include('Axioms/sum+2.ax').
fof(mem_c_2Erelation_2ECR,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2ECR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2EEMPTY__REL,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EEMPTY__REL(A_27a),arr(A_27a,arr(A_27a,bool))) ) )).
fof(mem_c_2Erelation_2EEQC,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EEQC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))) ) )).
fof(mem_c_2Erelation_2EIDEM,axiom,( ! [A_27z] : ( ne(A_27z) => mem(c_2Erelation_2EIDEM(A_27z),arr(arr(A_27z,A_27z),bool)) ) )).
fof(mem_c_2Erelation_2EINDUCTIVE__INVARIANT,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),bool)))) ) ) )).
fof(mem_c_2Erelation_2EINDUCTIVE__INVARIANT__ON,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),bool))))) ) ) )).
fof(mem_c_2Erelation_2EINVOL,axiom,( ! [A_27z] : ( ne(A_27z) => mem(c_2Erelation_2EINVOL(A_27z),arr(arr(A_27z,A_27z),bool)) ) )).
fof(mem_c_2Erelation_2ELinearOrder,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2ELinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2EO,axiom,( ! [A_27g] : ( ne(A_27g) => ! [A_27h] : ( ne(A_27h) => ! [A_27k] : ( ne(A_27k) => mem(c_2Erelation_2EO(A_27g,A_27h,A_27k),arr(arr(A_27h,arr(A_27k,bool)),arr(arr(A_27g,arr(A_27h,bool)),arr(A_27g,arr(A_27k,bool))))) ) ) ) )).
fof(mem_c_2Erelation_2EOrder,axiom,( ! [A_27g] : ( ne(A_27g) => mem(c_2Erelation_2EOrder(A_27g),arr(arr(A_27g,arr(A_27g,bool)),bool)) ) )).
fof(mem_c_2Erelation_2EPreOrder,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EPreOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2ERC,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2ERC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))) ) )).
fof(mem_c_2Erelation_2ERCOMPL,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERCOMPL(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27b,bool)))) ) ) )).
fof(mem_c_2Erelation_2ERDOM,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERDOM(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,bool))) ) ) )).
fof(mem_c_2Erelation_2ERDOM__DELETE,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERDOM__DELETE(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27a,arr(A_27b,bool))))) ) ) )).
fof(mem_c_2Erelation_2ERESTRICT,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERESTRICT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,A_27b))))) ) ) )).
fof(mem_c_2Erelation_2ERINTER,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERINTER(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27b,bool))))) ) ) )).
fof(mem_c_2Erelation_2ERRANGE,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERRANGE(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27b,bool))) ) ) )).
fof(mem_c_2Erelation_2ERRESTRICT,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERRESTRICT(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,bool),arr(A_27a,arr(A_27b,bool))))) ) ) )).
fof(mem_c_2Erelation_2ERSUBSET,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERSUBSET(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,arr(A_27b,bool)),bool))) ) ) )).
fof(mem_c_2Erelation_2ERTC,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2ERTC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))) ) )).
fof(mem_c_2Erelation_2ERUNION,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERUNION(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27b,bool))))) ) ) )).
fof(mem_c_2Erelation_2ERUNIV,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERUNIV(A_27a,A_27b),arr(A_27a,arr(A_27b,bool))) ) ) )).
fof(mem_c_2Erelation_2ESC,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2ESC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))) ) )).
fof(mem_c_2Erelation_2ESN,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2ESN(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2ESTRORD,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2ESTRORD(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))) ) )).
fof(mem_c_2Erelation_2EStrongLinearOrder,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EStrongLinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2EStrongOrder,axiom,( ! [A_27g] : ( ne(A_27g) => mem(c_2Erelation_2EStrongOrder(A_27g),arr(arr(A_27g,arr(A_27g,bool)),bool)) ) )).
fof(mem_c_2Erelation_2ETC,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2ETC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))) ) )).
fof(mem_c_2Erelation_2EWCR,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EWCR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2EWF,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EWF(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2EWFP,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EWFP(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,bool))) ) )).
fof(mem_c_2Erelation_2EWFREC,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2EWFREC(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,A_27b)))) ) ) )).
fof(mem_c_2Erelation_2EWeakLinearOrder,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EWeakLinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2EWeakOrder,axiom,( ! [A_27g] : ( ne(A_27g) => mem(c_2Erelation_2EWeakOrder(A_27g),arr(arr(A_27g,arr(A_27g,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Eantisymmetric,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Eantisymmetric(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Eapprox,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2Eapprox(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,arr(arr(A_27a,A_27b),bool))))) ) ) )).
fof(mem_c_2Erelation_2Ediag,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Ediag(A_27a),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) ) )).
fof(mem_c_2Erelation_2Ediamond,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Ediamond(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Eequivalence,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Eequivalence(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Einv,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2Einv(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27b,arr(A_27a,bool)))) ) ) )).
fof(mem_c_2Erelation_2Einv__image,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2Einv__image(A_27a,A_27b),arr(arr(A_27b,arr(A_27b,bool)),arr(arr(A_27a,A_27b),arr(A_27a,arr(A_27a,bool))))) ) ) )).
fof(mem_c_2Erelation_2Eirreflexive,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Eirreflexive(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Enf,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2Enf(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,bool))) ) ) )).
fof(mem_c_2Erelation_2Ercdiamond,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Ercdiamond(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Ereflexive,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Ereflexive(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Esymmetric,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Esymmetric(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Ethe__fun,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2Ethe__fun(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,arr(A_27a,A_27b))))) ) ) )).
fof(mem_c_2Erelation_2Etotal,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Etotal(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Etransitive,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Etransitive(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2Etrichotomous,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2Etrichotomous(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(ax_thm_2Erelation_2Etransitive__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) <=> ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ! [V3z] : ( mem(V3z,A_27a) => ( ( p(ap(ap(V0R,V1x),V2y)) & p(ap(ap(V0R,V2y),V3z)) ) => p(ap(ap(V0R,V1x),V3z)) ) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2Ereflexive__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) <=> ! [V1x] : ( mem(V1x,A_27a) => p(ap(ap(V0R,V1x),V1x)) ) ) ) ) )).
