2,arr(A_27b,bool)) => ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f584(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f650(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f651(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f603(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f652(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f653(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f590(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f654(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f655(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f656(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f657(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f658(A_27b,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f659(A_27b,V3P1))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f660(A_27b,V4P2))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f661(A_27b,V3P1,V4P2))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f662(A_27b,V3P1))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f663(A_27b,V4P2))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f664(A_27b,V3P1,V4P2))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f665(A_27b,V3P1))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f666(A_27b,V4P2))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f667(A_27b,V3P1,V4P2))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f668(A_27b,V3P1))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f669(A_27b,V4P2))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f670(A_27b,V3P1,V4P2))) ) ) ) ) ) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__COND,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27b,bool)) => ! [V3b] : ( mem(V3b,arr(A_27b,bool)) => ! [V4bc] : ( mem(V4bc,bool) => ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f584(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f650(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f671(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f603(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f652(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f672(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f590(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f654(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f673(A_27b,V4bc,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f656(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f657(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f674(A_27b,V4bc,V1P,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f616(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f675(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f676(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f677(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f678(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f679(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f680(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f621(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f681(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f682(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f624(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f683(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f684(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f685(A_27b,V1P))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f686(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f687(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f688(A_27b,V1P))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f689(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f690(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f691(A_27b,V1P))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f692(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f693(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f694(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f695(A_27b,V1P,V3b,V2Q))) ) & ( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f696(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f697(A_27b,V2Q))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f698(A_27b,V1P,V3b,V2Q))) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f699(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f700(A_27b,V1P))) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f701(A_27b,V1P,V3b,V2Q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__FORALL______NEW__FV,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0iy] : ( mem(V0iy,arr(A_27a,arr(A_27b,A_27c))) => ! [V1P] : ( mem(V1P,arr(A_27c,arr(A_27a,bool))) => ( ( ( ! [V2y] : ( mem(V2y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),ap(V0iy,V2y)),f702(A_27c,A_27a,V1P,V2y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f703(A_27c,A_27a,A_27b,V0iy)),f705(A_27c,A_27a,V1P))) ) & ( ( ( ! [V7y] : ( mem(V7y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b,A_27c),ap(V0iy,V7y)),f706(A_27c,A_27a,V1P,V7y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f707(A_27c,A_27a,A_27b,V0iy)),f709(A_27c,A_27a,V1P))) ) & ( ( ( ! [V12y] : ( mem(V12y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),ap(V0iy,V12y)),f710(A_27c,A_27a,V1P,V12y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f711(A_27c,A_27a,A_27b,V0iy)),f713(A_27c,A_27a,V1P))) ) & ( ( ! [V17y] : ( mem(V17y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),ap(V0iy,V17y)),f714(A_27c,A_27a,V1P,V17y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f715(A_27c,A_27a,A_27b,V0iy)),f717(A_27c,A_27a,V1P))) ) ) ) ) ) )))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__FORALL______NEW__FV__1,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27c]: ( ne(A_27c) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27c)) => ! [V1P] : ( mem(V1P,arr(A_27c,arr(A_27a,bool))) => ( ( ( ! [V2y] : ( mem(V2y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V2y))),f718(A_27c,A_27a,V1P,V2y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27c),V0i),f705(A_27c,A_27a,V1P))) ) & ( ( ( ! [V7y] : ( mem(V7y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V7y))),f719(A_27c,A_27a,V1P,V7y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27c),V0i),f709(A_27c,A_27a,V1P))) ) & ( ( ( ! [V12y] : ( mem(V12y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V12y))),f720(A_27c,A_27a,V1P,V12y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27c),V0i),f713(A_27c,A_27a,V1P))) ) & ( ( ! [V17y] : ( mem(V17y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V17y))),f721(A_27c,A_27a,V1P,V17y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27c),V0i),f717(A_27c,A_27a,V1P))) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__FORALL,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0i] : ( mem(V0i,arr(A_27b,A_27c)) => ! [V1P] : ( mem(V1P,arr(A_27c,arr(A_27a,bool))) => ! [V2iK] : ( mem(V2iK,A_27c) => ( ( ( ! [V3y] : ( mem(V3y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f722(A_27c,A_27a,V1P,V3y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f705(A_27c,A_27a,V1P))) ) & ( ( ( ! [V7y] : ( mem(V7y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b,A_27c),V0i),f706(A_27c,A_27a,V1P,V7y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b,A_27c),V0i),f724(A_27c,A_27a,V1P))) ) & ( ( ( ! [V11y] : ( mem(V11y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),V0i),f725(A_27c,A_27a,V1P,V11y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),V0i),f727(A_27c,A_27a,V1P))) ) & ( ( ( ! [V15y] : ( mem(V15y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),V0i),f728(A_27c,A_27a,V1P,V15y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),V0i),f730(A_27c,A_27a,V1P))) ) & ( ( ( ! [V19y] : ( mem(V19y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,V2iK)),f731(A_27c,A_27a,V1P,V19y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,V2iK)),f733(A_27c,A_27a,V1P))) ) & ( ( ! [V25y] : ( mem(V25y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f734(A_27c,A_27a,V1P,V25y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f736(A_27c,A_27a,V1P))) ) ) ) ) ) ) ) ) )))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__EXISTS______NEW__FV,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0iy] : ( mem(V0iy,arr(A_27a,arr(A_27b,A_27c))) => ! [V1P] : ( mem(V1P,arr(A_27c,arr(A_27a,bool))) => ( ( ( ! [V2y] : ( mem(V2y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),ap(V0iy,V2y)),f702(A_27c,A_27a,V1P,V2y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f703(A_27c,A_27a,A_27b,V0iy)),f737(A_27c,A_27a,V1P))) ) & ( ( ( ! [V7y] : ( mem(V7y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b,A_27c),ap(V0iy,V7y)),f706(A_27c,A_27a,V1P,V7y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f707(A_27c,A_27a,A_27b,V0iy)),f738(A_27c,A_27a,V1P))) ) & ( ( ( ! [V12y] : ( mem(V12y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),ap(V0iy,V12y)),f710(A_27c,A_27a,V1P,V12y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f711(A_27c,A_27a,A_27b,V0iy)),f739(A_27c,A_27a,V1P))) ) & ( ( ! [V17y] : ( mem(V17y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),ap(V0iy,V17y)),f714(A_27c,A_27a,V1P,V17y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f715(A_27c,A_27a,A_27b,V0iy)),f740(A_27c,A_27a,V1P))) ) ) ) ) ) )))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__EXISTS______NEW__FV__1,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27c]: ( ne(A_27c) => ! [V0i] : ( mem(V0i,arr(A_27a,A_27c)) => ! [V1P] : ( mem(V1P,arr(A_27c,arr(A_27a,bool))) => ( ( ( ! [V2y] : ( mem(V2y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V2y))),f718(A_27c,A_27a,V1P,V2y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27c),V0i),f737(A_27c,A_27a,V1P))) ) & ( ( ( ! [V7y] : ( mem(V7y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V7y))),f719(A_27c,A_27a,V1P,V7y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27c),V0i),f738(A_27c,A_27a,V1P))) ) & ( ( ( ! [V12y] : ( mem(V12y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V12y))),f720(A_27c,A_27a,V1P,V12y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27c),V0i),f739(A_27c,A_27a,V1P))) ) & ( ( ! [V17y] : ( mem(V17y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V17y))),f721(A_27c,A_27a,V1P,V17y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27c),V0i),f740(A_27c,A_27a,V1P))) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__EXISTS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0i] : ( mem(V0i,arr(A_27b,A_27c)) => ! [V1P] : ( mem(V1P,arr(A_27c,arr(A_27a,bool))) => ! [V2iK] : ( mem(V2iK,A_27c) => ( ( ( ! [V3y] : ( mem(V3y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),V0i),f722(A_27c,A_27a,V1P,V3y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),V0i),f737(A_27c,A_27a,V1P))) ) & ( ( ( ! [V7y] : ( mem(V7y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b,A_27c),V0i),f706(A_27c,A_27a,V1P,V7y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b,A_27c),V0i),f741(A_27c,A_27a,V1P))) ) & ( ( ( ! [V11y] : ( mem(V11y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f725(A_27c,A_27a,V1P,V11y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f742(A_27c,A_27a,V1P))) ) & ( ( ( ! [V15y] : ( mem(V15y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f728(A_27c,A_27a,V1P,V15y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f743(A_27c,A_27a,V1P))) ) & ( ( ( ! [V19y] : ( mem(V19y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,V2iK)),f731(A_27c,A_27a,V1P,V19y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,V2iK)),f744(A_27c,A_27a,V1P))) ) & ( ( ! [V25y] : ( mem(V25y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),V0i),f734(A_27c,A_27a,V1P,V25y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),V0i),f745(A_27c,A_27a,V1P))) ) ) ) ) ) ) ) ) )))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__EXISTS__UNIQUE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0i] : ( mem(V0i,arr(A_27b,A_27c)) => ! [V1P] : ( mem(V1P,arr(A_27c,arr(A_27a,bool))) => ( ( ( ! [V2y] : ( mem(V2y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f702(A_27c,A_27a,V1P,V2y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f747(A_27c,A_27a,V1P))) ) & ( ( ! [V6y] : ( mem(V6y,A_27a) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f748(A_27c,A_27a,V1P,V6y))) ) ) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f750(A_27c,A_27a,V1P))) ) ) ) )))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__ELIM__UNIT,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b)) => ! [V1vt] : ( mem(V1vt,arr(A_27b,bool)) => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),f751(A_27b,A_27a,V0i)),V1vt)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),f752(A_27b,A_27a,V0i)),V1vt)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),f753(A_27b,A_27a,V0i)),V1vt)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),f754(A_27b,A_27a,V0i)),V1vt)) ) & ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),f755(A_27b,A_27a,V0i)),V1vt)) ) & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),f756(A_27b,A_27a,V0i)),V1vt)) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__STRENGTHEN__EXISTS__POINT,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27b,A_27a)) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(V1P,V3x)) => p(ap(V2Q,V3x)) ) ) ) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27a),V0i),V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27a),V0i),V2Q)) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__STRENGTHEN__FORALL__GAP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27b,A_27a)) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(V1P,V3x)) => p(ap(V2Q,V3x)) ) ) ) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27a),V0i),V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27a),V0i),V2Q)) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27b,A_27a)) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(V2Q,V3x)) => p(ap(V1P,V3x)) ) ) ) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27a),V0i),V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27a),V0i),V2Q)) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__EXISTS__GAP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0i] : ( mem(V0i,arr(A_27b,A_27a)) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(V2Q,V3x)) => p(ap(V1P,V3x)) ) ) ) => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27a),V0i),V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27a),V0i),V2Q)) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2ECONJ__NOT__OR__THM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( p(V0A) & p(V1B) ) <=> ( ~~ ( ( ~~ p(V0A) ) | ( ~~ p(V1B) ) ) ) ) ) ))).
fof(conj_thm_2EquantHeuristics_2EEXISTS__NOT__FORALL__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ( ( ? [V1x] : ( mem(V1x,A_27a) & p(ap(V0P,V1x)) ) ) <=> ( ~~ ! [V2x] : ( mem(V2x,A_27a) => ( ~~ p(ap(V0P,V2x)) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2EMOVE__EXISTS__IMP__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,arr(A_27b,bool))) => ! [V1R] : ( mem(V1R,arr(A_27b,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27a,bool)) => ( ( ? [V3x] : ( mem(V3x,A_27a) & ( ( ! [V4y] : ( mem(V4y,A_27b) => ( ( ~~ p(ap(ap(V0P,V3x),V4y)) ) => p(ap(V1R,V4y)) ) ) ) => p(ap(V2Q,V3x)) ) ) ) <=> ( ( ! [V5y] : ( mem(V5y,A_27b) => ( ( ~~ ! [V6x] : ( mem(V6x,A_27a) => p(ap(ap(V0P,V6x),V5y)) ) ) => p(ap(V1R,V5y)) ) ) ) => ? [V7x] : ( mem(V7x,A_27a) & p(ap(V2Q,V7x)) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EUNWIND__EXISTS__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ? [V2x] : ( mem(V2x,A_27a) & p(ap(V1P,V2x)) ) ) <=> ( ( ! [V3x] : ( mem(V3x,A_27a) => ( ( ~~ ( V3x = V0a ) ) => ( ~~ p(ap(V1P,V3x)) ) ) ) ) => p(ap(V1P,V0a)) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELEFT__IMP__AND__INTRO,lemma,(! [V0x] : ( mem(V0x,bool) => ! [V1t1] : ( mem(V1t1,bool) => ! [V2t2] : ( mem(V2t2,bool) => ( ( p(V1t1) => p(V2t2) ) => ( ( p(V0x) & p(V1t1) ) => ( p(V0x) & p(V2t2) ) ) ) ) ) ))).
