fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,![A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))))).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,![A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))))).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,![A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),A_27c)),c_2EpatternMatches_2EPMATCH_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))))).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0))))).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27b,axiom,![A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),X2_2E0))))).
fof(patternMatchesTheory_2EPMATCH__ROWS__DROP__REDUNDANT__PMATCH__ROWS,axiom,![A_27a, A_27b, A_27c, A_27d]: ![V0p_2E0, V1g_2E0, V2r_2E0, V3p_27_2E0, V4g_27_2E0, V5r_27_2E0, V6rows1_2E0, V7rows2_2E0, V8rows3_2E0, V9v_2E0]: (![V10x_27_2E0]: (((s(A_27b,V9v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(A_27d,V10x_27_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_27_2E0),s(A_27d,V10x_27_2E0))))) => ?[V11x_2E0]: ((s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(A_27d,V10x_27_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V11x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(A_27a,V11x_2E0)))))) => (s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V9v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V6rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7rows2_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_27_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),V5r_27_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V8rows3_2E0))))))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V9v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V6rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7rows2_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V8rows3_2E0)))))))).