fof(ax_thm_2Erelation_2Eirreflexive__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R)) <=> ! [V1x] : ( mem(V1x,A_27a) => ( ~~ p(ap(ap(V0R,V1x),V1x)) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2Esymmetric__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) <=> ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V1x),V2y)) <=> p(ap(ap(V0R,V2y),V1x)) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2Eantisymmetric__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) <=> ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( ( p(ap(ap(V0R,V1x),V2y)) & p(ap(ap(V0R,V2y),V1x)) ) => ( V1x = V2y ) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2Eequivalence__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Eequivalence(A_27a),V0R)) <=> ( p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) & ( p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2Etotal__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Etotal(A_27a),V0R)) <=> ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V1x),V2y)) | p(ap(ap(V0R,V2y),V1x)) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2Etrichotomous,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) <=> ! [V1a] : ( mem(V1a,A_27a) => ! [V2b] : ( mem(V2b,A_27a) => ( p(ap(ap(V0R,V1a),V2b)) | ( p(ap(ap(V0R,V2b),V1a)) | ( V1a = V2b ) ) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2ETC__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1a] : ( mem(V1a,A_27a) => ! [V2b] : ( mem(V2b,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1a),V2b)) <=> ! [V3P] : ( mem(V3P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(V0R,V4x),V5y)) => p(ap(ap(V3P,V4x),V5y)) ) ) ) ) & ! [V6x] : ( mem(V6x,A_27a) => ! [V7y] : ( mem(V7y,A_27a) => ! [V8z] : ( mem(V8z,A_27a) => ( ( p(ap(ap(V3P,V6x),V7y)) & p(ap(ap(V3P,V7y),V8z)) ) => p(ap(ap(V3P,V6x),V8z)) ) ) ) ) ) => p(ap(ap(V3P,V1a),V2b)) ) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2ERTC__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1a] : ( mem(V1a,A_27a) => ! [V2b] : ( mem(V2b,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1a),V2b)) <=> ! [V3P] : ( mem(V3P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V4x] : ( mem(V4x,A_27a) => p(ap(ap(V3P,V4x),V4x)) ) ) & ! [V5x] : ( mem(V5x,A_27a) => ! [V6y] : ( mem(V6y,A_27a) => ! [V7z] : ( mem(V7z,A_27a) => ( ( p(ap(ap(V0R,V5x),V6y)) & p(ap(ap(V3P,V6y),V7z)) ) => p(ap(ap(V3P,V5x),V7z)) ) ) ) ) ) => p(ap(ap(V3P,V1a),V2b)) ) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2ERC__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y)) <=> ( ( V1x = V2y ) | p(ap(ap(V0R,V1x),V2y)) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2ESC__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V1x),V2y)) <=> ( p(ap(ap(V0R,V1x),V2y)) | p(ap(ap(V0R,V2y),V1x)) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2EEQC__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2EEQC(A_27a),V0R) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R))) ) ) ) )).
fof(conj_thm_2Erelation_2ESC__SYMMETRIC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2ETC__TRANSITIVE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2ERTC__INDUCT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => p(ap(ap(V1P,V2x),V2x)) ) ) & ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ! [V5z] : ( mem(V5z,A_27a) => ( ( p(ap(ap(V0R,V3x),V4y)) & p(ap(ap(V1P,V4y),V5z)) ) => p(ap(ap(V1P,V3x),V5z)) ) ) ) ) ) => ! [V6x] : ( mem(V6x,A_27a) => ! [V7y] : ( mem(V7y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) => p(ap(ap(V1P,V6x),V7y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__RULES,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) ) ) ) ) & ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ! [V5z] : ( mem(V5z,A_27a) => ( ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3x),V4y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4y),V5z)) ) => p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3x),V5z)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__RULES,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ! [V1x] : ( mem(V1x,A_27a) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)) ) ) & ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ! [V4z] : ( mem(V4z,A_27a) => ( ( p(ap(ap(V0R,V2x),V3y)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3y),V4z)) ) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V4z)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)) ) )))).
fof(conj_thm_2Erelation_2ERTC__SINGLE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__STRONG__INDUCT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => p(ap(ap(V1P,V2x),V2x)) ) ) & ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ! [V5z] : ( mem(V5z,A_27a) => ( ( p(ap(ap(V0R,V3x),V4y)) & ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V4y),V5z)) & p(ap(ap(V1P,V4y),V5z)) ) ) => p(ap(ap(V1P,V3x),V5z)) ) ) ) ) ) => ! [V6x] : ( mem(V6x,A_27a) => ! [V7y] : ( mem(V7y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) => p(ap(ap(V1P,V6x),V7y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__RTC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) => ! [V3z] : ( mem(V3z,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V3z)) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3z)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__TRANSITIVE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2Etransitive__RTC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2ERTC__REFLEXIVE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2Ereflexive__RTC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2ERC__REFLEXIVE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2Ereflexive__RC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2ERC__lifts__monotonicities,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27a)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y))) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V4x),V5y)) => p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERC__MONOTONE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1Q] : ( mem(V1Q,arr(A_27a,arr(A_27a,bool))) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( ( ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(V0R,V4x),V5y)) => p(ap(ap(V1Q,V4x),V5y)) ) ) ) ) => ( p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V2x),V3y)) => p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V1Q),V2x),V3y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERC__lifts__invariants,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( ( p(ap(V0P,V2x)) & p(ap(ap(V1R,V2x),V3y)) ) => p(ap(V0P,V3y)) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( ( p(ap(V0P,V4x)) & p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V1R),V4x),V5y)) ) => p(ap(V0P,V5y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERC__lifts__equalities,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => ( ap(V1f,V2x) = ap(V1f,V3y) ) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V4x),V5y)) => ( ap(V1f,V4x) = ap(V1f,V5y) ) ) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2ESC__lifts__monotonicities,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27a)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y))) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V4x),V5y)) => p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ESC__lifts__equalities,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => ( ap(V1f,V2x) = ap(V1f,V3y) ) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V4x),V5y)) => ( ap(V1f,V4x) = ap(V1f,V5y) ) ) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2ESC__MONOTONE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1Q] : ( mem(V1Q,arr(A_27a,arr(A_27a,bool))) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( ( ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(V0R,V4x),V5y)) => p(ap(ap(V1Q,V4x),V5y)) ) ) ) ) => ( p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V2x),V3y)) => p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V1Q),V2x),V3y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2Esymmetric__RC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <=> p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2Eantisymmetric__RC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <=> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2Etransitive__RC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) => p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) ) )))).
fof(conj_thm_2Erelation_2ETC__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) ) ) ) )))).
fof(conj_thm_2Erelation_2ERC__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y)) ) ) ) )))).