fof(conj_thm_2EquantHeuristics_2ERIGHT__IMP__AND__INTRO,lemma,(! [V0x] : ( mem(V0x,bool) => ! [V1t1] : ( mem(V1t1,bool) => ! [V2t2] : ( mem(V2t2,bool) => ( ( p(V1t1) => p(V2t2) ) => ( ( p(V1t1) & p(V0x) ) => ( p(V2t2) & p(V0x) ) ) ) ) ) ))).
fof(conj_thm_2EquantHeuristics_2ELEFT__IMP__OR__INTRO,lemma,(! [V0x] : ( mem(V0x,bool) => ! [V1t1] : ( mem(V1t1,bool) => ! [V2t2] : ( mem(V2t2,bool) => ( ( p(V1t1) => p(V2t2) ) => ( ( p(V0x) | p(V1t1) ) => ( p(V0x) | p(V2t2) ) ) ) ) ) ))).
fof(conj_thm_2EquantHeuristics_2ERIGHT__IMP__OR__INTRO,lemma,(! [V0x] : ( mem(V0x,bool) => ! [V1t1] : ( mem(V1t1,bool) => ! [V2t2] : ( mem(V2t2,bool) => ( ( p(V1t1) => p(V2t2) ) => ( ( p(V1t1) | p(V0x) ) => ( p(V2t2) | p(V0x) ) ) ) ) ) ))).
fof(conj_thm_2EquantHeuristics_2EIMP__NEG__CONTRA,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2x] : ( mem(V2x,A_27a) => ( ( ~~ p(ap(V0P,V1i)) ) => ( p(ap(V0P,V2x)) => ( ~~ ( V2x = V1i ) ) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2EDISJ__IMP__INTRO,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ! [V2y] : ( mem(V2y,A_27a) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(V0P,V3x)) | p(ap(V1Q,V3x)) ) ) ) => ( ( ( ~~ p(ap(V0P,V2y)) ) => p(ap(V1Q,V2y)) ) & ( ( ~~ p(ap(V1Q,V2y)) ) => p(ap(V0P,V2y)) ) ) ) ) ) )))).
fof(ax_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P] : ( mem(V2P,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),V2P)) <=> ( p(V2P) => ( V0v = V1i ) ) ) ) ) ) ) )).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__ALT__DEF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2v] : ( mem(V2v,A_27a) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V2v),V0i),ap(V1P,V2v))) ) ) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Eone_2Eone,A_27a),ap(c_2Ecombin_2EK(A_27a,ty_2Eone_2Eone),V0i)),f757(A_27a,V1P))) ) ) )))).
fof(ax_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P] : ( mem(V2P,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),V2P)) <=> ( ( ~~ p(V2P) ) => ( V0v = V1i ) ) ) ) ) ) ) )).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__ALT__DEF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2v] : ( mem(V2v,A_27a) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V2v),V0i),ap(V1P,V2v))) ) ) <=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Eone_2Eone,A_27a),ap(c_2Ecombin_2EK(A_27a,ty_2Eone_2Eone),V0i)),f757(A_27a,V1P))) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2v] : ( mem(V2v,A_27a) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V2v),V0i),ap(V1P,V2v))) ) ) => ( ( ! [V3v] : ( mem(V3v,A_27a) => p(ap(V1P,V3v)) ) ) <=> p(ap(V1P,V0i)) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2v] : ( mem(V2v,A_27a) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V2v),V0i),ap(V1P,V2v))) ) ) => ( ( ? [V3v] : ( mem(V3v,A_27a) & p(ap(V1P,V3v)) ) ) <=> p(ap(V1P,V0i)) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__UEXISTS__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2v] : ( mem(V2v,A_27a) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V2v),V0i),ap(V1P,V2v))) ) ) => ( p(ap(c_2Ebool_2E_3F_21(A_27a),f757(A_27a,V1P))) <=> p(ap(V1P,V0i)) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__SELECT__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2v] : ( mem(V2v,A_27a) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V2v),V0i),ap(V1P,V2v))) ) ) => ( ap(c_2Emin_2E_40(A_27a),f757(A_27a,V1P)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(V1P,V0i)),V0i),ap(c_2Emin_2E_40(A_27a),k(A_27a,c_2Ebool_2EF))) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__SOME__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2v] : ( mem(V2v,A_27a) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V2v),V0i),ap(V1P,V2v))) ) ) => ( ap(c_2Eoption_2Esome(A_27a),f757(A_27a,V1P)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(V1P,V0i)),ap(c_2Eoption_2ESOME(A_27a),V0i)),c_2Eoption_2ENONE(A_27a)) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__EQ__1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(ap(c_2Emin_2E_3D(A_27a),V0v),V1i))) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__EQ__2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(ap(c_2Emin_2E_3D(A_27a),V1i),V0v))) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__EQ__T,lemma,(! [V0v] : ( mem(V0v,bool) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(bool),V0v),c_2Ebool_2ET),V0v)) ))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__NEG,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P] : ( mem(V2P,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),V2P)) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),ap(c_2Ebool_2E_7E,V2P))) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__NEG,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P] : ( mem(V2P,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),V2P)) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(c_2Ebool_2E_7E,V2P))) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__OR__1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P1] : ( mem(V2P1,bool) => ! [V3P2] : ( mem(V3P2,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),V2P1)) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),ap(ap(c_2Ebool_2E_5C_2F,V2P1),V3P2))) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__OR__2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P1] : ( mem(V2P1,bool) => ! [V3P2] : ( mem(V3P2,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),V3P2)) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),ap(ap(c_2Ebool_2E_5C_2F,V2P1),V3P2))) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__AND__1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P1] : ( mem(V2P1,bool) => ! [V3P2] : ( mem(V3P2,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),V2P1)) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(ap(c_2Ebool_2E_2F_5C,V2P1),V3P2))) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__AND__2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P1] : ( mem(V2P1,bool) => ! [V3P2] : ( mem(V3P2,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),V3P2)) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(ap(c_2Ebool_2E_2F_5C,V2P1),V3P2))) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__EXISTS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P] : ( mem(V2P,arr(A_27b,bool)) => ( ( ! [V3v2] : ( mem(V3v2,A_27b) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(V2P,V3v2))) ) ) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(c_2Ebool_2E_3F(A_27b),f758(A_27b,V2P)))) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__FORALL,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P] : ( mem(V2P,arr(A_27b,bool)) => ( ( ! [V3v2] : ( mem(V3v2,A_27b) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(V2P,V3v2))) ) ) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(c_2Ebool_2E_21(A_27b),f758(A_27b,V2P)))) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__EXISTS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P] : ( mem(V2P,arr(A_27b,bool)) => ( ( ! [V3v2] : ( mem(V3v2,A_27b) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),ap(V2P,V3v2))) ) ) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),ap(c_2Ebool_2E_3F(A_27b),f758(A_27b,V2P)))) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__FORALL,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P] : ( mem(V2P,arr(A_27b,bool)) => ( ( ! [V3v2] : ( mem(V3v2,A_27b) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),ap(V2P,V3v2))) ) ) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),ap(c_2Ebool_2E_21(A_27b),f758(A_27b,V2P)))) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__IMP__1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P1] : ( mem(V2P1,bool) => ! [V3P2] : ( mem(V3P2,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),V2P1)) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),ap(ap(c_2Emin_2E_3D_3D_3E,V2P1),V3P2))) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__IMP__2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2P1] : ( mem(V2P1,bool) => ! [V3P2] : ( mem(V3P2,bool) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),V3P2)) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),V0v),V1i),ap(ap(c_2Emin_2E_3D_3D_3E,V2P1),V3P2))) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__EQ__FUN,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0v] : ( mem(V0v,A_27a) => ! [V1i] : ( mem(V1i,A_27a) => ! [V2t1] : ( mem(V2t1,A_27b) => ! [V3t2] : ( mem(V3t2,A_27b) => ! [V4f] : ( mem(V4f,arr(A_27b,A_27c)) => ( p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(ap(c_2Emin_2E_3D(A_27c),ap(V4f,V2t1)),ap(V4f,V3t2)))) => p(ap(ap(ap(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),V0v),V1i),ap(ap(c_2Emin_2E_3D(A_27b),V2t1),V3t2))) ) ) ) ) ) )))))).
fof(ax_thm_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ( p(ap(c_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN(A_27a,A_27b),V0f)) <=> ! [V1v] : ( mem(V1v,A_27b) => ? [V2x] : ( mem(V2x,A_27a) & ( ap(V0f,V2x) = V1v ) ) ) ) ) ) ) )).
fof(conj_thm_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN______EXISTS__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(c_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN(A_27a,A_27b),V0f)) => ( ( ? [V2x] : ( mem(V2x,A_27a) & p(ap(V1P,ap(V0f,V2x))) ) ) <=> ? [V3x_27] : ( mem(V3x_27,A_27b) & p(ap(V1P,V3x_27)) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN______FORALL__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27b,bool)) => ( p(ap(c_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN(A_27a,A_27b),V0f)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => p(ap(V1P,ap(V0f,V2x))) ) ) <=> ! [V3x_27] : ( mem(V3x_27,A_27b) => p(ap(V1P,V3x_27)) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EPAIR__EQ__EXPAND,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27b) => ! [V2X] : ( mem(V2X,ty_2Epair_2Eprod(A_27a,A_27b)) => ( ( ( ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = V2X ) <=> ( ( V0x = ap(c_2Epair_2EFST(A_27a,A_27b),V2X) ) & ( V1y = ap(c_2Epair_2ESND(A_27a,A_27b),V2X) ) ) ) & ( ( V2X = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) ) <=> ( ( ap(c_2Epair_2EFST(A_27a,A_27b),V2X) = V0x ) & ( ap(c_2Epair_2ESND(A_27a,A_27b),V2X) = V1y ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EPAIR__EQ__SIMPLE__EXPAND,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27b) => ! [V2y_27] : ( mem(V2y_27,A_27b) => ! [V3X] : ( mem(V3X,ty_2Epair_2Eprod(A_27a,A_27b)) => ( ( ( ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V2y_27) ) <=> ( V1y = V2y_27 ) ) & ( ( ( ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V1y),V0x) = ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V2y_27),V0x) ) <=> ( V1y = V2y_27 ) ) & ( ( ( ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(c_2Epair_2EFST(A_27a,A_27b),V3X)),V1y) = V3X ) <=> ( V1y = ap(c_2Epair_2ESND(A_27a,A_27b),V3X) ) ) & ( ( ( ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),ap(c_2Epair_2ESND(A_27a,A_27b),V3X)) = V3X ) <=> ( V0x = ap(c_2Epair_2EFST(A_27a,A_27b),V3X) ) ) & ( ( ( V3X = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(c_2Epair_2EFST(A_27a,A_27b),V3X)),V1y) ) <=> ( ap(c_2Epair_2ESND(A_27a,A_27b),V3X) = V1y ) ) & ( ( V3X = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),ap(c_2Epair_2ESND(A_27a,A_27b),V3X)) ) <=> ( ap(c_2Epair_2EFST(A_27a,A_27b),V3X) = V0x ) ) ) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EIS__SOME__EQ__NOT__NONE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Eoption_2Eoption(A_27a)) => ( p(ap(c_2Eoption_2EIS__SOME(A_27a),V0x)) <=> ( ~~ ( V0x = c_2Eoption_2ENONE(A_27a) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2EISL__exists,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) => ( p(ap(c_2Esum_2EISL(A_27a,A_27b),V0x)) <=> ? [V1l] : ( mem(V1l,A_27a) & ( V0x = ap(c_2Esum_2EINL(A_27a,A_27b),V1l) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EISR__exists,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) => ( p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)) <=> ? [V1r] : ( mem(V1r,A_27b) & ( V0x = ap(c_2Esum_2EINR(A_27a,A_27b),V1r) ) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EINL__NEQ__ELIM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) => ( ( ( ! [V1l] : ( mem(V1l,A_27a) => ( ~~ ( V0x = ap(c_2Esum_2EINL(A_27a,A_27b),V1l) ) ) ) ) <=> p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)) ) & ( ( ! [V2l] : ( mem(V2l,A_27a) => ( ~~ ( ap(c_2Esum_2EINL(A_27a,A_27b),V2l) = V0x ) ) ) ) <=> p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2EINR__NEQ__ELIM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,ty_2Esum_2Esum(A_27b,A_27a)) => ( ( ( ! [V1r] : ( mem(V1r,A_27a) => ( ~~ ( V0x = ap(c_2Esum_2EINR(A_27b,A_27a),V1r) ) ) ) ) <=> p(ap(c_2Esum_2EISL(A_27b,A_27a),V0x)) ) & ( ( ! [V2r] : ( mem(V2r,A_27a) => ( ~~ ( ap(c_2Esum_2EINR(A_27b,A_27a),V2r) = V0x ) ) ) ) <=> p(ap(c_2Esum_2EISL(A_27b,A_27a),V0x)) ) ) ))))).
