%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL852-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:45:15 PM UTC 2026
% Result : Unsatisfiable 0.37s 5.69s
% Output : CNFRefutation 5.57s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_608)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_substn_Osimps_I2_J_0,axiom,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
cnf(cls_substn__subst__n_0,axiom,
c_Lambda_Osubstn(X1,X2,X3) = c_Lambda_Osubst(X1,c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
cnf(cls_substn_Osimps_I1_J_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
cnf(cls_substn__subst__0_0,axiom,
c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
cnf(cls_substn_Osimps_I1_J_2,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
cnf(cls_add__nonneg__eq__0__iff_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
cnf(cls_var__app__types_0,axiom,
( X1 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),X2,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X1)
| ~ c_Type_Otypings(X3,X6,X7)
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_0) ).
cnf(cls_var__app__types_1,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otypings(X1,X6,X7)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_1) ).
cnf(cls_gb__semiring_Osemiring__rules_I15_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X1,X7,X8,X9,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I20_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X4)),hAPP(hAPP(X1,X3),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X6,X7,X8,X9,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I13_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X4)),hAPP(hAPP(X1,X3),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X1,X7,X8,X9,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I14_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X1,X7,X8,X9,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I1_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),hAPP(hAPP(X2,X5),X4)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X3),X5)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I8_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5) = hAPP(hAPP(X2,hAPP(hAPP(X1,X3),X5)),hAPP(hAPP(X1,X4),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X2,X1,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_gb__semiring_Opwr__mul_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5) = hAPP(hAPP(X2,hAPP(hAPP(X1,X3),X5)),hAPP(hAPP(X1,X4),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X2,X1,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
cnf(cls_gb__semiring_Omul__pwr_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),hAPP(hAPP(X2,X3),X5)) = hAPP(hAPP(X2,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X1,X2,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
cnf(cls_gb__semiring_Omul__d_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X5)) = hAPP(hAPP(X3,hAPP(hAPP(X1,X2),X4)),hAPP(hAPP(X1,X2),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X3,X1,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I23_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X4)),X3)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I16_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X4)),X3)
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I2_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X4) = hAPP(hAPP(X2,hAPP(hAPP(X1,X3),X5)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X6,X7,X5,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I21_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I17_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I25_J_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_gb__semiring_Oadd__a_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I18_J_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_gb__semiring_Omul__a_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I3_J_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X2)) = hAPP(hAPP(X3,hAPP(hAPP(X1,X4),X5)),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X3,X6,X7,X5,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I28_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X3) = hAPP(hAPP(X2,X3),c_Suc(X4))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X2,X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I28_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I22_J_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I19_J_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I4_J_0,axiom,
( hAPP(hAPP(X1,X2),X2) = hAPP(hAPP(X3,hAPP(hAPP(X1,X4),X4)),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X3,X5,X6,X4,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I27_J_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X2),X4)) = hAPP(hAPP(X3,X2),c_Suc(X4))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X3,X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I27_J_0) ).
cnf(cls_gb__semiring_Opwr__Suc_0,axiom,
( hAPP(hAPP(X1,X2),c_Suc(X3)) = hAPP(hAPP(X4,X2),hAPP(hAPP(X1,X2),X3))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X4,X1,X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__Suc_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I35_J_0,axiom,
( hAPP(hAPP(X1,X2),c_Suc(X3)) = hAPP(hAPP(X4,X2),hAPP(hAPP(X1,X2),X3))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X4,X1,X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I35_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I24_J_0,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_gb__semiring_Oadd__c_0,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I7_J_0,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_gb__semiring_Omul__c_0,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__c_0) ).