fof(conj_thm_2Erelation_2ERC__RTC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__INDUCT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V1P,V2x),V3y)) ) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ! [V6z] : ( mem(V6z,A_27a) => ( ( p(ap(ap(V1P,V4x),V5y)) & p(ap(ap(V1P,V5y),V6z)) ) => p(ap(ap(V1P,V4x),V6z)) ) ) ) ) ) => ! [V7u] : ( mem(V7u,A_27a) => ! [V8v] : ( mem(V8v,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) => p(ap(ap(V1P,V7u),V8v)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__INDUCT__LEFT1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V1P,V2x),V3y)) ) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ! [V6z] : ( mem(V6z,A_27a) => ( ( p(ap(ap(V0R,V4x),V5y)) & p(ap(ap(V1P,V5y),V6z)) ) => p(ap(ap(V1P,V4x),V6z)) ) ) ) ) ) => ! [V7x] : ( mem(V7x,A_27a) => ! [V8y] : ( mem(V8y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7x),V8y)) => p(ap(ap(V1P,V7x),V8y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__INDUCT__RIGHT1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V1P,V2x),V3y)) ) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ! [V6z] : ( mem(V6z,A_27a) => ( ( p(ap(ap(V1P,V4x),V5y)) & p(ap(ap(V0R,V5y),V6z)) ) => p(ap(ap(V1P,V4x),V6z)) ) ) ) ) ) => ! [V7x] : ( mem(V7x,A_27a) => ! [V8y] : ( mem(V8y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7x),V8y)) => p(ap(ap(V1P,V7x),V8y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__STRONG__INDUCT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V1P,V2x),V3y)) ) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ! [V6z] : ( mem(V6z,A_27a) => ( ( p(ap(ap(V1P,V4x),V5y)) & ( p(ap(ap(V1P,V5y),V6z)) & ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V5y),V6z)) ) ) ) => p(ap(ap(V1P,V4x),V6z)) ) ) ) ) ) => ! [V7u] : ( mem(V7u,A_27a) => ! [V8v] : ( mem(V8v,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) => p(ap(ap(V1P,V7u),V8v)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__STRONG__INDUCT__LEFT1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V1P,V2x),V3y)) ) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ! [V6z] : ( mem(V6z,A_27a) => ( ( p(ap(ap(V0R,V4x),V5y)) & ( p(ap(ap(V1P,V5y),V6z)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V5y),V6z)) ) ) => p(ap(ap(V1P,V4x),V6z)) ) ) ) ) ) => ! [V7u] : ( mem(V7u,A_27a) => ! [V8v] : ( mem(V8v,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) => p(ap(ap(V1P,V7u),V8v)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__STRONG__INDUCT__RIGHT1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V1P,V2x),V3y)) ) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ! [V6z] : ( mem(V6z,A_27a) => ( ( p(ap(ap(V1P,V4x),V5y)) & ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) & p(ap(ap(V0R,V5y),V6z)) ) ) => p(ap(ap(V1P,V4x),V6z)) ) ) ) ) ) => ! [V7u] : ( mem(V7u,A_27a) => ! [V8v] : ( mem(V8v,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) => p(ap(ap(V1P,V7u),V8v)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__INDUCT__ALT__LEFT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0b] : ( mem(V0b,A_27a) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ! [V2Q] : ( mem(V2Q,arr(A_27a,bool)) => ( ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(V1R,V3x),V0b)) => p(ap(V2Q,V3x)) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( ( p(ap(ap(V1R,V4x),V5y)) & p(ap(V2Q,V5y)) ) => p(ap(V2Q,V4x)) ) ) ) ) => ! [V6a] : ( mem(V6a,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V6a),V0b)) => p(ap(V2Q,V6a)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__INDUCT__ALT__RIGHT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,A_27a) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ! [V2Q] : ( mem(V2Q,arr(A_27a,bool)) => ( ( ( ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V1R,V0a),V3y)) => p(ap(V2Q,V3y)) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( ( p(ap(V2Q,V4x)) & p(ap(ap(V1R,V4x),V5y)) ) => p(ap(V2Q,V5y)) ) ) ) ) => ! [V6b] : ( mem(V6b,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V0a),V6b)) => p(ap(V2Q,V6b)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__lifts__monotonicities,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27a)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y))) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) => p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__lifts__invariants,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( ( p(ap(V0P,V2x)) & p(ap(ap(V1R,V2x),V3y)) ) => p(ap(V0P,V3y)) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( ( p(ap(V0P,V4x)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V4x),V5y)) ) => p(ap(V0P,V5y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__lifts__equalities,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => ( ap(V1f,V2x) = ap(V1f,V3y) ) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) => ( ap(V1f,V4x) = ap(V1f,V5y) ) ) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2ETC__lifts__transitive__relations,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1Q] : ( mem(V1Q,arr(A_27b,arr(A_27b,bool))) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ( ( ( ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ( p(ap(ap(V0R,V3x),V4y)) => p(ap(ap(V1Q,ap(V2f,V3x)),ap(V2f,V4y))) ) ) ) ) & p(ap(c_2Erelation_2Etransitive(A_27b),V1Q)) ) => ! [V5x] : ( mem(V5x,A_27a) => ! [V6y] : ( mem(V6y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V5x),V6y)) => p(ap(ap(V1Q,ap(V2f,V5x)),ap(V2f,V6y))) ) ) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2ETC__implies__one__step,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) & ( ~~ ( V1x = V2y ) ) ) => ? [V3z] : ( mem(V3z,A_27a) & ( p(ap(ap(V0R,V1x),V3z)) & ( ~~ ( V1x = V3z ) ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__RTC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__TC__RC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) => ( p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y)) | p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__RC__EQNS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ERTC(A_27a),V0R) ) & ( ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERTC(A_27a),V0R) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__ALT__DEF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1a] : ( mem(V1a,A_27a) => ! [V2b] : ( mem(V2b,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1a),V2b)) <=> ! [V3Q] : ( mem(V3Q,arr(A_27a,bool)) => ( ( p(ap(V3Q,V2b)) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( ( p(ap(ap(V0R,V4x),V5y)) & p(ap(V3Q,V5y)) ) => p(ap(V3Q,V4x)) ) ) ) ) => p(ap(V3Q,V1a)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__ALT__INDUCT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ! [V2b] : ( mem(V2b,A_27a) => ( ( p(ap(V1Q,V2b)) & ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ( ( p(ap(ap(V0R,V3x),V4y)) & p(ap(V1Q,V4y)) ) => p(ap(V1Q,V3x)) ) ) ) ) => ! [V5x] : ( mem(V5x,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V5x),V2b)) => p(ap(V1Q,V5x)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__ALT__RIGHT__DEF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1a] : ( mem(V1a,A_27a) => ! [V2b] : ( mem(V2b,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1a),V2b)) <=> ! [V3Q] : ( mem(V3Q,arr(A_27a,bool)) => ( ( p(ap(V3Q,V1a)) & ! [V4y] : ( mem(V4y,A_27a) => ! [V5z] : ( mem(V5z,A_27a) => ( ( p(ap(V3Q,V4y)) & p(ap(ap(V0R,V4y),V5z)) ) => p(ap(V3Q,V5z)) ) ) ) ) => p(ap(V3Q,V2b)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__ALT__RIGHT__INDUCT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ! [V2a] : ( mem(V2a,A_27a) => ( ( p(ap(V1Q,V2a)) & ! [V3y] : ( mem(V3y,A_27a) => ! [V4z] : ( mem(V4z,A_27a) => ( ( p(ap(V1Q,V3y)) & p(ap(ap(V0R,V3y),V4z)) ) => p(ap(V1Q,V4z)) ) ) ) ) => ! [V5z] : ( mem(V5z,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2a),V5z)) => p(ap(V1Q,V5z)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__INDUCT__RIGHT1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => p(ap(ap(V1P,V2x),V2x)) ) ) & ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ! [V5z] : ( mem(V5z,A_27a) => ( ( p(ap(ap(V1P,V3x),V4y)) & p(ap(ap(V0R,V4y),V5z)) ) => p(ap(ap(V1P,V3x),V5z)) ) ) ) ) ) => ! [V6x] : ( mem(V6x,A_27a) => ! [V7y] : ( mem(V7y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) => p(ap(ap(V1P,V6x),V7y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__RULES__RIGHT1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ! [V1x] : ( mem(V1x,A_27a) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)) ) ) & ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ! [V4z] : ( mem(V4z,A_27a) => ( ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V3y)) & p(ap(ap(V0R,V3y),V4z)) ) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V4z)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__STRONG__INDUCT__RIGHT1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => p(ap(ap(V1P,V2x),V2x)) ) ) & ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ! [V5z] : ( mem(V5z,A_27a) => ( ( p(ap(ap(V1P,V3x),V4y)) & ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3x),V4y)) & p(ap(ap(V0R,V4y),V5z)) ) ) => p(ap(ap(V1P,V3x),V5z)) ) ) ) ) ) => ! [V6x] : ( mem(V6x,A_27a) => ! [V7y] : ( mem(V7y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) => p(ap(ap(V1P,V6x),V7y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EEXTEND__RTC__TC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ! [V3z] : ( mem(V3z,A_27a) => ( ( p(ap(ap(V0R,V1x),V2y)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V3z)) ) => p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V3z)) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EEXTEND__RTC__TC__EQN,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2z] : ( mem(V2z,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) <=> ? [V3y] : ( mem(V3y,A_27a) & ( p(ap(ap(V0R,V1x),V3y)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3y),V2z)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2Ereflexive__RC__identity,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) => ( ap(c_2Erelation_2ERC(A_27a),V0R) = V0R ) ) )))).