fof(conj_thm_2EquantHeuristics_2ELENGTH__LE__PLUS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ! [V2l] : ( mem(V2l,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)),ap(c_2Elist_2ELENGTH(A_27a),V2l))) <=> ? [V3l1] : ( mem(V3l1,ty_2Elist_2Elist(A_27a)) & ? [V4l2] : ( mem(V4l2,ty_2Elist_2Elist(A_27a)) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V3l1) = V0n ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),ap(c_2Elist_2ELENGTH(A_27a),V4l2))) & ( V2l = ap(ap(c_2Elist_2EAPPEND(A_27a),V3l1),V4l2) ) ) ) ) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELENGTH__LE__NUM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l))) <=> ? [V2l1] : ( mem(V2l1,ty_2Elist_2Elist(A_27a)) & ? [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V2l1) = V0n ) & ( V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),V3l2) ) ) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELENGTH__NIL__SYM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ( ( c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELIST__LENGTH__COMPARE__1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELIST__LENGTH__0,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0 ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( ( c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELIST__LENGTH__1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) <=> ? [V2e1] : ( mem(V2e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V2e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V3e1] : ( mem(V3e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V3e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V4l_27] : ( mem(V4l_27,ty_2Elist_2Elist(A_27a)) & ? [V5e1] : ( mem(V5e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V5e1),V4l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ? [V6l_27] : ( mem(V6l_27,ty_2Elist_2Elist(A_27a)) & ? [V7e1] : ( mem(V7e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V7e1),V6l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V8l_27] : ( mem(V8l_27,ty_2Elist_2Elist(A_27a)) & ? [V9e1] : ( mem(V9e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V9e1),V8l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ? [V10l_27] : ( mem(V10l_27,ty_2Elist_2Elist(A_27a)) & ? [V11e1] : ( mem(V11e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V11e1),V10l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V12l_27] : ( mem(V12l_27,ty_2Elist_2Elist(A_27a)) & ? [V13e1] : ( mem(V13e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V12l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V13e1),V12l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x))) <=> ? [V14l_27] : ( mem(V14l_27,ty_2Elist_2Elist(A_27a)) & ? [V15e1] : ( mem(V15e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V14l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V15e1),V14l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V16l_27] : ( mem(V16l_27,ty_2Elist_2Elist(A_27a)) & ? [V17e1] : ( mem(V17e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V16l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V17e1),V16l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V18l_27] : ( mem(V18l_27,ty_2Elist_2Elist(A_27a)) & ? [V19e1] : ( mem(V19e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V18l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V19e1),V18l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) ) <=> ? [V20l_27] : ( mem(V20l_27,ty_2Elist_2Elist(A_27a)) & ? [V21e1] : ( mem(V21e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V20l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V21e1),V20l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V22l_27] : ( mem(V22l_27,ty_2Elist_2Elist(A_27a)) & ? [V23e1] : ( mem(V23e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V22l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V23e1),V22l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V24l_27] : ( mem(V24l_27,ty_2Elist_2Elist(A_27a)) & ? [V25e1] : ( mem(V25e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V24l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V25e1),V24l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V26l_27] : ( mem(V26l_27,ty_2Elist_2Elist(A_27a)) & ? [V27e1] : ( mem(V27e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V26l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V27e1),V26l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0 ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( ( c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELIST__LENGTH__2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) ) <=> ? [V2e1] : ( mem(V2e1,A_27a) & ? [V3e2] : ( mem(V3e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V2e1),ap(ap(c_2Elist_2ECONS(A_27a),V3e2),c_2Elist_2ENIL(A_27a))) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V4e1] : ( mem(V4e1,A_27a) & ? [V5e2] : ( mem(V5e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V4e1),ap(ap(c_2Elist_2ECONS(A_27a),V5e2),c_2Elist_2ENIL(A_27a))) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V6l_27] : ( mem(V6l_27,ty_2Elist_2Elist(A_27a)) & ? [V7e1] : ( mem(V7e1,A_27a) & ? [V8e2] : ( mem(V8e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V7e1),ap(ap(c_2Elist_2ECONS(A_27a),V8e2),V6l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ? [V9l_27] : ( mem(V9l_27,ty_2Elist_2Elist(A_27a)) & ? [V10e1] : ( mem(V10e1,A_27a) & ? [V11e2] : ( mem(V11e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V10e1),ap(ap(c_2Elist_2ECONS(A_27a),V11e2),V9l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V12l_27] : ( mem(V12l_27,ty_2Elist_2Elist(A_27a)) & ? [V13e1] : ( mem(V13e1,A_27a) & ? [V14e2] : ( mem(V14e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V13e1),ap(ap(c_2Elist_2ECONS(A_27a),V14e2),V12l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) <=> ? [V15l_27] : ( mem(V15l_27,ty_2Elist_2Elist(A_27a)) & ? [V16e1] : ( mem(V16e1,A_27a) & ? [V17e2] : ( mem(V17e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V16e1),ap(ap(c_2Elist_2ECONS(A_27a),V17e2),V15l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V18l_27] : ( mem(V18l_27,ty_2Elist_2Elist(A_27a)) & ? [V19e1] : ( mem(V19e1,A_27a) & ? [V20e2] : ( mem(V20e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V18l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V19e1),ap(ap(c_2Elist_2ECONS(A_27a),V20e2),V18l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x))) <=> ? [V21l_27] : ( mem(V21l_27,ty_2Elist_2Elist(A_27a)) & ? [V22e1] : ( mem(V22e1,A_27a) & ? [V23e2] : ( mem(V23e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V21l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V22e1),ap(ap(c_2Elist_2ECONS(A_27a),V23e2),V21l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V24l_27] : ( mem(V24l_27,ty_2Elist_2Elist(A_27a)) & ? [V25e1] : ( mem(V25e1,A_27a) & ? [V26e2] : ( mem(V26e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V24l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V25e1),ap(ap(c_2Elist_2ECONS(A_27a),V26e2),V24l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) <=> ? [V27l_27] : ( mem(V27l_27,ty_2Elist_2Elist(A_27a)) & ? [V28e1] : ( mem(V28e1,A_27a) & ? [V29e2] : ( mem(V29e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V27l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V28e1),ap(ap(c_2Elist_2ECONS(A_27a),V29e2),V27l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x) ) <=> ? [V30l_27] : ( mem(V30l_27,ty_2Elist_2Elist(A_27a)) & ? [V31e1] : ( mem(V31e1,A_27a) & ? [V32e2] : ( mem(V32e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V30l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V31e1),ap(ap(c_2Elist_2ECONS(A_27a),V32e2),V30l_27)) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V33l_27] : ( mem(V33l_27,ty_2Elist_2Elist(A_27a)) & ? [V34e1] : ( mem(V34e1,A_27a) & ? [V35e2] : ( mem(V35e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V33l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V34e1),ap(ap(c_2Elist_2ECONS(A_27a),V35e2),V33l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) <=> ? [V36l_27] : ( mem(V36l_27,ty_2Elist_2Elist(A_27a)) & ? [V37e1] : ( mem(V37e1,A_27a) & ? [V38e2] : ( mem(V38e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V36l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V37e1),ap(ap(c_2Elist_2ECONS(A_27a),V38e2),V36l_27)) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V39l_27] : ( mem(V39l_27,ty_2Elist_2Elist(A_27a)) & ? [V40e1] : ( mem(V40e1,A_27a) & ? [V41e2] : ( mem(V41e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V39l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V40e1),ap(ap(c_2Elist_2ECONS(A_27a),V41e2),V39l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) <=> ? [V42e1] : ( mem(V42e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V42e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V43e1] : ( mem(V43e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V43e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V44l_27] : ( mem(V44l_27,ty_2Elist_2Elist(A_27a)) & ? [V45e1] : ( mem(V45e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V45e1),V44l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ? [V46l_27] : ( mem(V46l_27,ty_2Elist_2Elist(A_27a)) & ? [V47e1] : ( mem(V47e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V47e1),V46l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V48l_27] : ( mem(V48l_27,ty_2Elist_2Elist(A_27a)) & ? [V49e1] : ( mem(V49e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V49e1),V48l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ? [V50l_27] : ( mem(V50l_27,ty_2Elist_2Elist(A_27a)) & ? [V51e1] : ( mem(V51e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V51e1),V50l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V52l_27] : ( mem(V52l_27,ty_2Elist_2Elist(A_27a)) & ? [V53e1] : ( mem(V53e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V52l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V53e1),V52l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x))) <=> ? [V54l_27] : ( mem(V54l_27,ty_2Elist_2Elist(A_27a)) & ? [V55e1] : ( mem(V55e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V54l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V55e1),V54l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V56l_27] : ( mem(V56l_27,ty_2Elist_2Elist(A_27a)) & ? [V57e1] : ( mem(V57e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V56l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V57e1),V56l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V58l_27] : ( mem(V58l_27,ty_2Elist_2Elist(A_27a)) & ? [V59e1] : ( mem(V59e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V58l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V59e1),V58l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) ) <=> ? [V60l_27] : ( mem(V60l_27,ty_2Elist_2Elist(A_27a)) & ? [V61e1] : ( mem(V61e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V60l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V61e1),V60l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V62l_27] : ( mem(V62l_27,ty_2Elist_2Elist(A_27a)) & ? [V63e1] : ( mem(V63e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V62l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V63e1),V62l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V64l_27] : ( mem(V64l_27,ty_2Elist_2Elist(A_27a)) & ? [V65e1] : ( mem(V65e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V64l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V65e1),V64l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V66l_27] : ( mem(V66l_27,ty_2Elist_2Elist(A_27a)) & ? [V67e1] : ( mem(V67e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V66l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V67e1),V66l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0 ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( ( c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELIST__LENGTH__3,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V2e1] : ( mem(V2e1,A_27a) & ? [V3e2] : ( mem(V3e2,A_27a) & ? [V4e3] : ( mem(V4e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V2e1),ap(ap(c_2Elist_2ECONS(A_27a),V3e2),ap(ap(c_2Elist_2ECONS(A_27a),V4e3),c_2Elist_2ENIL(A_27a)))) ) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V5e1] : ( mem(V5e1,A_27a) & ? [V6e2] : ( mem(V6e2,A_27a) & ? [V7e3] : ( mem(V7e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V5e1),ap(ap(c_2Elist_2ECONS(A_27a),V6e2),ap(ap(c_2Elist_2ECONS(A_27a),V7e3),c_2Elist_2ENIL(A_27a)))) ) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V8l_27] : ( mem(V8l_27,ty_2Elist_2Elist(A_27a)) & ? [V9e1] : ( mem(V9e1,A_27a) & ? [V10e2] : ( mem(V10e2,A_27a) & ? [V11e3] : ( mem(V11e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V9e1),ap(ap(c_2Elist_2ECONS(A_27a),V10e2),ap(ap(c_2Elist_2ECONS(A_27a),V11e3),V8l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) <=> ? [V12l_27] : ( mem(V12l_27,ty_2Elist_2Elist(A_27a)) & ? [V13e1] : ( mem(V13e1,A_27a) & ? [V14e2] : ( mem(V14e2,A_27a) & ? [V15e3] : ( mem(V15e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V13e1),ap(ap(c_2Elist_2ECONS(A_27a),V14e2),ap(ap(c_2Elist_2ECONS(A_27a),V15e3),V12l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V16l_27] : ( mem(V16l_27,ty_2Elist_2Elist(A_27a)) & ? [V17e1] : ( mem(V17e1,A_27a) & ? [V18e2] : ( mem(V18e2,A_27a) & ? [V19e3] : ( mem(V19e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V17e1),ap(ap(c_2Elist_2ECONS(A_27a),V18e2),ap(ap(c_2Elist_2ECONS(A_27a),V19e3),V16l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V20l_27] : ( mem(V20l_27,ty_2Elist_2Elist(A_27a)) & ? [V21e1] : ( mem(V21e1,A_27a) & ? [V22e2] : ( mem(V22e2,A_27a) & ? [V23e3] : ( mem(V23e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V21e1),ap(ap(c_2Elist_2ECONS(A_27a),V22e2),ap(ap(c_2Elist_2ECONS(A_27a),V23e3),V20l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V24l_27] : ( mem(V24l_27,ty_2Elist_2Elist(A_27a)) & ? [V25e1] : ( mem(V25e1,A_27a) & ? [V26e2] : ( mem(V26e2,A_27a) & ? [V27e3] : ( mem(V27e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V24l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V25e1),ap(ap(c_2Elist_2ECONS(A_27a),V26e2),ap(ap(c_2Elist_2ECONS(A_27a),V27e3),V24l_27))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x))) <=> ? [V28l_27] : ( mem(V28l_27,ty_2Elist_2Elist(A_27a)) & ? [V29e1] : ( mem(V29e1,A_27a) & ? [V30e2] : ( mem(V30e2,A_27a) & ? [V31e3] : ( mem(V31e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V28l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V29e1),ap(ap(c_2Elist_2ECONS(A_27a),V30e2),ap(ap(c_2Elist_2ECONS(A_27a),V31e3),V28l_27))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V32l_27] : ( mem(V32l_27,ty_2Elist_2Elist(A_27a)) & ? [V33e1] : ( mem(V33e1,A_27a) & ? [V34e2] : ( mem(V34e2,A_27a) & ? [V35e3] : ( mem(V35e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V32l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V33e1),ap(ap(c_2Elist_2ECONS(A_27a),V34e2),ap(ap(c_2Elist_2ECONS(A_27a),V35e3),V32l_27))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) <=> ? [V36l_27] : ( mem(V36l_27,ty_2Elist_2Elist(A_27a)) & ? [V37e1] : ( mem(V37e1,A_27a) & ? [V38e2] : ( mem(V38e2,A_27a) & ? [V39e3] : ( mem(V39e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V36l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V37e1),ap(ap(c_2Elist_2ECONS(A_27a),V38e2),ap(ap(c_2Elist_2ECONS(A_27a),V39e3),V36l_27))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) ) <=> ? [V40l_27] : ( mem(V40l_27,ty_2Elist_2Elist(A_27a)) & ? [V41e1] : ( mem(V41e1,A_27a) & ? [V42e2] : ( mem(V42e2,A_27a) & ? [V43e3] : ( mem(V43e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V40l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V41e1),ap(ap(c_2Elist_2ECONS(A_27a),V42e2),ap(ap(c_2Elist_2ECONS(A_27a),V43e3),V40l_27))) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V44l_27] : ( mem(V44l_27,ty_2Elist_2Elist(A_27a)) & ? [V45e1] : ( mem(V45e1,A_27a) & ? [V46e2] : ( mem(V46e2,A_27a) & ? [V47e3] : ( mem(V47e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V44l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V45e1),ap(ap(c_2Elist_2ECONS(A_27a),V46e2),ap(ap(c_2Elist_2ECONS(A_27a),V47e3),V44l_27))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) <=> ? [V48l_27] : ( mem(V48l_27,ty_2Elist_2Elist(A_27a)) & ? [V49e1] : ( mem(V49e1,A_27a) & ? [V50e2] : ( mem(V50e2,A_27a) & ? [V51e3] : ( mem(V51e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V48l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V49e1),ap(ap(c_2Elist_2ECONS(A_27a),V50e2),ap(ap(c_2Elist_2ECONS(A_27a),V51e3),V48l_27))) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V52l_27] : ( mem(V52l_27,ty_2Elist_2Elist(A_27a)) & ? [V53e1] : ( mem(V53e1,A_27a) & ? [V54e2] : ( mem(V54e2,A_27a) & ? [V55e3] : ( mem(V55e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V52l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V53e1),ap(ap(c_2Elist_2ECONS(A_27a),V54e2),ap(ap(c_2Elist_2ECONS(A_27a),V55e3),V52l_27))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) ) <=> ? [V56e1] : ( mem(V56e1,A_27a) & ? [V57e2] : ( mem(V57e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V56e1),ap(ap(c_2Elist_2ECONS(A_27a),V57e2),c_2Elist_2ENIL(A_27a))) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V58e1] : ( mem(V58e1,A_27a) & ? [V59e2] : ( mem(V59e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V58e1),ap(ap(c_2Elist_2ECONS(A_27a),V59e2),c_2Elist_2ENIL(A_27a))) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V60l_27] : ( mem(V60l_27,ty_2Elist_2Elist(A_27a)) & ? [V61e1] : ( mem(V61e1,A_27a) & ? [V62e2] : ( mem(V62e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V61e1),ap(ap(c_2Elist_2ECONS(A_27a),V62e2),V60l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ? [V63l_27] : ( mem(V63l_27,ty_2Elist_2Elist(A_27a)) & ? [V64e1] : ( mem(V64e1,A_27a) & ? [V65e2] : ( mem(V65e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V64e1),ap(ap(c_2Elist_2ECONS(A_27a),V65e2),V63l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V66l_27] : ( mem(V66l_27,ty_2Elist_2Elist(A_27a)) & ? [V67e1] : ( mem(V67e1,A_27a) & ? [V68e2] : ( mem(V68e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V67e1),ap(ap(c_2Elist_2ECONS(A_27a),V68e2),V66l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) <=> ? [V69l_27] : ( mem(V69l_27,ty_2Elist_2Elist(A_27a)) & ? [V70e1] : ( mem(V70e1,A_27a) & ? [V71e2] : ( mem(V71e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V70e1),ap(ap(c_2Elist_2ECONS(A_27a),V71e2),V69l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V72l_27] : ( mem(V72l_27,ty_2Elist_2Elist(A_27a)) & ? [V73e1] : ( mem(V73e1,A_27a) & ? [V74e2] : ( mem(V74e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V72l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V73e1),ap(ap(c_2Elist_2ECONS(A_27a),V74e2),V72l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x))) <=> ? [V75l_27] : ( mem(V75l_27,ty_2Elist_2Elist(A_27a)) & ? [V76e1] : ( mem(V76e1,A_27a) & ? [V77e2] : ( mem(V77e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V75l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V76e1),ap(ap(c_2Elist_2ECONS(A_27a),V77e2),V75l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V78l_27] : ( mem(V78l_27,ty_2Elist_2Elist(A_27a)) & ? [V79e1] : ( mem(V79e1,A_27a) & ? [V80e2] : ( mem(V80e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V78l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V79e1),ap(ap(c_2Elist_2ECONS(A_27a),V80e2),V78l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) <=> ? [V81l_27] : ( mem(V81l_27,ty_2Elist_2Elist(A_27a)) & ? [V82e1] : ( mem(V82e1,A_27a) & ? [V83e2] : ( mem(V83e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V81l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V82e1),ap(ap(c_2Elist_2ECONS(A_27a),V83e2),V81l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x) ) <=> ? [V84l_27] : ( mem(V84l_27,ty_2Elist_2Elist(A_27a)) & ? [V85e1] : ( mem(V85e1,A_27a) & ? [V86e2] : ( mem(V86e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V84l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V85e1),ap(ap(c_2Elist_2ECONS(A_27a),V86e2),V84l_27)) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V87l_27] : ( mem(V87l_27,ty_2Elist_2Elist(A_27a)) & ? [V88e1] : ( mem(V88e1,A_27a) & ? [V89e2] : ( mem(V89e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V87l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V88e1),ap(ap(c_2Elist_2ECONS(A_27a),V89e2),V87l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) <=> ? [V90l_27] : ( mem(V90l_27,ty_2Elist_2Elist(A_27a)) & ? [V91e1] : ( mem(V91e1,A_27a) & ? [V92e2] : ( mem(V92e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V90l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V91e1),ap(ap(c_2Elist_2ECONS(A_27a),V92e2),V90l_27)) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V93l_27] : ( mem(V93l_27,ty_2Elist_2Elist(A_27a)) & ? [V94e1] : ( mem(V94e1,A_27a) & ? [V95e2] : ( mem(V95e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V93l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V94e1),ap(ap(c_2Elist_2ECONS(A_27a),V95e2),V93l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) <=> ? [V96e1] : ( mem(V96e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V96e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V97e1] : ( mem(V97e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V97e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V98l_27] : ( mem(V98l_27,ty_2Elist_2Elist(A_27a)) & ? [V99e1] : ( mem(V99e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V99e1),V98l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ? [V100l_27] : ( mem(V100l_27,ty_2Elist_2Elist(A_27a)) & ? [V101e1] : ( mem(V101e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V101e1),V100l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V102l_27] : ( mem(V102l_27,ty_2Elist_2Elist(A_27a)) & ? [V103e1] : ( mem(V103e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V103e1),V102l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ? [V104l_27] : ( mem(V104l_27,ty_2Elist_2Elist(A_27a)) & ? [V105e1] : ( mem(V105e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V105e1),V104l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V106l_27] : ( mem(V106l_27,ty_2Elist_2Elist(A_27a)) & ? [V107e1] : ( mem(V107e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V106l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V107e1),V106l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x))) <=> ? [V108l_27] : ( mem(V108l_27,ty_2Elist_2Elist(A_27a)) & ? [V109e1] : ( mem(V109e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V108l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V109e1),V108l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V110l_27] : ( mem(V110l_27,ty_2Elist_2Elist(A_27a)) & ? [V111e1] : ( mem(V111e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V110l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V111e1),V110l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V112l_27] : ( mem(V112l_27,ty_2Elist_2Elist(A_27a)) & ? [V113e1] : ( mem(V113e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V112l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V113e1),V112l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) ) <=> ? [V114l_27] : ( mem(V114l_27,ty_2Elist_2Elist(A_27a)) & ? [V115e1] : ( mem(V115e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V114l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V115e1),V114l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V116l_27] : ( mem(V116l_27,ty_2Elist_2Elist(A_27a)) & ? [V117e1] : ( mem(V117e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V116l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V117e1),V116l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V118l_27] : ( mem(V118l_27,ty_2Elist_2Elist(A_27a)) & ? [V119e1] : ( mem(V119e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V118l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V119e1),V118l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V120l_27] : ( mem(V120l_27,ty_2Elist_2Elist(A_27a)) & ? [V121e1] : ( mem(V121e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V120l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V121e1),V120l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0 ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( ( c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELIST__LENGTH__4,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V2e1] : ( mem(V2e1,A_27a) & ? [V3e2] : ( mem(V3e2,A_27a) & ? [V4e3] : ( mem(V4e3,A_27a) & ? [V5e4] : ( mem(V5e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V2e1),ap(ap(c_2Elist_2ECONS(A_27a),V3e2),ap(ap(c_2Elist_2ECONS(A_27a),V4e3),ap(ap(c_2Elist_2ECONS(A_27a),V5e4),c_2Elist_2ENIL(A_27a))))) ) ) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V6e1] : ( mem(V6e1,A_27a) & ? [V7e2] : ( mem(V7e2,A_27a) & ? [V8e3] : ( mem(V8e3,A_27a) & ? [V9e4] : ( mem(V9e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V6e1),ap(ap(c_2Elist_2ECONS(A_27a),V7e2),ap(ap(c_2Elist_2ECONS(A_27a),V8e3),ap(ap(c_2Elist_2ECONS(A_27a),V9e4),c_2Elist_2ENIL(A_27a))))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V10l_27] : ( mem(V10l_27,ty_2Elist_2Elist(A_27a)) & ? [V11e1] : ( mem(V11e1,A_27a) & ? [V12e2] : ( mem(V12e2,A_27a) & ? [V13e3] : ( mem(V13e3,A_27a) & ? [V14e4] : ( mem(V14e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V11e1),ap(ap(c_2Elist_2ECONS(A_27a),V12e2),ap(ap(c_2Elist_2ECONS(A_27a),V13e3),ap(ap(c_2Elist_2ECONS(A_27a),V14e4),V10l_27)))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V15l_27] : ( mem(V15l_27,ty_2Elist_2Elist(A_27a)) & ? [V16e1] : ( mem(V16e1,A_27a) & ? [V17e2] : ( mem(V17e2,A_27a) & ? [V18e3] : ( mem(V18e3,A_27a) & ? [V19e4] : ( mem(V19e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V16e1),ap(ap(c_2Elist_2ECONS(A_27a),V17e2),ap(ap(c_2Elist_2ECONS(A_27a),V18e3),ap(ap(c_2Elist_2ECONS(A_27a),V19e4),V15l_27)))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V20l_27] : ( mem(V20l_27,ty_2Elist_2Elist(A_27a)) & ? [V21e1] : ( mem(V21e1,A_27a) & ? [V22e2] : ( mem(V22e2,A_27a) & ? [V23e3] : ( mem(V23e3,A_27a) & ? [V24e4] : ( mem(V24e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V21e1),ap(ap(c_2Elist_2ECONS(A_27a),V22e2),ap(ap(c_2Elist_2ECONS(A_27a),V23e3),ap(ap(c_2Elist_2ECONS(A_27a),V24e4),V20l_27)))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V25l_27] : ( mem(V25l_27,ty_2Elist_2Elist(A_27a)) & ? [V26e1] : ( mem(V26e1,A_27a) & ? [V27e2] : ( mem(V27e2,A_27a) & ? [V28e3] : ( mem(V28e3,A_27a) & ? [V29e4] : ( mem(V29e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V26e1),ap(ap(c_2Elist_2ECONS(A_27a),V27e2),ap(ap(c_2Elist_2ECONS(A_27a),V28e3),ap(ap(c_2Elist_2ECONS(A_27a),V29e4),V25l_27)))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V30l_27] : ( mem(V30l_27,ty_2Elist_2Elist(A_27a)) & ? [V31e1] : ( mem(V31e1,A_27a) & ? [V32e2] : ( mem(V32e2,A_27a) & ? [V33e3] : ( mem(V33e3,A_27a) & ? [V34e4] : ( mem(V34e4,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V30l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V31e1),ap(ap(c_2Elist_2ECONS(A_27a),V32e2),ap(ap(c_2Elist_2ECONS(A_27a),V33e3),ap(ap(c_2Elist_2ECONS(A_27a),V34e4),V30l_27)))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x))) <=> ? [V35l_27] : ( mem(V35l_27,ty_2Elist_2Elist(A_27a)) & ? [V36e1] : ( mem(V36e1,A_27a) & ? [V37e2] : ( mem(V37e2,A_27a) & ? [V38e3] : ( mem(V38e3,A_27a) & ? [V39e4] : ( mem(V39e4,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V35l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V36e1),ap(ap(c_2Elist_2ECONS(A_27a),V37e2),ap(ap(c_2Elist_2ECONS(A_27a),V38e3),ap(ap(c_2Elist_2ECONS(A_27a),V39e4),V35l_27)))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V40l_27] : ( mem(V40l_27,ty_2Elist_2Elist(A_27a)) & ? [V41e1] : ( mem(V41e1,A_27a) & ? [V42e2] : ( mem(V42e2,A_27a) & ? [V43e3] : ( mem(V43e3,A_27a) & ? [V44e4] : ( mem(V44e4,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V40l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V41e1),ap(ap(c_2Elist_2ECONS(A_27a),V42e2),ap(ap(c_2Elist_2ECONS(A_27a),V43e3),ap(ap(c_2Elist_2ECONS(A_27a),V44e4),V40l_27)))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) <=> ? [V45l_27] : ( mem(V45l_27,ty_2Elist_2Elist(A_27a)) & ? [V46e1] : ( mem(V46e1,A_27a) & ? [V47e2] : ( mem(V47e2,A_27a) & ? [V48e3] : ( mem(V48e3,A_27a) & ? [V49e4] : ( mem(V49e4,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V45l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V46e1),ap(ap(c_2Elist_2ECONS(A_27a),V47e2),ap(ap(c_2Elist_2ECONS(A_27a),V48e3),ap(ap(c_2Elist_2ECONS(A_27a),V49e4),V45l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) ) <=> ? [V50l_27] : ( mem(V50l_27,ty_2Elist_2Elist(A_27a)) & ? [V51e1] : ( mem(V51e1,A_27a) & ? [V52e2] : ( mem(V52e2,A_27a) & ? [V53e3] : ( mem(V53e3,A_27a) & ? [V54e4] : ( mem(V54e4,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V50l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V51e1),ap(ap(c_2Elist_2ECONS(A_27a),V52e2),ap(ap(c_2Elist_2ECONS(A_27a),V53e3),ap(ap(c_2Elist_2ECONS(A_27a),V54e4),V50l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V55l_27] : ( mem(V55l_27,ty_2Elist_2Elist(A_27a)) & ? [V56e1] : ( mem(V56e1,A_27a) & ? [V57e2] : ( mem(V57e2,A_27a) & ? [V58e3] : ( mem(V58e3,A_27a) & ? [V59e4] : ( mem(V59e4,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V55l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V56e1),ap(ap(c_2Elist_2ECONS(A_27a),V57e2),ap(ap(c_2Elist_2ECONS(A_27a),V58e3),ap(ap(c_2Elist_2ECONS(A_27a),V59e4),V55l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) <=> ? [V60l_27] : ( mem(V60l_27,ty_2Elist_2Elist(A_27a)) & ? [V61e1] : ( mem(V61e1,A_27a) & ? [V62e2] : ( mem(V62e2,A_27a) & ? [V63e3] : ( mem(V63e3,A_27a) & ? [V64e4] : ( mem(V64e4,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V60l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V61e1),ap(ap(c_2Elist_2ECONS(A_27a),V62e2),ap(ap(c_2Elist_2ECONS(A_27a),V63e3),ap(ap(c_2Elist_2ECONS(A_27a),V64e4),V60l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V65l_27] : ( mem(V65l_27,ty_2Elist_2Elist(A_27a)) & ? [V66e1] : ( mem(V66e1,A_27a) & ? [V67e2] : ( mem(V67e2,A_27a) & ? [V68e3] : ( mem(V68e3,A_27a) & ? [V69e4] : ( mem(V69e4,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V65l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V66e1),ap(ap(c_2Elist_2ECONS(A_27a),V67e2),ap(ap(c_2Elist_2ECONS(A_27a),V68e3),ap(ap(c_2Elist_2ECONS(A_27a),V69e4),V65l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V70e1] : ( mem(V70e1,A_27a) & ? [V71e2] : ( mem(V71e2,A_27a) & ? [V72e3] : ( mem(V72e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V70e1),ap(ap(c_2Elist_2ECONS(A_27a),V71e2),ap(ap(c_2Elist_2ECONS(A_27a),V72e3),c_2Elist_2ENIL(A_27a)))) ) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V73e1] : ( mem(V73e1,A_27a) & ? [V74e2] : ( mem(V74e2,A_27a) & ? [V75e3] : ( mem(V75e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V73e1),ap(ap(c_2Elist_2ECONS(A_27a),V74e2),ap(ap(c_2Elist_2ECONS(A_27a),V75e3),c_2Elist_2ENIL(A_27a)))) ) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V76l_27] : ( mem(V76l_27,ty_2Elist_2Elist(A_27a)) & ? [V77e1] : ( mem(V77e1,A_27a) & ? [V78e2] : ( mem(V78e2,A_27a) & ? [V79e3] : ( mem(V79e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V77e1),ap(ap(c_2Elist_2ECONS(A_27a),V78e2),ap(ap(c_2Elist_2ECONS(A_27a),V79e3),V76l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) <=> ? [V80l_27] : ( mem(V80l_27,ty_2Elist_2Elist(A_27a)) & ? [V81e1] : ( mem(V81e1,A_27a) & ? [V82e2] : ( mem(V82e2,A_27a) & ? [V83e3] : ( mem(V83e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V81e1),ap(ap(c_2Elist_2ECONS(A_27a),V82e2),ap(ap(c_2Elist_2ECONS(A_27a),V83e3),V80l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V84l_27] : ( mem(V84l_27,ty_2Elist_2Elist(A_27a)) & ? [V85e1] : ( mem(V85e1,A_27a) & ? [V86e2] : ( mem(V86e2,A_27a) & ? [V87e3] : ( mem(V87e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V85e1),ap(ap(c_2Elist_2ECONS(A_27a),V86e2),ap(ap(c_2Elist_2ECONS(A_27a),V87e3),V84l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V88l_27] : ( mem(V88l_27,ty_2Elist_2Elist(A_27a)) & ? [V89e1] : ( mem(V89e1,A_27a) & ? [V90e2] : ( mem(V90e2,A_27a) & ? [V91e3] : ( mem(V91e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V89e1),ap(ap(c_2Elist_2ECONS(A_27a),V90e2),ap(ap(c_2Elist_2ECONS(A_27a),V91e3),V88l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V92l_27] : ( mem(V92l_27,ty_2Elist_2Elist(A_27a)) & ? [V93e1] : ( mem(V93e1,A_27a) & ? [V94e2] : ( mem(V94e2,A_27a) & ? [V95e3] : ( mem(V95e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V92l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V93e1),ap(ap(c_2Elist_2ECONS(A_27a),V94e2),ap(ap(c_2Elist_2ECONS(A_27a),V95e3),V92l_27))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x))) <=> ? [V96l_27] : ( mem(V96l_27,ty_2Elist_2Elist(A_27a)) & ? [V97e1] : ( mem(V97e1,A_27a) & ? [V98e2] : ( mem(V98e2,A_27a) & ? [V99e3] : ( mem(V99e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V96l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V97e1),ap(ap(c_2Elist_2ECONS(A_27a),V98e2),ap(ap(c_2Elist_2ECONS(A_27a),V99e3),V96l_27))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V100l_27] : ( mem(V100l_27,ty_2Elist_2Elist(A_27a)) & ? [V101e1] : ( mem(V101e1,A_27a) & ? [V102e2] : ( mem(V102e2,A_27a) & ? [V103e3] : ( mem(V103e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V100l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V101e1),ap(ap(c_2Elist_2ECONS(A_27a),V102e2),ap(ap(c_2Elist_2ECONS(A_27a),V103e3),V100l_27))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) <=> ? [V104l_27] : ( mem(V104l_27,ty_2Elist_2Elist(A_27a)) & ? [V105e1] : ( mem(V105e1,A_27a) & ? [V106e2] : ( mem(V106e2,A_27a) & ? [V107e3] : ( mem(V107e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V104l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V105e1),ap(ap(c_2Elist_2ECONS(A_27a),V106e2),ap(ap(c_2Elist_2ECONS(A_27a),V107e3),V104l_27))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) ) <=> ? [V108l_27] : ( mem(V108l_27,ty_2Elist_2Elist(A_27a)) & ? [V109e1] : ( mem(V109e1,A_27a) & ? [V110e2] : ( mem(V110e2,A_27a) & ? [V111e3] : ( mem(V111e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V108l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V109e1),ap(ap(c_2Elist_2ECONS(A_27a),V110e2),ap(ap(c_2Elist_2ECONS(A_27a),V111e3),V108l_27))) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V112l_27] : ( mem(V112l_27,ty_2Elist_2Elist(A_27a)) & ? [V113e1] : ( mem(V113e1,A_27a) & ? [V114e2] : ( mem(V114e2,A_27a) & ? [V115e3] : ( mem(V115e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V112l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V113e1),ap(ap(c_2Elist_2ECONS(A_27a),V114e2),ap(ap(c_2Elist_2ECONS(A_27a),V115e3),V112l_27))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) <=> ? [V116l_27] : ( mem(V116l_27,ty_2Elist_2Elist(A