cnf(cls_gb__semiring_Opwr__0_0,axiom,
( hAPP(hAPP(X1,X2),c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X4,X5,X1,X6,X3,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I6_J_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X3,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I9_J_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X2,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
cnf(cls_gb__semiring_Omul__0_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X2,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I12_J_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X3,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I5_J_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X2,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_gb__semiring_Oadd__0_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X2,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I10_J_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X3,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I11_J_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
cnf(cls_gb__semiring_Omul__1_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
cnf(cls_dB_Orecs_I2_J_0,axiom,
c_Lambda_OdB_OdB__rec(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(hAPP(hAPP(X2,X4),X5),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X6)),c_Lambda_OdB_OdB__rec(X1,X2,X3,X5,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
cnf(cls_dB_Osplit_1,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X3,X5),X6)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X6),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).
cnf(cls_dB_Osplit__asm_1,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X3,X5),X6)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X6),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).
cnf(cls_var__app__type__eq_0,axiom,
( X1 = X2
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
cnf(cls_dB_Osplit_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X5)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).
cnf(cls_dB_Osplit__asm_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X5)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).
cnf(cls_dB_Osplit__asm_2,axiom,
( hBOOL(hAPP(X1,hAPP(X4,X5)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OAbs(X5),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).
cnf(cls_dB_Osplit_2,axiom,
( hBOOL(hAPP(X1,hAPP(X4,X5)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OAbs(X5),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).
cnf(cls_var__app__typesE_0,axiom,
( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).
cnf(cls_list__app__typeD_0,axiom,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
cnf(cls_list__app__typeE_0,axiom,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
cnf(cls_Beta_0,axiom,
( c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))
| ~ c_InductTermi_OIT(X2)
| ~ c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
cnf(cls_list__app__typeI_0,axiom,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otypings(X1,X3,X5)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
cnf(cls_apps__preserves__beta_0,axiom,
( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB))
| ~ c_Lambda_Obeta(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
cnf(cls_var__app__typesE_1,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
cnf(cls_list__app__typeD_1,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
cnf(cls_list__app__typeE_1,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom,
( X2 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom,
( X2 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
cnf(cls_foldl__assoc_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
cnf(cls_apps__eq__tail__conv_0,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
cnf(cls_foldl__absorb0_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
cnf(cls_foldl__foldr1__lemma_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
cnf(cls_dB_Orecs_I3_J_0,axiom,
c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(hAPP(X3,X4),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
cnf(cls_foldl__foldr1_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
cnf(cls_foldr__conv__foldl_0,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
cnf(cls_typing__elims_I2_J_0,axiom,
( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
cnf(cls_type_Osplit_1,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,hAPP(hAPP(c_Type_Otype_OFun,X4),X5),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_1) ).
cnf(cls_type_Osplit__asm_1,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,hAPP(hAPP(c_Type_Otype_OFun,X4),X5),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).
cnf(cls_type_Orecs_I2_J_0,axiom,
c_Type_Otype_Otype__rec(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),X5) = hAPP(hAPP(hAPP(hAPP(X2,X3),X4),c_Type_Otype_Otype__rec(X1,X2,X3,X5)),c_Type_Otype_Otype__rec(X1,X2,X4,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_0) ).
cnf(cls_App__eq__foldl__conv_0,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
cnf(cls_Abs__App__neq__Var__apps_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
cnf(cls_Abs__eq__apps__conv_0,axiom,
( c_Lambda_OdB_OAbs(X1) = X2
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
cnf(cls_Var__eq__apps__conv_0,axiom,
( c_Lambda_OdB_OVar(X1) = X2
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
cnf(cls_apps__eq__Abs__conv_0,axiom,
( X1 = c_Lambda_OdB_OAbs(X3)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
cnf(cls_apps__eq__Abs__conv_1,axiom,
( X2 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
cnf(cls_Abs__eq__apps__conv_1,axiom,
( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
cnf(cls_Var__eq__apps__conv_1,axiom,
( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
cnf(cls_type_Osplit_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X4)))
| ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,c_Type_Otype_OAtom(X4),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_0) ).
cnf(cls_type_Osplit__asm_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X4)))
| ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,c_Type_Otype_OAtom(X4),t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).
cnf(cls_shift__commute_0,axiom,
c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4) = c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__commute_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_U____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_dB_Osimps_I11_J_0,axiom,
c_Lambda_OdB_OdB__case(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(X2,X4),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
cnf(cls_App__eq__foldl__conv_4,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
cnf(cls_dB_Orecs_I1_J_0,axiom,
c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).