fof(conj_thm_2Erelation_2Esymmetric__SC__identity,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) => ( ap(c_2Erelation_2ESC(A_27a),V0R) = V0R ) ) )))).
fof(conj_thm_2Erelation_2Etransitive__TC__identity,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) => ( ap(c_2Erelation_2ETC(A_27a),V0R) = V0R ) ) )))).
fof(conj_thm_2Erelation_2ERC__IDEM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),V0R) ) )))).
fof(conj_thm_2Erelation_2ESC__IDEM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),V0R) ) )))).
fof(conj_thm_2Erelation_2ETC__IDEM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ETC(A_27a),V0R) ) )))).
fof(conj_thm_2Erelation_2ERC__MOVES__OUT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)) ) & ( ( ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),V0R) ) & ( ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) ) ) ) )))).
fof(conj_thm_2Erelation_2Esymmetric__TC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) => p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R))) ) )))).
fof(conj_thm_2Erelation_2Ereflexive__TC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) => p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R))) ) )))).
fof(conj_thm_2Erelation_2EEQC__EQUIVALENCE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Eequivalence(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2EEQC__IDEM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) ) )))).
fof(conj_thm_2Erelation_2ERTC__IDEM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2ERTC(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R)) = ap(c_2Erelation_2ERTC(A_27a),V0R) ) )))).
fof(conj_thm_2Erelation_2ERTC__CASES1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <=> ( ( V1x = V2y ) | ? [V3u] : ( mem(V3u,A_27a) & ( p(ap(ap(V0R,V1x),V3u)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3u),V2y)) ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__CASES__TC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <=> ( ( V1x = V2y ) | p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__CASES2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <=> ( ( V1x = V2y ) | ? [V3u] : ( mem(V3u,A_27a) & ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3u)) & p(ap(ap(V0R,V3u),V2y)) ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__CASES__RTC__TWICE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <=> ? [V3u] : ( mem(V3u,A_27a) & ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3u)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3u),V2y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__CASES1__E,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2z] : ( mem(V2z,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) => ( p(ap(ap(V0R,V1x),V2z)) | ? [V3y] : ( mem(V3y,A_27a) & ( p(ap(ap(V0R,V1x),V3y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3y),V2z)) ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__CASES1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2z] : ( mem(V2z,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) <=> ( p(ap(ap(V0R,V1x),V2z)) | ? [V3y] : ( mem(V3y,A_27a) & ( p(ap(ap(V0R,V1x),V3y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3y),V2z)) ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__CASES2__E,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2z] : ( mem(V2z,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) => ( p(ap(ap(V0R,V1x),V2z)) | ? [V3y] : ( mem(V3y,A_27a) & ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V3y)) & p(ap(ap(V0R,V3y),V2z)) ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__CASES2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2z] : ( mem(V2z,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) <=> ( p(ap(ap(V0R,V1x),V2z)) | ? [V3y] : ( mem(V3y,A_27a) & ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V3y)) & p(ap(ap(V0R,V3y),V2z)) ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ETC__MONOTONE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1Q] : ( mem(V1Q,arr(A_27a,arr(A_27a,bool))) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( ( ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(V0R,V4x),V5y)) => p(ap(ap(V1Q,V4x),V5y)) ) ) ) ) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V2x),V3y)) => p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1Q),V2x),V3y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__MONOTONE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1Q] : ( mem(V1Q,arr(A_27a,arr(A_27a,bool))) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( ( ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(V0R,V4x),V5y)) => p(ap(ap(V1Q,V4x),V5y)) ) ) ) ) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V3y)) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V1Q),V2x),V3y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EEQC__INDUCTION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V1P,V2x),V3y)) ) ) ) ) & ( ( ! [V4x] : ( mem(V4x,A_27a) => p(ap(ap(V1P,V4x),V4x)) ) ) & ( ( ! [V5x] : ( mem(V5x,A_27a) => ! [V6y] : ( mem(V6y,A_27a) => ( p(ap(ap(V1P,V5x),V6y)) => p(ap(ap(V1P,V6y),V5x)) ) ) ) ) & ! [V7x] : ( mem(V7x,A_27a) => ! [V8y] : ( mem(V8y,A_27a) => ! [V9z] : ( mem(V9z,A_27a) => ( ( p(ap(ap(V1P,V7x),V8y)) & p(ap(ap(V1P,V8y),V9z)) ) => p(ap(ap(V1P,V7x),V9z)) ) ) ) ) ) ) ) => ! [V10x] : ( mem(V10x,A_27a) => ! [V11y] : ( mem(V11y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V10x),V11y)) => p(ap(ap(V1P,V10x),V11y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EEQC__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V1x)) ) )))).
fof(conj_thm_2Erelation_2EEQC__R,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y)) ) ) ) )))).
fof(conj_thm_2Erelation_2EEQC__SYM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V2y),V1x)) ) ) ) )))).
fof(conj_thm_2Erelation_2EEQC__TRANS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ! [V3z] : ( mem(V3z,A_27a) => ( ( p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y)) & p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V2y),V3z)) ) => p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V3z)) ) ) ) ) )))).