_27a)) & ? [V117e1] : ( mem(V117e1,A_27a) & ? [V118e2] : ( mem(V118e2,A_27a) & ? [V119e3] : ( mem(V119e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V116l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V117e1),ap(ap(c_2Elist_2ECONS(A_27a),V118e2),ap(ap(c_2Elist_2ECONS(A_27a),V119e3),V116l_27))) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V120l_27] : ( mem(V120l_27,ty_2Elist_2Elist(A_27a)) & ? [V121e1] : ( mem(V121e1,A_27a) & ? [V122e2] : ( mem(V122e2,A_27a) & ? [V123e3] : ( mem(V123e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V120l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V121e1),ap(ap(c_2Elist_2ECONS(A_27a),V122e2),ap(ap(c_2Elist_2ECONS(A_27a),V123e3),V120l_27))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) ) <=> ? [V124e1] : ( mem(V124e1,A_27a) & ? [V125e2] : ( mem(V125e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V124e1),ap(ap(c_2Elist_2ECONS(A_27a),V125e2),c_2Elist_2ENIL(A_27a))) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V126e1] : ( mem(V126e1,A_27a) & ? [V127e2] : ( mem(V127e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V126e1),ap(ap(c_2Elist_2ECONS(A_27a),V127e2),c_2Elist_2ENIL(A_27a))) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V128l_27] : ( mem(V128l_27,ty_2Elist_2Elist(A_27a)) & ? [V129e1] : ( mem(V129e1,A_27a) & ? [V130e2] : ( mem(V130e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V129e1),ap(ap(c_2Elist_2ECONS(A_27a),V130e2),V128l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ? [V131l_27] : ( mem(V131l_27,ty_2Elist_2Elist(A_27a)) & ? [V132e1] : ( mem(V132e1,A_27a) & ? [V133e2] : ( mem(V133e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V132e1),ap(ap(c_2Elist_2ECONS(A_27a),V133e2),V131l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V134l_27] : ( mem(V134l_27,ty_2Elist_2Elist(A_27a)) & ? [V135e1] : ( mem(V135e1,A_27a) & ? [V136e2] : ( mem(V136e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V135e1),ap(ap(c_2Elist_2ECONS(A_27a),V136e2),V134l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) <=> ? [V137l_27] : ( mem(V137l_27,ty_2Elist_2Elist(A_27a)) & ? [V138e1] : ( mem(V138e1,A_27a) & ? [V139e2] : ( mem(V139e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V138e1),ap(ap(c_2Elist_2ECONS(A_27a),V139e2),V137l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V140l_27] : ( mem(V140l_27,ty_2Elist_2Elist(A_27a)) & ? [V141e1] : ( mem(V141e1,A_27a) & ? [V142e2] : ( mem(V142e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V140l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V141e1),ap(ap(c_2Elist_2ECONS(A_27a),V142e2),V140l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x))) <=> ? [V143l_27] : ( mem(V143l_27,ty_2Elist_2Elist(A_27a)) & ? [V144e1] : ( mem(V144e1,A_27a) & ? [V145e2] : ( mem(V145e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V143l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V144e1),ap(ap(c_2Elist_2ECONS(A_27a),V145e2),V143l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V146l_27] : ( mem(V146l_27,ty_2Elist_2Elist(A_27a)) & ? [V147e1] : ( mem(V147e1,A_27a) & ? [V148e2] : ( mem(V148e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V146l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V147e1),ap(ap(c_2Elist_2ECONS(A_27a),V148e2),V146l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) <=> ? [V149l_27] : ( mem(V149l_27,ty_2Elist_2Elist(A_27a)) & ? [V150e1] : ( mem(V150e1,A_27a) & ? [V151e2] : ( mem(V151e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V149l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V150e1),ap(ap(c_2Elist_2ECONS(A_27a),V151e2),V149l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x) ) <=> ? [V152l_27] : ( mem(V152l_27,ty_2Elist_2Elist(A_27a)) & ? [V153e1] : ( mem(V153e1,A_27a) & ? [V154e2] : ( mem(V154e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V152l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V153e1),ap(ap(c_2Elist_2ECONS(A_27a),V154e2),V152l_27)) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V155l_27] : ( mem(V155l_27,ty_2Elist_2Elist(A_27a)) & ? [V156e1] : ( mem(V156e1,A_27a) & ? [V157e2] : ( mem(V157e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V155l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V156e1),ap(ap(c_2Elist_2ECONS(A_27a),V157e2),V155l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) <=> ? [V158l_27] : ( mem(V158l_27,ty_2Elist_2Elist(A_27a)) & ? [V159e1] : ( mem(V159e1,A_27a) & ? [V160e2] : ( mem(V160e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V158l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V159e1),ap(ap(c_2Elist_2ECONS(A_27a),V160e2),V158l_27)) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V161l_27] : ( mem(V161l_27,ty_2Elist_2Elist(A_27a)) & ? [V162e1] : ( mem(V162e1,A_27a) & ? [V163e2] : ( mem(V163e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V161l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V162e1),ap(ap(c_2Elist_2ECONS(A_27a),V163e2),V161l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) <=> ? [V164e1] : ( mem(V164e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V164e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V165e1] : ( mem(V165e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V165e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V166l_27] : ( mem(V166l_27,ty_2Elist_2Elist(A_27a)) & ? [V167e1] : ( mem(V167e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V167e1),V166l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ? [V168l_27] : ( mem(V168l_27,ty_2Elist_2Elist(A_27a)) & ? [V169e1] : ( mem(V169e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V169e1),V168l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V170l_27] : ( mem(V170l_27,ty_2Elist_2Elist(A_27a)) & ? [V171e1] : ( mem(V171e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V171e1),V170l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ? [V172l_27] : ( mem(V172l_27,ty_2Elist_2Elist(A_27a)) & ? [V173e1] : ( mem(V173e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V173e1),V172l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V174l_27] : ( mem(V174l_27,ty_2Elist_2Elist(A_27a)) & ? [V175e1] : ( mem(V175e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V174l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V175e1),V174l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x))) <=> ? [V176l_27] : ( mem(V176l_27,ty_2Elist_2Elist(A_27a)) & ? [V177e1] : ( mem(V177e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V176l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V177e1),V176l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V178l_27] : ( mem(V178l_27,ty_2Elist_2Elist(A_27a)) & ? [V179e1] : ( mem(V179e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V178l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V179e1),V178l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V180l_27] : ( mem(V180l_27,ty_2Elist_2Elist(A_27a)) & ? [V181e1] : ( mem(V181e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V180l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V181e1),V180l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) ) <=> ? [V182l_27] : ( mem(V182l_27,ty_2Elist_2Elist(A_27a)) & ? [V183e1] : ( mem(V183e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V182l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V183e1),V182l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V184l_27] : ( mem(V184l_27,ty_2Elist_2Elist(A_27a)) & ? [V185e1] : ( mem(V185e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V184l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V185e1),V184l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V186l_27] : ( mem(V186l_27,ty_2Elist_2Elist(A_27a)) & ? [V187e1] : ( mem(V187e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V186l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V187e1),V186l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V188l_27] : ( mem(V188l_27,ty_2Elist_2Elist(A_27a)) & ? [V189e1] : ( mem(V189e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V188l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V189e1),V188l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0 ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( ( c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )))).
fof(conj_thm_2EquantHeuristics_2ELIST__LENGTH__5,conjecture,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) <=> ? [V2e1] : ( mem(V2e1,A_27a) & ? [V3e2] : ( mem(V3e2,A_27a) & ? [V4e3] : ( mem(V4e3,A_27a) & ? [V5e4] : ( mem(V5e4,A_27a) & ? [V6e5] : ( mem(V6e5,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V2e1),ap(ap(c_2Elist_2ECONS(A_27a),V3e2),ap(ap(c_2Elist_2ECONS(A_27a),V4e3),ap(ap(c_2Elist_2ECONS(A_27a),V5e4),ap(ap(c_2Elist_2ECONS(A_27a),V6e5),c_2Elist_2ENIL(A_27a)))))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V7e1] : ( mem(V7e1,A_27a) & ? [V8e2] : ( mem(V8e2,A_27a) & ? [V9e3] : ( mem(V9e3,A_27a) & ? [V10e4] : ( mem(V10e4,A_27a) & ? [V11e5] : ( mem(V11e5,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V7e1),ap(ap(c_2Elist_2ECONS(A_27a),V8e2),ap(ap(c_2Elist_2ECONS(A_27a),V9e3),ap(ap(c_2Elist_2ECONS(A_27a),V10e4),ap(ap(c_2Elist_2ECONS(A_27a),V11e5),c_2Elist_2ENIL(A_27a)))))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V12l_27] : ( mem(V12l_27,ty_2Elist_2Elist(A_27a)) & ? [V13e1] : ( mem(V13e1,A_27a) & ? [V14e2] : ( mem(V14e2,A_27a) & ? [V15e3] : ( mem(V15e3,A_27a) & ? [V16e4] : ( mem(V16e4,A_27a) & ? [V17e5] : ( mem(V17e5,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V13e1),ap(ap(c_2Elist_2ECONS(A_27a),V14e2),ap(ap(c_2Elist_2ECONS(A_27a),V15e3),ap(ap(c_2Elist_2ECONS(A_27a),V16e4),ap(ap(c_2Elist_2ECONS(A_27a),V17e5),V12l_27))))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V18l_27] : ( mem(V18l_27,ty_2Elist_2Elist(A_27a)) & ? [V19e1] : ( mem(V19e1,A_27a) & ? [V20e2] : ( mem(V20e2,A_27a) & ? [V21e3] : ( mem(V21e3,A_27a) & ? [V22e4] : ( mem(V22e4,A_27a) & ? [V23e5] : ( mem(V23e5,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V19e1),ap(ap(c_2Elist_2ECONS(A_27a),V20e2),ap(ap(c_2Elist_2ECONS(A_27a),V21e3),ap(ap(c_2Elist_2ECONS(A_27a),V22e4),ap(ap(c_2Elist_2ECONS(A_27a),V23e5),V18l_27))))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V24l_27] : ( mem(V24l_27,ty_2Elist_2Elist(A_27a)) & ? [V25e1] : ( mem(V25e1,A_27a) & ? [V26e2] : ( mem(V26e2,A_27a) & ? [V27e3] : ( mem(V27e3,A_27a) & ? [V28e4] : ( mem(V28e4,A_27a) & ? [V29e5] : ( mem(V29e5,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V25e1),ap(ap(c_2Elist_2ECONS(A_27a),V26e2),ap(ap(c_2Elist_2ECONS(A_27a),V27e3),ap(ap(c_2Elist_2ECONS(A_27a),V28e4),ap(ap(c_2Elist_2ECONS(A_27a),V29e5),V24l_27))))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) <=> ? [V30l_27] : ( mem(V30l_27,ty_2Elist_2Elist(A_27a)) & ? [V31e1] : ( mem(V31e1,A_27a) & ? [V32e2] : ( mem(V32e2,A_27a) & ? [V33e3] : ( mem(V33e3,A_27a) & ? [V34e4] : ( mem(V34e4,A_27a) & ? [V35e5] : ( mem(V35e5,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V31e1),ap(ap(c_2Elist_2ECONS(A_27a),V32e2),ap(ap(c_2Elist_2ECONS(A_27a),V33e3),ap(ap(c_2Elist_2ECONS(A_27a),V34e4),ap(ap(c_2Elist_2ECONS(A_27a),V35e5),V30l_27))))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V36l_27] : ( mem(V36l_27,ty_2Elist_2Elist(A_27a)) & ? [V37e1] : ( mem(V37e1,A_27a) & ? [V38e2] : ( mem(V38e2,A_27a) & ? [V39e3] : ( mem(V39e3,A_27a) & ? [V40e4] : ( mem(V40e4,A_27a) & ? [V41e5] : ( mem(V41e5,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V36l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V37e1),ap(ap(c_2Elist_2ECONS(A_27a),V38e2),ap(ap(c_2Elist_2ECONS(A_27a),V39e3),ap(ap(c_2Elist_2ECONS(A_27a),V40e4),ap(ap(c_2Elist_2ECONS(A_27a),V41e5),