cnf(cls_dB_Osimps_I12_J_0,axiom,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
cnf(cls_dB_Osimps_I10_J_0,axiom,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
cnf(cls_apps__eq__Abs__conv_2,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
cnf(cls_Abs__eq__apps__conv_2,axiom,
c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
cnf(cls_Var__eq__apps__conv_2,axiom,
c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
cnf(cls_foldr_Osimps_I1_J_0,axiom,
c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
cnf(cls_foldl__Nil_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
cnf(cls_subst__lemma_0,axiom,
( c_Type_Otyping(X1,c_Lambda_Osubst(X5,X2,X4),X6)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
cnf(cls_subst__type__IT_0,axiom,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,X2,X3))
| ~ c_Type_Otyping(X4,X2,X5)
| ~ c_InductTermi_OIT(X2)
| ~ c_Type_Otyping(c_Type_Oshift(X4,X3,X5,tc_Type_Otype),X1,X6)
| ~ c_InductTermi_OIT(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__type__IT_0) ).
cnf(cls_Abs_0,axiom,
( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_Type_Otype),X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs_0) ).
cnf(cls_nat__diff__split__asm_1,axiom,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).
cnf(cls_nat__diff__split_1,axiom,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).
cnf(cls_typing__elims_I3_J_1,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X2,X1,X3),tc_Type_Otype),X3,c_Type_Osko__Type__Xtyping__elims__3__2(X2,X1,X3))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).
cnf(cls_CHAINED_0_01,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_typing__elims_I2_J_1,axiom,
( c_Type_Otyping(X1,X2,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_abs__typeE_0,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__typeE_0) ).
cnf(cls_CHAINED_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_lift__type_0,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),c_Lambda_Olift(X4,X2),X5)
| ~ c_Type_Otyping(X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
cnf(cls_le__diff__iff_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
cnf(cls_less__diff__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
cnf(cls_power__le__imp__le__base_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Suc(X4),X1),c_Power_Opower__class_Opower(X3,c_Suc(X4),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
cnf(cls_shift__gt_0,axiom,
( hAPP(c_Type_Oshift(X1,X2,X3,X4),X5) = hAPP(X1,X5)
| ~ c_HOL_Oord__class_Oless(X5,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).
cnf(cls_dB_Osize_I5_J_0,axiom,
c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).
cnf(cls_power__less__imp__less__base_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
cnf(cls_power__strict__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
cnf(cls_max__add__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_le__diff__iff_1,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
cnf(cls_less__diff__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
cnf(cls_shift__eq_0,axiom,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
cnf(cls_diff__Suc__diff__eq2_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
cnf(cls_diff__Suc__diff__eq1_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),c_Suc(X2),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
cnf(cls_le__add__right__mono_0,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(cls_nat__diff__split_0,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
cnf(cls_subst__App_0,axiom,
c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
cnf(cls_liftn_Osimps_I2_J_0,axiom,
c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
cnf(cls_Nat_Odiff__diff__eq_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
cnf(cls_diff__add__assoc2_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat)),X2)
| ~ c_lessequals(X3,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
cnf(cls_add__diff__assoc2_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X3) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
cnf(cls_le__diff__conv2_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
cnf(cls_add__le__cancel__right_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
cnf(cls_add__le__cancel__left_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
cnf(cls_add__less__cancel__right_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
cnf(cls_add__less__cancel__left_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_le__diff__conv2_1,axiom,
( c_lessequals(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
cnf(cls_power__eq__imp__eq__base_0,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
cnf(cls_power__mono_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
cnf(cls_typing__elims_I3_J_0,axiom,
( X1 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X1,X2,X3)),c_Type_Osko__Type__Xtyping__elims__3__2(X1,X2,X3))
| ~ c_Type_Otyping(X2,c_Lambda_OdB_OAbs(X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).