fof(conj_thm_2Erelation_2Etransitive__EQC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2Esymmetric__EQC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2Ereflexive__EQC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))) )))).
fof(conj_thm_2Erelation_2EEQC__MOVES__IN,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) ) & ( ( ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) ) & ( ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) ) ) ) )))).
fof(conj_thm_2Erelation_2ESTRONG__EQC__INDUCTION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V1P,V2x),V3y)) ) ) ) ) & ( ( ! [V4x] : ( mem(V4x,A_27a) => p(ap(ap(V1P,V4x),V4x)) ) ) & ( ( ! [V5x] : ( mem(V5x,A_27a) => ! [V6y] : ( mem(V6y,A_27a) => ( ( p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V5x),V6y)) & p(ap(ap(V1P,V5x),V6y)) ) => p(ap(ap(V1P,V6y),V5x)) ) ) ) ) & ! [V7x] : ( mem(V7x,A_27a) => ! [V8y] : ( mem(V8y,A_27a) => ! [V9z] : ( mem(V9z,A_27a) => ( ( p(ap(ap(V1P,V7x),V8y)) & ( p(ap(ap(V1P,V8y),V9z)) & ( p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V7x),V8y)) & p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V8y),V9z)) ) ) ) => p(ap(ap(V1P,V7x),V9z)) ) ) ) ) ) ) ) => ! [V10x] : ( mem(V10x,A_27a) => ! [V11y] : ( mem(V11y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V10x),V11y)) => p(ap(ap(V1P,V10x),V11y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EALT__equivalence,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Eequivalence(A_27a),V0R)) <=> ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V1x),V2y)) <=> ( ap(V0R,V1x) = ap(V0R,V2y) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EEQC__MONOTONE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1R_27] : ( mem(V1R_27,arr(A_27a,arr(A_27a,bool))) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( ( ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(V0R,V4x),V5y)) => p(ap(ap(V1R_27,V4x),V5y)) ) ) ) ) => ( p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V2x),V3y)) => p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V1R_27),V2x),V3y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__EQC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) => p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y)) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__lifts__monotonicities,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27a)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y))) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V4x),V5y)) => p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERTC__lifts__reflexive__transitive__relations,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1Q] : ( mem(V1Q,arr(A_27b,arr(A_27b,bool))) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ( ( ( ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ( p(ap(ap(V0R,V3x),V4y)) => p(ap(ap(V1Q,ap(V2f,V3x)),ap(V2f,V4y))) ) ) ) ) & ( p(ap(c_2Erelation_2Ereflexive(A_27b),V1Q)) & p(ap(c_2Erelation_2Etransitive(A_27b),V1Q)) ) ) => ! [V5x] : ( mem(V5x,A_27a) => ! [V6y] : ( mem(V6y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V5x),V6y)) => p(ap(ap(V1Q,ap(V2f,V5x)),ap(V2f,V6y))) ) ) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2ERTC__lifts__equalities,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V2x),V3y)) => ( ap(V1f,V2x) = ap(V1f,V3y) ) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V4x),V5y)) => ( ap(V1f,V4x) = ap(V1f,V5y) ) ) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2ERTC__lifts__invariants,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( ( p(ap(V0P,V2x)) & p(ap(ap(V1R,V2x),V3y)) ) => p(ap(V0P,V3y)) ) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( ( p(ap(V0P,V4x)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V1R),V4x),V5y)) ) => p(ap(V0P,V5y)) ) ) ) ) ) )))).
fof(ax_thm_2Erelation_2EWF__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) <=> ! [V1B] : ( mem(V1B,arr(A_27a,bool)) => ( ( ? [V2w] : ( mem(V2w,A_27a) & p(ap(V1B,V2w)) ) ) => ? [V3min] : ( mem(V3min,A_27a) & ( p(ap(V1B,V3min)) & ! [V4b] : ( mem(V4b,A_27a) => ( p(ap(ap(V0R,V4b),V3min)) => ( ~~ p(ap(V1B,V4b)) ) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2EWF__INDUCTION__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( ( ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V3y),V2x)) => p(ap(V1P,V3y)) ) ) ) => p(ap(V1P,V2x)) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => p(ap(V1P,V4x)) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EINDUCTION__WF__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( ( ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V3y),V2x)) => p(ap(V1P,V3y)) ) ) ) => p(ap(V1P,V2x)) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => p(ap(V1P,V4x)) ) ) ) ) => p(ap(c_2Erelation_2EWF(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2EWF__EQ__INDUCTION__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) <=> ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( ( ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V3y),V2x)) => p(ap(V1P,V3y)) ) ) ) => p(ap(V1P,V2x)) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => p(ap(V1P,V4x)) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EWF__NOT__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) => ( p(ap(ap(V0R,V1x),V2y)) => ( ~~ ( V1x = V2y ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EWF__irreflexive,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) => p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R)) ) )))).
fof(ax_thm_2Erelation_2EEMPTY__REL__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ( p(ap(ap(c_2Erelation_2EEMPTY__REL(A_27a),V0x),V1y)) <=> $false ) ) ) ) )).
fof(conj_thm_2Erelation_2EWF__EMPTY__REL,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(c_2Erelation_2EWF(A_27a),c_2Erelation_2EEMPTY__REL(A_27a)))))).
fof(conj_thm_2Erelation_2EWF__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) & ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V1P,V2x),V3y)) => p(ap(ap(V0R,V2x),V3y)) ) ) ) ) => p(ap(c_2Erelation_2EWF(A_27a),V1P)) ) ) )))).
fof(conj_thm_2Erelation_2EWF__TC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) => p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R))) ) )))).
fof(conj_thm_2Erelation_2EWF__TC__EQN,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R))) <=> p(ap(c_2Erelation_2EWF(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2EWF__noloops,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) => ( p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) => ( ~~ ( V1x = V2y ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EWF__antisymmetric,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) => p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) ) )))).
fof(ax_thm_2Erelation_2Einv__image__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27b,arr(A_27b,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ( ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f) = f98(A_27b,A_27a,V0R,V1f) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2Einv__image__thm,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27b,arr(A_27b,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f),V2x),V3y)) <=> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y))) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2EWF__inv__image,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27b,arr(A_27b,bool))) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ( p(ap(c_2Erelation_2EWF(A_27b),V0R)) => p(ap(c_2Erelation_2EWF(A_27a),ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f))) ) ) ))))).
fof(conj_thm_2Erelation_2Etotal__inv__image,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27b,A_27a)) => ( p(ap(c_2Erelation_2Etotal(A_27a),V0R)) => p(ap(c_2Erelation_2Etotal(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f))) ) ) ))))).
fof(conj_thm_2Erelation_2Ereflexive__inv__image,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27b,A_27a)) => ( p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) => p(ap(c_2Erelation_2Ereflexive(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f))) ) ) ))))).
fof(conj_thm_2Erelation_2Esymmetric__inv__image,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27b,A_27a)) => ( p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) => p(ap(c_2Erelation_2Esymmetric(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f))) ) ) ))))).