V36l_27))))) ) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1x))) <=> ? [V42l_27] : ( mem(V42l_27,ty_2Elist_2Elist(A_27a)) & ? [V43e1] : ( mem(V43e1,A_27a) & ? [V44e2] : ( mem(V44e2,A_27a) & ? [V45e3] : ( mem(V45e3,A_27a) & ? [V46e4] : ( mem(V46e4,A_27a) & ? [V47e5] : ( mem(V47e5,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V42l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V43e1),ap(ap(c_2Elist_2ECONS(A_27a),V44e2),ap(ap(c_2Elist_2ECONS(A_27a),V45e3),ap(ap(c_2Elist_2ECONS(A_27a),V46e4),ap(ap(c_2Elist_2ECONS(A_27a),V47e5),V42l_27))))) ) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V48l_27] : ( mem(V48l_27,ty_2Elist_2Elist(A_27a)) & ? [V49e1] : ( mem(V49e1,A_27a) & ? [V50e2] : ( mem(V50e2,A_27a) & ? [V51e3] : ( mem(V51e3,A_27a) & ? [V52e4] : ( mem(V52e4,A_27a) & ? [V53e5] : ( mem(V53e5,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V48l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V49e1),ap(ap(c_2Elist_2ECONS(A_27a),V50e2),ap(ap(c_2Elist_2ECONS(A_27a),V51e3),ap(ap(c_2Elist_2ECONS(A_27a),V52e4),ap(ap(c_2Elist_2ECONS(A_27a),V53e5),V48l_27))))) ) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) <=> ? [V54l_27] : ( mem(V54l_27,ty_2Elist_2Elist(A_27a)) & ? [V55e1] : ( mem(V55e1,A_27a) & ? [V56e2] : ( mem(V56e2,A_27a) & ? [V57e3] : ( mem(V57e3,A_27a) & ? [V58e4] : ( mem(V58e4,A_27a) & ? [V59e5] : ( mem(V59e5,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V54l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V55e1),ap(ap(c_2Elist_2ECONS(A_27a),V56e2),ap(ap(c_2Elist_2ECONS(A_27a),V57e3),ap(ap(c_2Elist_2ECONS(A_27a),V58e4),ap(ap(c_2Elist_2ECONS(A_27a),V59e5),V54l_27))))) ) ) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1x) ) <=> ? [V60l_27] : ( mem(V60l_27,ty_2Elist_2Elist(A_27a)) & ? [V61e1] : ( mem(V61e1,A_27a) & ? [V62e2] : ( mem(V62e2,A_27a) & ? [V63e3] : ( mem(V63e3,A_27a) & ? [V64e4] : ( mem(V64e4,A_27a) & ? [V65e5] : ( mem(V65e5,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V60l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V61e1),ap(ap(c_2Elist_2ECONS(A_27a),V62e2),ap(ap(c_2Elist_2ECONS(A_27a),V63e3),ap(ap(c_2Elist_2ECONS(A_27a),V64e4),ap(ap(c_2Elist_2ECONS(A_27a),V65e5),V60l_27))))) ) ) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V66l_27] : ( mem(V66l_27,ty_2Elist_2Elist(A_27a)) & ? [V67e1] : ( mem(V67e1,A_27a) & ? [V68e2] : ( mem(V68e2,A_27a) & ? [V69e3] : ( mem(V69e3,A_27a) & ? [V70e4] : ( mem(V70e4,A_27a) & ? [V71e5] : ( mem(V71e5,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V66l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V67e1),ap(ap(c_2Elist_2ECONS(A_27a),V68e2),ap(ap(c_2Elist_2ECONS(A_27a),V69e3),ap(ap(c_2Elist_2ECONS(A_27a),V70e4),ap(ap(c_2Elist_2ECONS(A_27a),V71e5),V66l_27))))) ) ) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) ) <=> ? [V72l_27] : ( mem(V72l_27,ty_2Elist_2Elist(A_27a)) & ? [V73e1] : ( mem(V73e1,A_27a) & ? [V74e2] : ( mem(V74e2,A_27a) & ? [V75e3] : ( mem(V75e3,A_27a) & ? [V76e4] : ( mem(V76e4,A_27a) & ? [V77e5] : ( mem(V77e5,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V72l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V73e1),ap(ap(c_2Elist_2ECONS(A_27a),V74e2),ap(ap(c_2Elist_2ECONS(A_27a),V75e3),ap(ap(c_2Elist_2ECONS(A_27a),V76e4),ap(ap(c_2Elist_2ECONS(A_27a),V77e5),V72l_27))))) ) ) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V78l_27] : ( mem(V78l_27,ty_2Elist_2Elist(A_27a)) & ? [V79e1] : ( mem(V79e1,A_27a) & ? [V80e2] : ( mem(V80e2,A_27a) & ? [V81e3] : ( mem(V81e3,A_27a) & ? [V82e4] : ( mem(V82e4,A_27a) & ? [V83e5] : ( mem(V83e5,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V78l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V79e1),ap(ap(c_2Elist_2ECONS(A_27a),V80e2),ap(ap(c_2Elist_2ECONS(A_27a),V81e3),ap(ap(c_2Elist_2ECONS(A_27a),V82e4),ap(ap(c_2Elist_2ECONS(A_27a),V83e5),V78l_27))))) ) ) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V84e1] : ( mem(V84e1,A_27a) & ? [V85e2] : ( mem(V85e2,A_27a) & ? [V86e3] : ( mem(V86e3,A_27a) & ? [V87e4] : ( mem(V87e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V84e1),ap(ap(c_2Elist_2ECONS(A_27a),V85e2),ap(ap(c_2Elist_2ECONS(A_27a),V86e3),ap(ap(c_2Elist_2ECONS(A_27a),V87e4),c_2Elist_2ENIL(A_27a))))) ) ) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V88e1] : ( mem(V88e1,A_27a) & ? [V89e2] : ( mem(V89e2,A_27a) & ? [V90e3] : ( mem(V90e3,A_27a) & ? [V91e4] : ( mem(V91e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V88e1),ap(ap(c_2Elist_2ECONS(A_27a),V89e2),ap(ap(c_2Elist_2ECONS(A_27a),V90e3),ap(ap(c_2Elist_2ECONS(A_27a),V91e4),c_2Elist_2ENIL(A_27a))))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V92l_27] : ( mem(V92l_27,ty_2Elist_2Elist(A_27a)) & ? [V93e1] : ( mem(V93e1,A_27a) & ? [V94e2] : ( mem(V94e2,A_27a) & ? [V95e3] : ( mem(V95e3,A_27a) & ? [V96e4] : ( mem(V96e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V93e1),ap(ap(c_2Elist_2ECONS(A_27a),V94e2),ap(ap(c_2Elist_2ECONS(A_27a),V95e3),ap(ap(c_2Elist_2ECONS(A_27a),V96e4),V92l_27)))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V97l_27] : ( mem(V97l_27,ty_2Elist_2Elist(A_27a)) & ? [V98e1] : ( mem(V98e1,A_27a) & ? [V99e2] : ( mem(V99e2,A_27a) & ? [V100e3] : ( mem(V100e3,A_27a) & ? [V101e4] : ( mem(V101e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V98e1),ap(ap(c_2Elist_2ECONS(A_27a),V99e2),ap(ap(c_2Elist_2ECONS(A_27a),V100e3),ap(ap(c_2Elist_2ECONS(A_27a),V101e4),V97l_27)))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V102l_27] : ( mem(V102l_27,ty_2Elist_2Elist(A_27a)) & ? [V103e1] : ( mem(V103e1,A_27a) & ? [V104e2] : ( mem(V104e2,A_27a) & ? [V105e3] : ( mem(V105e3,A_27a) & ? [V106e4] : ( mem(V106e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V103e1),ap(ap(c_2Elist_2ECONS(A_27a),V104e2),ap(ap(c_2Elist_2ECONS(A_27a),V105e3),ap(ap(c_2Elist_2ECONS(A_27a),V106e4),V102l_27)))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V107l_27] : ( mem(V107l_27,ty_2Elist_2Elist(A_27a)) & ? [V108e1] : ( mem(V108e1,A_27a) & ? [V109e2] : ( mem(V109e2,A_27a) & ? [V110e3] : ( mem(V110e3,A_27a) & ? [V111e4] : ( mem(V111e4,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V108e1),ap(ap(c_2Elist_2ECONS(A_27a),V109e2),ap(ap(c_2Elist_2ECONS(A_27a),V110e3),ap(ap(c_2Elist_2ECONS(A_27a),V111e4),V107l_27)))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V112l_27] : ( mem(V112l_27,ty_2Elist_2Elist(A_27a)) & ? [V113e1] : ( mem(V113e1,A_27a) & ? [V114e2] : ( mem(V114e2,A_27a) & ? [V115e3] : ( mem(V115e3,A_27a) & ? [V116e4] : ( mem(V116e4,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V112l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V113e1),ap(ap(c_2Elist_2ECONS(A_27a),V114e2),ap(ap(c_2Elist_2ECONS(A_27a),V115e3),ap(ap(c_2Elist_2ECONS(A_27a),V116e4),V112l_27)))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x))) <=> ? [V117l_27] : ( mem(V117l_27,ty_2Elist_2Elist(A_27a)) & ? [V118e1] : ( mem(V118e1,A_27a) & ? [V119e2] : ( mem(V119e2,A_27a) & ? [V120e3] : ( mem(V120e3,A_27a) & ? [V121e4] : ( mem(V121e4,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V117l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V118e1),ap(ap(c_2Elist_2ECONS(A_27a),V119e2),ap(ap(c_2Elist_2ECONS(A_27a),V120e3),ap(ap(c_2Elist_2ECONS(A_27a),V121e4),V117l_27)))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V122l_27] : ( mem(V122l_27,ty_2Elist_2Elist(A_27a)) & ? [V123e1] : ( mem(V123e1,A_27a) & ? [V124e2] : ( mem(V124e2,A_27a) & ? [V125e3] : ( mem(V125e3,A_27a) & ? [V126e4] : ( mem(V126e4,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V122l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V123e1),ap(ap(c_2Elist_2ECONS(A_27a),V124e2),ap(ap(c_2Elist_2ECONS(A_27a),V125e3),ap(ap(c_2Elist_2ECONS(A_27a),V126e4),V122l_27)))) ) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) <=> ? [V127l_27] : ( mem(V127l_27,ty_2Elist_2Elist(A_27a)) & ? [V128e1] : ( mem(V128e1,A_27a) & ? [V129e2] : ( mem(V129e2,A_27a) & ? [V130e3] : ( mem(V130e3,A_27a) & ? [V131e4] : ( mem(V131e4,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V127l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V128e1),ap(ap(c_2Elist_2ECONS(A_27a),V129e2),ap(ap(c_2Elist_2ECONS(A_27a),V130e3),ap(ap(c_2Elist_2ECONS(A_27a),V131e4),V127l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) ) <=> ? [V132l_27] : ( mem(V132l_27,ty_2Elist_2Elist(A_27a)) & ? [V133e1] : ( mem(V133e1,A_27a) & ? [V134e2] : ( mem(V134e2,A_27a) & ? [V135e3] : ( mem(V135e3,A_27a) & ? [V136e4] : ( mem(V136e4,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V132l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V133e1),ap(ap(c_2Elist_2ECONS(A_27a),V134e2),ap(ap(c_2Elist_2ECONS(A_27a),V135e3),ap(ap(c_2Elist_2ECONS(A_27a),V136e4),V132l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V137l_27] : ( mem(V137l_27,ty_2Elist_2Elist(A_27a)) & ? [V138e1] : ( mem(V138e1,A_27a) & ? [V139e2] : ( mem(V139e2,A_27a) & ? [V140e3] : ( mem(V140e3,A_27a) & ? [V141e4] : ( mem(V141e4,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V137l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V138e1),ap(ap(c_2Elist_2ECONS(A_27a),V139e2),ap(ap(c_2Elist_2ECONS(A_27a),V140e3),ap(ap(c_2Elist_2ECONS(A_27a),V141e4),V137l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) <=> ? [V142l_27] : ( mem(V142l_27,ty_2Elist_2Elist(A_27a)) & ? [V143e1] : ( mem(V143e1,A_27a) & ? [V144e2] : ( mem(V144e2,A_27a) & ? [V145e3] : ( mem(V145e3,A_27a) & ? [V146e4] : ( mem(V146e4,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V142l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V143e1),ap(ap(c_2Elist_2ECONS(A_27a),V144e2),ap(ap(c_2Elist_2ECONS(A_27a),V145e3),ap(ap(c_2Elist_2ECONS(A_27a),V146e4),V142l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V147l_27] : ( mem(V147l_27,ty_2Elist_2Elist(A_27a)) & ? [V148e1] : ( mem(V148e1,A_27a) & ? [V149e2] : ( mem(V149e2,A_27a) & ? [V150e3] : ( mem(V150e3,A_27a) & ? [V151e4] : ( mem(V151e4,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V147l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V148e1),ap(ap(c_2Elist_2ECONS(A_27a),V149e2),ap(ap(c_2Elist_2ECONS(A_27a),V150e3),ap(ap(c_2Elist_2ECONS(A_27a),V151e4),V147l_27)))) ) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V152e1] : ( mem(V152e1,A_27a) & ? [V153e2] : ( mem(V153e2,A_27a) & ? [V154e3] : ( mem(V154e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V152e1),ap(ap(c_2Elist_2ECONS(A_27a),V153e2),ap(ap(c_2Elist_2ECONS(A_27a),V154e3),c_2Elist_2ENIL(A_27a)))) ) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V155e1] : ( mem(V155e1,A_27a) & ? [V156e2] : ( mem(V156e2,A_27a) & ? [V157e3] : ( mem(V157e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V155e1),ap(ap(c_2Elist_2ECONS(A_27a),V156e2),ap(ap(c_2Elist_2ECONS(A_27a),V157e3),c_2Elist_2ENIL(A_27a)))) ) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V158l_27] : ( mem(V158l_27,ty_2Elist_2Elist(A_27a)) & ? [V159e1] : ( mem(V159e1,A_27a) & ? [V160e2] : ( mem(V160e2,A_27a) & ? [V161e3] : ( mem(V161e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V159e1),ap(ap(c_2Elist_2ECONS(A_27a),V160e2),ap(ap(c_2Elist_2ECONS(A_27a),V161e3),V158l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) <=> ? [V162l_27] : ( mem(V162l_27,ty_2Elist_2Elist(A_27a)) & ? [V163e1] : ( mem(V163e1,A_27a) & ? [V164e2] : ( mem(V164e2,A_27a) & ? [V165e3] : ( mem(V165e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V163e1),ap(ap(c_2Elist_2ECONS(A_27a),V164e2),ap(ap(c_2Elist_2ECONS(A_27a),V165e3),V162l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V166l_27] : ( mem(V166l_27,ty_2Elist_2Elist(A_27a)) & ? [V167e1] : ( mem(V167e1,A_27a) & ? [V168e2] : ( mem(V168e2,A_27a) & ? [V169e3] : ( mem(V169e