cnf(cls_add__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
cnf(cls_add__less__le__mono_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
cnf(cls_add__le__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
cnf(cls_add__strict__mono_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
cnf(cls_max__diff__distrib__left_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
cnf(cls_diff__less__mono2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
cnf(cls_diff__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
cnf(cls_le__add__diff_0,axiom,
( c_lessequals(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
cnf(cls_nat__add__left__cancel__le_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
cnf(cls_nat__add__left__cancel__less_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_typing_OApp_0,axiom,
( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
| ~ c_Type_Otyping(X1,X3,X5)
| ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X5),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OApp_0) ).
cnf(cls_add__le__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat)
| ~ c_lessequals(X2,X4,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
cnf(cls_add__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
cnf(cls_power__inject__base_0,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) != c_Power_Opower__class_Opower(X4,c_Suc(X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
cnf(cls_less__diff__conv_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
cnf(cls_le__diff__conv_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
cnf(cls_dB_Osize_I2_J_0,axiom,
c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).
cnf(cls_add__cancel__21_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_diff__diff__right_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
cnf(cls_le__diff__conv_1,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
cnf(cls_less__diff__conv_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
cnf(cls_diff__add__assoc_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))
| ~ c_lessequals(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
cnf(cls_add__diff__assoc_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
cnf(cls_le__max__iff__disj_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
cnf(cls_less__max__iff__disj_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
cnf(cls_le__imp__diff__is__add_1,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X1,tc_nat) = X2
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
cnf(cls_nat__add__assoc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
cnf(cls_add__nonpos__nonpos_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
cnf(cls_add__neg__nonpos_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
cnf(cls_add__nonpos__neg_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
cnf(cls_add__neg__neg_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
cnf(cls_add__nonneg__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
cnf(cls_add__pos__nonneg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
cnf(cls_add__nonneg__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
cnf(cls_add__pos__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
cnf(cls_type_Osimps_I6_J_0,axiom,
c_Type_Otype_Otype__case(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),X5) = hAPP(hAPP(X2,X3),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).
cnf(cls_add__increasing2_0,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
cnf(cls_add__increasing_0,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
cnf(cls_add__strict__increasing_0,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
cnf(cls_add__strict__increasing2_0,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
cnf(cls_add__le__cancel__left_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
cnf(cls_add__left__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
cnf(cls_add__le__cancel__right_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
cnf(cls_add__right__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
cnf(cls_add__strict__left__mono_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
cnf(cls_add__less__cancel__left_1,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
cnf(cls_add__strict__right__mono_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
cnf(cls_add__less__cancel__right_1,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_pos__add__strict_0,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
cnf(cls_diff__le__mono2_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
cnf(cls_diff__le__mono_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
cnf(cls_add__gr__0_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
cnf(cls_min__max_Ole__supI_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
cnf(cls_min__max_Osup__least_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
cnf(cls_min__max_Ole__sup__iff_2,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
cnf(cls_max__less__iff__conj_2,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
cnf(cls_le__add__diff__inverse2_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X2) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
cnf(cls_le__imp__diff__is__add_0,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X1)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
cnf(cls_eq__diff__iff_0,axiom,
( X1 = X3
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
cnf(cls_diff__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
cnf(cls_Suc__diff__diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
cnf(cls_min__max_Osup__assoc_0,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
cnf(cls_min__max_Osup__left__commute_0,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
cnf(cls_le__iff__diff__le__0_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
cnf(cls_even__less__0__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
cnf(cls_le__eqI_1,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
cnf(cls_le__eqI_0,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
cnf(cls_less__eqI_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
cnf(cls_less__eqI_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_drop__replicate_0,axiom,
c_List_Odrop(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
cnf(cls_nat__add__left__cancel__le_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
cnf(cls_add__le__mono1_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
cnf(cls_nat__add__left__cancel__less_1,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
cnf(cls_add__less__mono1_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
cnf(cls_min__max_Ole__supE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
cnf(cls_min__max_Ole__sup__iff_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
cnf(cls_min__max_Ole__supE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
cnf(cls_min__max_Ole__sup__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
cnf(cls_max__less__iff__conj_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
cnf(cls_max__less__iff__conj_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
cnf(cls_add__cancel__21_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_lem0_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lem0_0) ).