fof(conj_thm_2Erelation_2Etransitive__inv__image,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(A_27b,A_27a)) => ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) => p(ap(c_2Erelation_2Etransitive(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f))) ) ) ))))).
fof(ax_thm_2Erelation_2ERESTRICT__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ! [V2x] : ( mem(V2x,A_27a) => ( ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V0f),V1R),V2x) = f99(A_27a,A_27b,V0f,V2x,V1R) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2ERESTRICT__LEMMA,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ! [V2y] : ( mem(V2y,A_27a) => ! [V3z] : ( mem(V3z,A_27a) => ( p(ap(ap(V1R,V2y),V3z)) => ( ap(ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V0f),V1R),V3z),V2y) = ap(V0f,V2y) ) ) ) ) ) ))))).
fof(ax_thm_2Erelation_2Eapprox__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1M] : ( mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3f] : ( mem(V3f,arr(A_27a,A_27b)) => ( p(ap(ap(ap(ap(c_2Erelation_2Eapprox(A_27a,A_27b),V0R),V1M),V2x),V3f)) <=> ( V3f = ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),f100(A_27b,A_27a,V1M,V0R,V3f)),V0R),V2x) ) ) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2Ethe__fun__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1M] : ( mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ! [V2x] : ( mem(V2x,A_27a) => ( ap(ap(ap(c_2Erelation_2Ethe__fun(A_27a,A_27b),V0R),V1M),V2x) = ap(c_2Emin_2E_40(arr(A_27a,A_27b)),f101(A_27a,A_27b,V2x,V0R,V1M)) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2EWFREC__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1M] : ( mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ( ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M) = f104(A_27b,A_27a,V1M,V0R) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2EWFREC__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1M] : ( mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) => ! [V2x] : ( mem(V2x,A_27a) => ( ap(ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M),V2x) = ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M)),V0R),V2x)),V2x) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2EWFREC__COROLLARY,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0M] : ( mem(V0M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ( ( V2f = ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V0M) ) => ( p(ap(c_2Erelation_2EWF(A_27a),V1R)) => ! [V3x] : ( mem(V3x,A_27a) => ( ap(V2f,V3x) = ap(ap(V0M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V2f),V1R),V3x)),V3x) ) ) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2EWF__RECURSION__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) => ! [V1M] : ( mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => p(ap(c_2Ebool_2E_3F_21(arr(A_27a,A_27b)),f106(A_27b,A_27a,V1M,V0R))) ) ) ))))).
fof(ax_thm_2Erelation_2EWFP__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1a] : ( mem(V1a,A_27a) => ( p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1a)) <=> ! [V2P] : ( mem(V2P,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ( ( ! [V4y] : ( mem(V4y,A_27a) => ( p(ap(ap(V0R,V4y),V3x)) => p(ap(V2P,V4y)) ) ) ) => p(ap(V2P,V3x)) ) ) ) => p(ap(V2P,V1a)) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2EWFP__RULES,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ( ( ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V2y),V1x)) => p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V2y)) ) ) ) => p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1x)) ) ) )))).
fof(conj_thm_2Erelation_2EWFP__INDUCT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( ( ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V0R,V3y),V2x)) => p(ap(V1P,V3y)) ) ) ) => p(ap(V1P,V2x)) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ( p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V4x)) => p(ap(V1P,V4x)) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EWFP__CASES,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ( p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1x)) <=> ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0R,V2y),V1x)) => p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V2y)) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EWFP__STRONG__INDUCT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( ( p(ap(ap(c_2Erelation_2EWFP(A_27a),V1R),V2x)) & ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(V1R,V3y),V2x)) => p(ap(V0P,V3y)) ) ) ) => p(ap(V0P,V2x)) ) ) ) => ! [V4x] : ( mem(V4x,A_27a) => ( p(ap(ap(c_2Erelation_2EWFP(A_27a),V1R),V4x)) => p(ap(V0P,V4x)) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EWF__EQ__WFP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) <=> ! [V1x] : ( mem(V1x,A_27a) => p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1x)) ) ) )))).
fof(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27b,bool))) => ! [V2M] : ( mem(V2M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ( p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V0R),V1P),V2M)) <=> ! [V3f] : ( mem(V3f,arr(A_27a,A_27b)) => ! [V4x] : ( mem(V4x,A_27a) => ( ( ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(V0R,V5y),V4x)) => p(ap(ap(V1P,V5y),ap(V3f,V5y))) ) ) ) => p(ap(ap(V1P,V4x),ap(ap(V2M,V3f),V4x))) ) ) ) ) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1D] : ( mem(V1D,arr(A_27a,bool)) => ! [V2P] : ( mem(V2P,arr(A_27a,arr(A_27b,bool))) => ! [V3M] : ( mem(V3M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ( p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V0R),V1D),V2P),V3M)) <=> ! [V4f] : ( mem(V4f,arr(A_27a,A_27b)) => ! [V5x] : ( mem(V5x,A_27a) => ( ( p(ap(V1D,V5x)) & ! [V6y] : ( mem(V6y,A_27a) => ( p(ap(V1D,V6y)) => ( p(ap(ap(V0R,V6y),V5x)) => p(ap(ap(V2P,V6y),ap(V4f,V6y))) ) ) ) ) => p(ap(ap(V2P,V5x),ap(ap(V3M,V4f),V5x))) ) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2EINDUCTIVE__INVARIANT__WFREC,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27b,bool))) => ! [V2M] : ( mem(V2M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ( ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) & p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V0R),V1P),V2M)) ) => ! [V3x] : ( mem(V3x,A_27a) => p(ap(ap(V1P,V3x),ap(ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V2M),V3x))) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__WFREC,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ! [V2P] : ( mem(V2P,arr(A_27a,arr(A_27b,bool))) => ! [V3M] : ( mem(V3M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ! [V4x] : ( mem(V4x,A_27a) => ( ( ( V0f = ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V3M) ) & ( p(ap(c_2Erelation_2EWF(A_27a),V1R)) & p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V1R),V2P),V3M)) ) ) => p(ap(ap(V2P,V4x),ap(V0f,V4x))) ) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__WFREC,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,arr(A_27b,bool))) => ! [V2M] : ( mem(V2M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ! [V3D] : ( mem(V3D,arr(A_27a,bool)) => ! [V4x] : ( mem(V4x,A_27a) => ( ( p(ap(c_2Erelation_2EWF(A_27a),V0R)) & ( p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V0R),V3D),V1P),V2M)) & p(ap(V3D,V4x)) ) ) => p(ap(ap(V1P,V4x),ap(ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V2M),V4x))) ) ) ) ) ) ))))).
