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(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))))).
fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0]: (s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))))).
fof(comparisonTheory_2Ecmp__thms,axiom,![A_27a]: ((~ ((s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0))) & (~ ((s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))) & ~ ((s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))))) & ((![V0v0_2E0, V1v1_2E0, V2v2_2E0]: (s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0),s(A_27a,V0v0_2E0),s(A_27a,V1v1_2E0),s(A_27a,V2v2_2E0))) = s(A_27a,V0v0_2E0)) & (![V3v0_2E0, V4v1_2E0, V5v2_2E0]: (s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0),s(A_27a,V3v0_2E0),s(A_27a,V4v1_2E0),s(A_27a,V5v2_2E0))) = s(A_27a,V4v1_2E0)) & ![V6v0_2E0, V7v1_2E0, V8v2_2E0]: (s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0),s(A_27a,V6v0_2E0),s(A_27a,V7v1_2E0),s(A_27a,V8v2_2E0))) = s(A_27a,V8v2_2E0)))) & (![V9a_2E0]: ((s(tyop_2EternaryComparisons_2Eordering,V9a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)) | ((s(tyop_2EternaryComparisons_2Eordering,V9a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)) | (s(tyop_2EternaryComparisons_2Eordering,V9a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)))) & ![V10cmp_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0)))) <=> (![V11x_2E0]: (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V11x_2E0))),s(A_27a,V11x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)) & (![V12x_2E0, V13y_2E0]: ((s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V12x_2E0))),s(A_27a,V13y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)) => (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V13y_2E0))),s(A_27a,V12x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0))) & (![V14x_2E0, V15y_2E0]: ((s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V14x_2E0))),s(A_27a,V15y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)) <=> (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V15y_2E0))),s(A_27a,V14x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))) & (![V16x_2E0, V17y_2E0, V18z_2E0]: (((s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V16x_2E0))),s(A_27a,V17y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)) & (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V17y_2E0))),s(A_27a,V18z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))) => (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V16x_2E0))),s(A_27a,V18z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))) & (![V19x_2E0, V20y_2E0, V21z_2E0]: (((s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V19x_2E0))),s(A_27a,V20y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)) & (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V20y_2E0))),s(A_27a,V21z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0))) => (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V19x_2E0))),s(A_27a,V21z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))) & (![V22x_2E0, V23y_2E0, V24z_2E0]: (((s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V22x_2E0))),s(A_27a,V23y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)) & (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V23y_2E0))),s(A_27a,V24z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0))) => (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V22x_2E0))),s(A_27a,V24z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0))) & ![V25x_2E0, V26y_2E0, V27z_2E0]: (((s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V25x_2E0))),s(A_27a,V26y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)) & (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V26y_2E0))),s(A_27a,V27z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0))) => (s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V25x_2E0))),s(A_27a,V27z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)))))))))))))).