cnf(cls_of__nat__diff_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X1) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oring__1(X1)
| ~ c_lessequals(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).
cnf(cls_diff__commute_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
cnf(cls_nat__minus__add__max_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X2) = c_Orderings_Oord__class_Omax(X1,X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
cnf(cls_drop__drop_0,axiom,
c_List_Odrop(X1,c_List_Odrop(X2,X3,X4),X4) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__drop_0) ).
cnf(cls_zero__less__diff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
cnf(cls_diff__diff__left_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
cnf(cls_add__nonneg__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
cnf(cls_add__nonneg__eq__0__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
cnf(cls_diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
cnf(cls_diff__cancel2_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
cnf(cls_less__add__eq__less_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
cnf(cls_add__leE_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
cnf(cls_add__leE_1,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
cnf(cls_add__lessD1_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_nat__add__left__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
cnf(cls_zero__le__power_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
cnf(cls_zero__less__power_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
cnf(cls_type_Osimps_I5_J_0,axiom,
c_Type_Otype_Otype__case(X1,X2,c_Type_Otype_OAtom(X3),X4) = hAPP(X1,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
cnf(cls_type_Orecs_I1_J_0,axiom,
c_Type_Otype_Otype__rec(X1,X2,c_Type_Otype_OAtom(X3),X4) = hAPP(X1,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
cnf(cls_even__less__0__iff_1,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
cnf(cls_le__iff__diff__le__0_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
cnf(cls_diff__Suc__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
cnf(cls_min__max_Ole__supI1_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
cnf(cls_le__max__iff__disj_1,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
cnf(cls_min__max_Ole__supI2_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
cnf(cls_le__max__iff__disj_2,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
cnf(cls_less__max__iff__disj_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
cnf(cls_min__max_Oless__supI1_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
cnf(cls_less__max__iff__disj_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
cnf(cls_min__max_Oless__supI2_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
cnf(cls_Suc__diff__le_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
cnf(cls_subst__preserves__beta_0,axiom,
( c_Lambda_Obeta(c_Lambda_Osubst(X1,X2,X3),c_Lambda_Osubst(X4,X2,X3))
| ~ c_Lambda_Obeta(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
cnf(cls_zero__less__diff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
cnf(cls_diff__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X2
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
cnf(cls_of__nat__add_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1)),c_Nat_Osemiring__1__class_Oof__nat(X3,X1))
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
cnf(cls_less__imp__diff__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
cnf(cls_less__iff__Suc__add_1,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
cnf(cls_less__add__Suc1_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
cnf(cls_less__add__Suc2_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
cnf(cls_add__gr__0_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
cnf(cls_add__gr__0_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
cnf(cls_le__add__diff__inverse_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
cnf(cls_order__trans_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
cnf(cls_xt1_I6_J_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_order__less__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(cls_order__le__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
cnf(cls_order__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
cnf(cls_xt1_I8_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_xt1_I10_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
cnf(cls_of__nat__le__iff_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
cnf(cls_of__nat__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
cnf(cls_less__trans__Suc_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
cnf(cls_termination__basic__simps_I3_J_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
cnf(cls_trans__le__add1_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
cnf(cls_termination__basic__simps_I4_J_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
cnf(cls_trans__le__add2_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
cnf(cls_trans__less__add1_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
cnf(cls_termination__basic__simps_I1_J_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
cnf(cls_trans__less__add2_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
cnf(cls_termination__basic__simps_I2_J_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
cnf(cls_not__add__less1_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
cnf(cls_not__add__less2_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
cnf(cls_beta_0,axiom,
c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
cnf(cls_min__max_Osup__left__idem_0,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = c_Orderings_Oord__class_Omax(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
cnf(cls_Suc__pred_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
cnf(cls_le__trans_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
cnf(cls_infinite__descent0_2,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_HOL_Oord__class_Oless(X3,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_2) ).