fof(conj_thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__ON__WFREC,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ! [V2D] : ( mem(V2D,arr(A_27a,bool)) => ! [V3P] : ( mem(V3P,arr(A_27a,arr(A_27b,bool))) => ! [V4M] : ( mem(V4M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ! [V5x] : ( mem(V5x,A_27a) => ( ( ( V0f = ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V4M) ) & ( p(ap(c_2Erelation_2EWF(A_27a),V1R)) & ( p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V1R),V2D),V3P),V4M)) & p(ap(V2D,V5x)) ) ) ) => p(ap(ap(V3P,V5x),ap(V0f,V5x))) ) ) ) ) ) ) ))))).
fof(ax_thm_2Erelation_2Einv__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27b,bool))) => ! [V1x] : ( mem(V1x,A_27b) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Erelation_2Einv(A_27a,A_27b),V0R),V1x),V2y)) <=> p(ap(ap(V0R,V2y),V1x)) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2Einv__inv,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27b,bool))) => ( ap(c_2Erelation_2Einv(A_27b,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27b),V0R)) = V0R ) ))))).
fof(conj_thm_2Erelation_2Einv__RC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2Einv__SC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),V0R) ) & ( ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),V0R) ) ) )))).
fof(conj_thm_2Erelation_2Einv__TC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2Einv__EQC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) ) & ( ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) ) ) )))).
fof(conj_thm_2Erelation_2Einv__MOVES__OUT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = V0R ) & ( ( ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),V0R) ) & ( ( ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) ) & ( ( ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) ) & ( ( ap(c_2Erelation_2ERTC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R)) ) & ( ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) ) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2Ereflexive__inv,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <=> p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2Eirreflexive__inv,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <=> p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2Esymmetric__inv,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <=> p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2Eantisymmetric__inv,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <=> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2Etransitive__inv,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <=> p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2Esymmetric__inv__identity,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) => ( ap(c_2Erelation_2Einv(A_27a,A_27a),V0R) = V0R ) ) )))).
fof(conj_thm_2Erelation_2Eequivalence__inv__identity,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Eequivalence(A_27a),V0R)) => ( ap(c_2Erelation_2Einv(A_27a,A_27a),V0R) = V0R ) ) )))).
fof(ax_thm_2Erelation_2EINVOL__DEF,axiom,( ! [A_27z] : ( ne(A_27z) => ! [V0f] : ( mem(V0f,arr(A_27z,A_27z)) => ( p(ap(c_2Erelation_2EINVOL(A_27z),V0f)) <=> ( ap(ap(c_2Ecombin_2Eo(A_27z,A_27z,A_27z),V0f),V0f) = c_2Ecombin_2EI(A_27z) ) ) ) ) )).
fof(conj_thm_2Erelation_2EINVOL,lemma,( ! [A_27z]: ( ne(A_27z) => ! [V0f] : ( mem(V0f,arr(A_27z,A_27z)) => ( p(ap(c_2Erelation_2EINVOL(A_27z),V0f)) <=> ! [V1x] : ( mem(V1x,A_27z) => ( ap(V0f,ap(V0f,V1x)) = V1x ) ) ) )))).
fof(conj_thm_2Erelation_2EINVOL__ONE__ONE,lemma,( ! [A_27z]: ( ne(A_27z) => ! [V0f] : ( mem(V0f,arr(A_27z,A_27z)) => ( p(ap(c_2Erelation_2EINVOL(A_27z),V0f)) => ! [V1a] : ( mem(V1a,A_27z) => ! [V2b] : ( mem(V2b,A_27z) => ( ( ap(V0f,V1a) = ap(V0f,V2b) ) <=> ( V1a = V2b ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2EINVOL__ONE__ENO,lemma,( ! [A_27z]: ( ne(A_27z) => ! [V0f] : ( mem(V0f,arr(A_27z,A_27z)) => ( p(ap(c_2Erelation_2EINVOL(A_27z),V0f)) => ! [V1a] : ( mem(V1a,A_27z) => ! [V2b] : ( mem(V2b,A_27z) => ( ( ap(V0f,V1a) = V2b ) <=> ( V1a = ap(V0f,V2b) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ENOT__INVOL,lemma,(p(ap(c_2Erelation_2EINVOL(bool),c_2Ebool_2E_7E)))).
fof(ax_thm_2Erelation_2EIDEM__DEF,axiom,( ! [A_27z] : ( ne(A_27z) => ! [V0f] : ( mem(V0f,arr(A_27z,A_27z)) => ( p(ap(c_2Erelation_2EIDEM(A_27z),V0f)) <=> ( ap(ap(c_2Ecombin_2Eo(A_27z,A_27z,A_27z),V0f),V0f) = V0f ) ) ) ) )).
fof(conj_thm_2Erelation_2EIDEM,lemma,( ! [A_27z]: ( ne(A_27z) => ! [V0f] : ( mem(V0f,arr(A_27z,A_27z)) => ( p(ap(c_2Erelation_2EIDEM(A_27z),V0f)) <=> ! [V1x] : ( mem(V1x,A_27z) => ( ap(V0f,ap(V0f,V1x)) = ap(V0f,V1x) ) ) ) )))).
fof(conj_thm_2Erelation_2Einv__INVOL,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(c_2Erelation_2EINVOL(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2Einv(A_27a,A_27a)))))).
fof(ax_thm_2Erelation_2EO__DEF,axiom,( ! [A_27g] : ( ne(A_27g) => ! [A_27h] : ( ne(A_27h) => ! [A_27k] : ( ne(A_27k) => ! [V0R1] : ( mem(V0R1,arr(A_27h,arr(A_27k,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27g,arr(A_27h,bool))) => ! [V2x] : ( mem(V2x,A_27g) => ! [V3z] : ( mem(V3z,A_27k) => ( p(ap(ap(ap(ap(c_2Erelation_2EO(A_27g,A_27h,A_27k),V0R1),V1R2),V2x),V3z)) <=> ? [V4y] : ( mem(V4y,A_27h) & ( p(ap(ap(V1R2,V2x),V4y)) & p(ap(ap(V0R1,V4y),V3z)) ) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2Einv__O,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27b,bool))) => ! [V1R_27] : ( mem(V1R_27,arr(A_27c,arr(A_27a,bool))) => ( ap(c_2Erelation_2Einv(A_27c,A_27b),ap(ap(c_2Erelation_2EO(A_27c,A_27a,A_27b),V0R),V1R_27)) = ap(ap(c_2Erelation_2EO(A_27b,A_27a,A_27c),ap(c_2Erelation_2Einv(A_27c,A_27a),V1R_27)),ap(c_2Erelation_2Einv(A_27a,A_27b),V0R)) ) ) )))))).
fof(ax_thm_2Erelation_2ERSUBSET,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27b,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27b,bool))) => ( p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R1),V1R2)) <=> ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27b) => ( p(ap(ap(V0R1,V2x),V3y)) => p(ap(ap(V1R2,V2x),V3y)) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2Eirreflexive__RSUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27a,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Eirreflexive(A_27a),V1R2)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),V0R1),V1R2)) ) => p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R1)) ) ) )))).