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V167e1),ap(ap(c_2Elist_2ECONS(A_27a),V168e2),ap(ap(c_2Elist_2ECONS(A_27a),V169e3),V166l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V170l_27] : ( mem(V170l_27,ty_2Elist_2Elist(A_27a)) & ? [V171e1] : ( mem(V171e1,A_27a) & ? [V172e2] : ( mem(V172e2,A_27a) & ? [V173e3] : ( mem(V173e3,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V171e1),ap(ap(c_2Elist_2ECONS(A_27a),V172e2),ap(ap(c_2Elist_2ECONS(A_27a),V173e3),V170l_27))) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V174l_27] : ( mem(V174l_27,ty_2Elist_2Elist(A_27a)) & ? [V175e1] : ( mem(V175e1,A_27a) & ? [V176e2] : ( mem(V176e2,A_27a) & ? [V177e3] : ( mem(V177e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V174l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V175e1),ap(ap(c_2Elist_2ECONS(A_27a),V176e2),ap(ap(c_2Elist_2ECONS(A_27a),V177e3),V174l_27))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x))) <=> ? [V178l_27] : ( mem(V178l_27,ty_2Elist_2Elist(A_27a)) & ? [V179e1] : ( mem(V179e1,A_27a) & ? [V180e2] : ( mem(V180e2,A_27a) & ? [V181e3] : ( mem(V181e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V178l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V179e1),ap(ap(c_2Elist_2ECONS(A_27a),V180e2),ap(ap(c_2Elist_2ECONS(A_27a),V181e3),V178l_27))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V182l_27] : ( mem(V182l_27,ty_2Elist_2Elist(A_27a)) & ? [V183e1] : ( mem(V183e1,A_27a) & ? [V184e2] : ( mem(V184e2,A_27a) & ? [V185e3] : ( mem(V185e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V182l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V183e1),ap(ap(c_2Elist_2ECONS(A_27a),V184e2),ap(ap(c_2Elist_2ECONS(A_27a),V185e3),V182l_27))) ) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) <=> ? [V186l_27] : ( mem(V186l_27,ty_2Elist_2Elist(A_27a)) & ? [V187e1] : ( mem(V187e1,A_27a) & ? [V188e2] : ( mem(V188e2,A_27a) & ? [V189e3] : ( mem(V189e3,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V186l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V187e1),ap(ap(c_2Elist_2ECONS(A_27a),V188e2),ap(ap(c_2Elist_2ECONS(A_27a),V189e3),V186l_27))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) ) <=> ? [V190l_27] : ( mem(V190l_27,ty_2Elist_2Elist(A_27a)) & ? [V191e1] : ( mem(V191e1,A_27a) & ? [V192e2] : ( mem(V192e2,A_27a) & ? [V193e3] : ( mem(V193e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V190l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V191e1),ap(ap(c_2Elist_2ECONS(A_27a),V192e2),ap(ap(c_2Elist_2ECONS(A_27a),V193e3),V190l_27))) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V194l_27] : ( mem(V194l_27,ty_2Elist_2Elist(A_27a)) & ? [V195e1] : ( mem(V195e1,A_27a) & ? [V196e2] : ( mem(V196e2,A_27a) & ? [V197e3] : ( mem(V197e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V194l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V195e1),ap(ap(c_2Elist_2ECONS(A_27a),V196e2),ap(ap(c_2Elist_2ECONS(A_27a),V197e3),V194l_27))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) <=> ? [V198l_27] : ( mem(V198l_27,ty_2Elist_2Elist(A_27a)) & ? [V199e1] : ( mem(V199e1,A_27a) & ? [V200e2] : ( mem(V200e2,A_27a) & ? [V201e3] : ( mem(V201e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V198l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V199e1),ap(ap(c_2Elist_2ECONS(A_27a),V200e2),ap(ap(c_2Elist_2ECONS(A_27a),V201e3),V198l_27))) ) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V202l_27] : ( mem(V202l_27,ty_2Elist_2Elist(A_27a)) & ? [V203e1] : ( mem(V203e1,A_27a) & ? [V204e2] : ( mem(V204e2,A_27a) & ? [V205e3] : ( mem(V205e3,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V202l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V203e1),ap(ap(c_2Elist_2ECONS(A_27a),V204e2),ap(ap(c_2Elist_2ECONS(A_27a),V205e3),V202l_27))) ) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) ) <=> ? [V206e1] : ( mem(V206e1,A_27a) & ? [V207e2] : ( mem(V207e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V206e1),ap(ap(c_2Elist_2ECONS(A_27a),V207e2),c_2Elist_2ENIL(A_27a))) ) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V208e1] : ( mem(V208e1,A_27a) & ? [V209e2] : ( mem(V209e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V208e1),ap(ap(c_2Elist_2ECONS(A_27a),V209e2),c_2Elist_2ENIL(A_27a))) ) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V210l_27] : ( mem(V210l_27,ty_2Elist_2Elist(A_27a)) & ? [V211e1] : ( mem(V211e1,A_27a) & ? [V212e2] : ( mem(V212e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V211e1),ap(ap(c_2Elist_2ECONS(A_27a),V212e2),V210l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ? [V213l_27] : ( mem(V213l_27,ty_2Elist_2Elist(A_27a)) & ? [V214e1] : ( mem(V214e1,A_27a) & ? [V215e2] : ( mem(V215e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V214e1),ap(ap(c_2Elist_2ECONS(A_27a),V215e2),V213l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V216l_27] : ( mem(V216l_27,ty_2Elist_2Elist(A_27a)) & ? [V217e1] : ( mem(V217e1,A_27a) & ? [V218e2] : ( mem(V218e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V217e1),ap(ap(c_2Elist_2ECONS(A_27a),V218e2),V216l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) <=> ? [V219l_27] : ( mem(V219l_27,ty_2Elist_2Elist(A_27a)) & ? [V220e1] : ( mem(V220e1,A_27a) & ? [V221e2] : ( mem(V221e2,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V220e1),ap(ap(c_2Elist_2ECONS(A_27a),V221e2),V219l_27)) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V222l_27] : ( mem(V222l_27,ty_2Elist_2Elist(A_27a)) & ? [V223e1] : ( mem(V223e1,A_27a) & ? [V224e2] : ( mem(V224e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V222l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V223e1),ap(ap(c_2Elist_2ECONS(A_27a),V224e2),V222l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x))) <=> ? [V225l_27] : ( mem(V225l_27,ty_2Elist_2Elist(A_27a)) & ? [V226e1] : ( mem(V226e1,A_27a) & ? [V227e2] : ( mem(V227e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V225l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V226e1),ap(ap(c_2Elist_2ECONS(A_27a),V227e2),V225l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V228l_27] : ( mem(V228l_27,ty_2Elist_2Elist(A_27a)) & ? [V229e1] : ( mem(V229e1,A_27a) & ? [V230e2] : ( mem(V230e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V228l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V229e1),ap(ap(c_2Elist_2ECONS(A_27a),V230e2),V228l_27)) ) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) <=> ? [V231l_27] : ( mem(V231l_27,ty_2Elist_2Elist(A_27a)) & ? [V232e1] : ( mem(V232e1,A_27a) & ? [V233e2] : ( mem(V233e2,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V231l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V232e1),ap(ap(c_2Elist_2ECONS(A_27a),V233e2),V231l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x) ) <=> ? [V234l_27] : ( mem(V234l_27,ty_2Elist_2Elist(A_27a)) & ? [V235e1] : ( mem(V235e1,A_27a) & ? [V236e2] : ( mem(V236e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V234l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V235e1),ap(ap(c_2Elist_2ECONS(A_27a),V236e2),V234l_27)) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V237l_27] : ( mem(V237l_27,ty_2Elist_2Elist(A_27a)) & ? [V238e1] : ( mem(V238e1,A_27a) & ? [V239e2] : ( mem(V239e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V237l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V238e1),ap(ap(c_2Elist_2ECONS(A_27a),V239e2),V237l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) <=> ? [V240l_27] : ( mem(V240l_27,ty_2Elist_2Elist(A_27a)) & ? [V241e1] : ( mem(V241e1,A_27a) & ? [V242e2] : ( mem(V242e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V240l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V241e1),ap(ap(c_2Elist_2ECONS(A_27a),V242e2),V240l_27)) ) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V243l_27] : ( mem(V243l_27,ty_2Elist_2Elist(A_27a)) & ? [V244e1] : ( mem(V244e1,A_27a) & ? [V245e2] : ( mem(V245e2,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V243l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V244e1),ap(ap(c_2Elist_2ECONS(A_27a),V245e2),V243l_27)) ) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) <=> ? [V246e1] : ( mem(V246e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V246e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V247e1] : ( mem(V247e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V247e1),c_2Elist_2ENIL(A_27a)) ) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V248l_27] : ( mem(V248l_27,ty_2Elist_2Elist(A_27a)) & ? [V249e1] : ( mem(V249e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V249e1),V248l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ? [V250l_27] : ( mem(V250l_27,ty_2Elist_2Elist(A_27a)) & ? [V251e1] : ( mem(V251e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V251e1),V250l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V252l_27] : ( mem(V252l_27,ty_2Elist_2Elist(A_27a)) & ? [V253e1] : ( mem(V253e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V253e1),V252l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ? [V254l_27] : ( mem(V254l_27,ty_2Elist_2Elist(A_27a)) & ? [V255e1] : ( mem(V255e1,A_27a) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V255e1),V254l_27) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x)),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V256l_27] : ( mem(V256l_27,ty_2Elist_2Elist(A_27a)) & ? [V257e1] : ( mem(V257e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V256l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V257e1),V256l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x))) <=> ? [V258l_27] : ( mem(V258l_27,ty_2Elist_2Elist(A_27a)) & ? [V259e1] : ( mem(V259e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V258l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V259e1),V258l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ? [V260l_27] : ( mem(V260l_27,ty_2Elist_2Elist(A_27a)) & ? [V261e1] : ( mem(V261e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V260l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V261e1),V260l_27) ) ) ) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <=> ? [V262l_27] : ( mem(V262l_27,ty_2Elist_2Elist(A_27a)) & ? [V263e1] : ( mem(V263e1,A_27a) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Elist_2ELENGTH(A_27a),V262l_27))) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V263e1),V262l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) ) <=> ? [V264l_27] : ( mem(V264l_27,ty_2Elist_2Elist(A_27a)) & ? [V265e1] : ( mem(V265e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V264l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V265e1),V264l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V266l_27] : ( mem(V266l_27,ty_2Elist_2Elist(A_27a)) & ? [V267e1] : ( mem(V267e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V266l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V267e1),V266l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) <=> ? [V268l_27] : ( mem(V268l_27,ty_2Elist_2Elist(A_27a)) & ? [V269e1] : ( mem(V269e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V268l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V269e1),V268l_27) ) ) ) ) ) & ( ( ( ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ? [V270l_27] : ( mem(V270l_27,ty_2Elist_2Elist(A_27a)) & ? [V271e1] : ( mem(V271e1,A_27a) & ( ( ap(c_2Elist_2ELENGTH(A_27a),V270l_27) = V1x ) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V271e1),V270l_27) ) ) ) ) ) & ( ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0 ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( ( c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),c_2Enum_2E0)) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )))).