cnf(cls_liftn_Osimps_I1_J_1,axiom,
( c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
cnf(cls_add__diff__inverse_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
cnf(cls_less__le__not__le_2,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_lift_Osimps_I2_J_0,axiom,
c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
cnf(cls_of__nat__0__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
cnf(cls_of__nat__le__iff_1,axiom,
( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
cnf(cls_of__nat__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
cnf(cls_upt_Oinduct_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upt_Oinduct_1) ).
cnf(cls_nat_Oinduct_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinduct_1) ).
cnf(cls_nat__less__cases_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
cnf(cls_of__nat__0__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_order__antisym_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_liftn__lift_0,axiom,
c_Lambda_Oliftn(c_Suc(X1),X2,X3) = c_Lambda_Olift(c_Lambda_Oliftn(X1,X2,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_eq__eqI_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_eq__eqI_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_appR_0,axiom,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3))
| ~ c_Lambda_Obeta(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
cnf(cls_appL_0,axiom,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
| ~ c_Lambda_Obeta(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_le__less__Suc__eq_0,axiom,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
cnf(cls_replicate__eq__replicate_1,axiom,
( X2 = X5
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
cnf(cls_not__less__eq__eq_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
cnf(cls_not__less__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
cnf(cls_diffs0__imp__equal_0,axiom,
( X2 = X1
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_add__left__cancel_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_replicate__eq__replicate_0,axiom,
( X1 = X4
| c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
cnf(cls_max__Suc__Suc_0,axiom,
c_Orderings_Oord__class_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X1,X2,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
cnf(cls_le__antisym_0,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
cnf(cls_le__maxI1_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
cnf(cls_le__maxI2_0,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X2,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
cnf(cls_add__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_subject__reduction_0,axiom,
( c_Type_Otyping(X1,X2,X3)
| ~ c_Lambda_Obeta(X4,X2)
| ~ c_Type_Otyping(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
cnf(cls_diff__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
cnf(cls_diff__le__self_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
cnf(cls_Suc__le__mono_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
cnf(cls_Suc__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
cnf(cls_infinite__descent0_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_1) ).
cnf(cls_add__Suc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
cnf(cls_le__SucE_0,axiom,
( X1 = c_Suc(X2)
| c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
cnf(cls_order__neq__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(cls_order__le__neq__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
cnf(cls_order__less__le_2,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
cnf(cls_order__le__less_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
cnf(cls_xt1_I12_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_infinite__descent0_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_0) ).
cnf(cls_min__max_Ole__iff__sup_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Omax(X2,X3,X1) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
cnf(cls_Suc__le__mono_1,axiom,
( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
cnf(cls_Suc__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
cnf(cls_less__Suc__eq__0__disj_3,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
cnf(cls_min__max_Osup__absorb1_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
cnf(cls_min__max_Ole__iff__sup_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
cnf(cls_less__SucE_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
cnf(cls_less__antisym_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
cnf(cls_Suc__lessI_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
cnf(cls_subst__lt_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
cnf(cls_liftn_Osimps_I1_J_0,axiom,
( c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3) = c_Lambda_OdB_OVar(X2)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
cnf(cls_order__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
cnf(cls_order__le__less_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
cnf(cls_nat__add__right__cancel_0,axiom,
( X1 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
cnf(cls_Suc__leD_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
cnf(cls_less__eq__Suc__le_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
cnf(cls_Suc__le__eq_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
cnf(cls_Suc__lessD_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
cnf(cls_less__Suc__eq__le_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
cnf(cls_add__Suc__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
cnf(cls_diff__add__0_0,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
cnf(cls_diff__add__inverse_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(cls_diff__add__inverse2_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
cnf(cls_of__nat__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
cnf(cls_less__eq__Suc__le_0,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
cnf(cls_Suc__leI_0,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
cnf(cls_le__SucI_0,axiom,
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
cnf(cls_le__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
cnf(cls_less__Suc__eq__le_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
cnf(cls_less__SucI_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
cnf(cls_le__iff__add_1,axiom,
c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
cnf(cls_le__add1_0,axiom,
c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
cnf(cls_le__add2_0,axiom,
c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
cnf(cls_diff__is__0__eq_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
cnf(cls_le__neq__implies__less_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
cnf(cls_le__eq__less__or__eq_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
cnf(cls_nat__less__le_2,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
cnf(cls_diff__is__0__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
cnf(cls_nat__less__le_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
cnf(cls_termination__basic__simps_I5_J_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
cnf(cls_upt_Oinduct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).