fof(ax_thm_2Erelation_2ERUNION,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27b,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27b,bool))) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27b) => ( p(ap(ap(ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2),V2x),V3y)) <=> ( p(ap(ap(V0R1,V2x),V3y)) | p(ap(ap(V1R2,V2x),V3y)) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2ERUNION__COMM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27b,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27b,bool))) => ( ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2) = ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V1R2),V0R1) ) ) ))))).
fof(conj_thm_2Erelation_2ERUNION__ASSOC,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27b,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27b,bool))) => ! [V2R3] : ( mem(V2R3,arr(A_27a,arr(A_27b,bool))) => ( ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V1R2),V2R3)) = ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2)),V2R3) ) ) ) ))))).
fof(ax_thm_2Erelation_2ERINTER,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27b,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27b,bool))) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27b) => ( p(ap(ap(ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),V1R2),V2x),V3y)) <=> ( p(ap(ap(V0R1,V2x),V3y)) & p(ap(ap(V1R2,V2x),V3y)) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2ERINTER__COMM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27b,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27b,bool))) => ( ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),V1R2) = ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V1R2),V0R1) ) ) ))))).
fof(conj_thm_2Erelation_2ERINTER__ASSOC,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27b,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27b,bool))) => ! [V2R3] : ( mem(V2R3,arr(A_27a,arr(A_27b,bool))) => ( ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V1R2),V2R3)) = ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),V1R2)),V2R3) ) ) ) ))))).
fof(conj_thm_2Erelation_2Eantisymmetric__RINTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27a,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R1)) => p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R1),V1R2))) ) & ( p(ap(c_2Erelation_2Eantisymmetric(A_27a),V1R2)) => p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R1),V1R2))) ) ) ) )))).
fof(conj_thm_2Erelation_2Etransitive__RINTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27a,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R1)) & p(ap(c_2Erelation_2Etransitive(A_27a),V1R2)) ) => p(ap(c_2Erelation_2Etransitive(A_27a),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R1),V1R2))) ) ) )))).
fof(ax_thm_2Erelation_2ERCOMPL,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27b,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27b) => ( p(ap(ap(ap(c_2Erelation_2ERCOMPL(A_27a,A_27b),V0R),V1x),V2y)) <=> ( ~~ p(ap(ap(V0R,V1x),V2y)) ) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2Ereflexive__Id__RSUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) <=> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),c_2Emin_2E_3D(A_27a)),V0R)) ) )))).
fof(conj_thm_2Erelation_2Esymmetric__inv__RSUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) <=> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)),V0R)) ) )))).
fof(conj_thm_2Erelation_2Etransitive__O__RSUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) <=> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(ap(c_2Erelation_2EO(A_27a,A_27a,A_27a),V0R),V0R)),V0R)) ) )))).
fof(ax_thm_2Erelation_2EPreOrder,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EPreOrder(A_27a),V0R)) <=> ( p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) ) ) ) ) )).
fof(ax_thm_2Erelation_2EOrder,axiom,( ! [A_27g] : ( ne(A_27g) => ! [V0Z] : ( mem(V0Z,arr(A_27g,arr(A_27g,bool))) => ( p(ap(c_2Erelation_2EOrder(A_27g),V0Z)) <=> ( p(ap(c_2Erelation_2Eantisymmetric(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) ) ) ) ) )).
fof(ax_thm_2Erelation_2EWeakOrder,axiom,( ! [A_27g] : ( ne(A_27g) => ! [V0Z] : ( mem(V0Z,arr(A_27g,arr(A_27g,bool))) => ( p(ap(c_2Erelation_2EWeakOrder(A_27g),V0Z)) <=> ( p(ap(c_2Erelation_2Ereflexive(A_27g),V0Z)) & ( p(ap(c_2Erelation_2Eantisymmetric(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) ) ) ) ) ) )).
fof(ax_thm_2Erelation_2EStrongOrder,axiom,( ! [A_27g] : ( ne(A_27g) => ! [V0Z] : ( mem(V0Z,arr(A_27g,arr(A_27g,bool))) => ( p(ap(c_2Erelation_2EStrongOrder(A_27g),V0Z)) <=> ( p(ap(c_2Erelation_2Eirreflexive(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) ) ) ) ) )).
fof(conj_thm_2Erelation_2Eirrefl__trans__implies__antisym,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) ) => p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2EStrongOrd__Ord,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EStrongOrder(A_27a),V0R)) => p(ap(c_2Erelation_2EOrder(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2EWeakOrd__Ord,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) => p(ap(c_2Erelation_2EOrder(A_27a),V0R)) ) )))).
fof(conj_thm_2Erelation_2EWeakOrder__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2z] : ( mem(V2z,A_27a) => ( ( V1y = V2z ) <=> ( p(ap(ap(V0R,V1y),V2z)) & p(ap(ap(V0R,V2z),V1y)) ) ) ) ) ) )))).
fof(conj_thm_2Erelation_2ERSUBSET__ANTISYM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27b,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27a,arr(A_27b,bool))) => ( ( p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R1),V1R2)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V1R2),V0R1)) ) => ( V0R1 = V1R2 ) ) ) ))))).
fof(conj_thm_2Erelation_2ERSUBSET__antisymmetric,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => p(ap(c_2Erelation_2Eantisymmetric(arr(A_27a,arr(A_27b,bool))),c_2Erelation_2ERSUBSET(A_27a,A_27b))))))).
fof(conj_thm_2Erelation_2ERSUBSET__WeakOrder,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => p(ap(c_2Erelation_2EWeakOrder(arr(A_27a,arr(A_27b,bool))),c_2Erelation_2ERSUBSET(A_27a,A_27b))))))).
fof(conj_thm_2Erelation_2EEqIsBothRSUBSET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0y] : ( mem(V0y,arr(A_27a,arr(A_27b,bool))) => ! [V1z] : ( mem(V1z,arr(A_27a,arr(A_27b,bool))) => ( ( V0y = V1z ) <=> ( p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0y),V1z)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V1z),V0y)) ) ) ) ))))).
fof(ax_thm_2Erelation_2ESTRORD,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1a] : ( mem(V1a,A_27a) => ! [V2b] : ( mem(V2b,A_27a) => ( p(ap(ap(ap(c_2Erelation_2ESTRORD(A_27a),V0R),V1a),V2b)) <=> ( p(ap(ap(V0R,V1a),V2b)) & ( ~~ ( V1a = V2b ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Erelation_2ESTRORD__AND__NOT__Id,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2ESTRORD(A_27a),V0R) = ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R),ap(c_2Erelation_2ERCOMPL(A_27a,A_27a),c_2Emin_2E_3D(A_27a))) ) )))).
fof(conj_thm_2Erelation_2ERC__OR__Id,conjecture,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(c_2Erelation_2ERC(A_27a),V0R) = ap(ap(c_2Erelation_2ERUNION(A_27a,A_27a),V0R),c_2Emin_2E_3D(A_27a)) ) )))).