cnf(cls_nat_Oinduct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).
cnf(cls_subst__Var__IT_0,axiom,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))
| ~ c_InductTermi_OIT(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
cnf(cls_power__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
cnf(cls_power__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
cnf(cls_type__induct_0,axiom,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X2))
| c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_0) ).
cnf(cls_type__induct_1,axiom,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X3))
| c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_1) ).
cnf(cls_dB_Osize_I6_J_0,axiom,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).
cnf(cls_subst__Var_2,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
cnf(cls_linorder__less__linear_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
cnf(cls_linorder__neqE_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
cnf(cls_type_Osimps_I2_J_0,axiom,
( X1 = X3
| hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
cnf(cls_dB_Osimps_I2_J_0,axiom,
( X1 = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
cnf(cls_type_Osimps_I2_J_1,axiom,
( X2 = X4
| hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
cnf(cls_dB_Osimps_I2_J_1,axiom,
( X2 = X4
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
cnf(cls_diff__Suc__Suc_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( c_HOL_Oord__class_Oless(X2,X2,X1)
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
cnf(cls_linorder__not__le_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
cnf(cls_not__leE_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
cnf(cls_linorder__not__less_0,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
cnf(cls_min__max_Osup__commute_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = c_Orderings_Oord__class_Omax(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
cnf(cls_subst__Var_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
cnf(cls_replicate__eq__replicate_2,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
cnf(cls_App_I1_J_0,axiom,
c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I1_J_0) ).
cnf(cls_not__less__eq__eq_0,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
cnf(cls_not__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_typing__elims_I1_J_0,axiom,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
cnf(cls_add__Suc__shift_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
cnf(cls_nat__neq__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
cnf(cls_lift_Osimps_I1_J_0,axiom,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
cnf(cls_less__Suc0_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
cnf(cls_nat__le__linear_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
cnf(cls_field__power__not__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
cnf(cls_right__minus__eq_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_add__is__1_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
cnf(cls_one__is__add_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
cnf(cls_type__induct_2,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Type_Osko__Type__Xtype__induct__1__1(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_2) ).
cnf(cls_power__eq__0__iff_2,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
cnf(cls_add__is__1_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
cnf(cls_add__is__1_3,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
cnf(cls_one__is__add_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
cnf(cls_one__is__add_3,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
cnf(cls_replicate__empty_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
cnf(cls_empty__replicate_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Olist_ONil(X1) != c_List_Oreplicate(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
cnf(cls_app__Var__IT_0,axiom,
( c_InductTermi_OIT(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2)))
| ~ c_InductTermi_OIT(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
cnf(cls_zero__le__imp__of__nat_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
cnf(cls_of__nat__0__le__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_neq0__conv_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
cnf(cls_Suc__n__not__le__n_0,axiom,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
cnf(cls_le__0__eq_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
cnf(cls_nat__add__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
cnf(cls_add__is__1_2,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
cnf(cls_one__is__add_2,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
cnf(cls_lift__preserves__beta_0,axiom,
( c_Lambda_Obeta(c_Lambda_Olift(X1,X2),c_Lambda_Olift(X3,X2))
| ~ c_Lambda_Obeta(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
cnf(cls_power__0__Suc_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
cnf(cls_power__0__left_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
cnf(cls_double__eq__0__iff_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
cnf(cls_subst__lift_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
cnf(cls_add__is__1_4,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
cnf(cls_one__is__add_4,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
cnf(cls_dB_Osize_I3_J_0,axiom,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).
cnf(cls_add__is__0_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
cnf(cls_add__is__0_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
cnf(cls_add__eq__self__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
cnf(cls_natgb_Oadd__r0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
cnf(cls_add__0__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_add__is__1_5,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
cnf(cls_one__is__add_5,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
cnf(cls_diff__0__right_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_less__Suc0_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_diff__self_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
cnf(cls_le__Suc__eq_2,axiom,
c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
cnf(cls_drop__Nil_0,axiom,
c_List_Odrop(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
cnf(cls_type_Osimps_I4_J_0,axiom,
hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != c_Type_Otype_OAtom(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
cnf(cls_dB_Osimps_I8_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
cnf(cls_dB_Osimps_I5_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
cnf(cls_type_Osimps_I3_J_0,axiom,
c_Type_Otype_OAtom(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).
cnf(cls_dB_Osimps_I9_J_0,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
cnf(cls_dB_Osimps_I4_J_0,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
cnf(cls_min__max_Osup__idem_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X2,X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
cnf(cls_gr0__conv__Suc_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
cnf(cls_zero__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_replicate__empty_1,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
cnf(cls_empty__replicate_1,axiom,
c_List_Olist_ONil(X1) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
cnf(cls_subst__eq_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
cnf(cls_gr0I_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
cnf(cls_le__0__eq_1,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
cnf(cls_less__Suc__eq_2,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
cnf(cls_lessI_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
cnf(cls_diff__0__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
cnf(cls_drop__0_0,axiom,
c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
cnf(cls_liftn__0_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__0_0) ).
cnf(cls_add__is__0_2,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
cnf(cls_max__0L_0,axiom,
c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0L_0) ).
cnf(cls_max__0R_0,axiom,
c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0R_0) ).
cnf(cls_minus__nat_Odiff__0_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
cnf(cls_le0_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
cnf(cls_diff__self__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(X1,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_of__nat__eq__iff_0,axiom,
( X2 = X3
| ~ class_Nat_Osemiring__char__0(X1)
| c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
cnf(cls_le__refl_0,axiom,
c_lessequals(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(cls_App_I3_J_0,axiom,
c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I3_J_0) ).
cnf(cls_abs_0,axiom,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
cnf(cls_lift__IT_0,axiom,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( class_Orderings_Obot(tc_fun(X1,X2))
| ~ class_Orderings_Obot(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
cnf(cls_beta__cases_I1_J_0,axiom,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
cnf(cls_of__nat__0_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
cnf(cls_dB_Osize_I4_J_0,axiom,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
cnf(cls_Lambda_0,axiom,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
cnf(cls_type_Osimps_I1_J_0,axiom,
( X1 = X2
| c_Type_Otype_OAtom(X1) != c_Type_Otype_OAtom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
cnf(cls_dB_Osimps_I3_J_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
cnf(cls_dB_Osimps_I1_J_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
cnf(cls_nat_Oinject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
cnf(cls_Suc__inject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
cnf(cls_size__char_0,axiom,
c_Nat_Osize__class_Osize(X1,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_size__char_0) ).
cnf(cls_dB_Osimps_I7_J_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
cnf(cls_dB_Osimps_I6_J_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
cnf(cls_dB_Osize_I1_J_0,axiom,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
cnf(cls_Var__IT_0,axiom,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(X1) != X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(cls_n__not__Suc__n_0,axiom,
X1 != c_Suc(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(cls_bot__nat__def_0,axiom,
c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__nat__def_0) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(cls_App_I4_J_0,axiom,
c_InductTermi_OIT(v_ta____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I4_J_0) ).
cnf(cls_App_I2_J_0,axiom,
c_InductTermi_OIT(v_s____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I2_J_0) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
cnf(clsarity_nat__Power_Opower,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(i_0_607,axiom,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)),
cls_substn_Osimps_I2_J_0 ).
cnf(i_0_608,axiom,
c_Lambda_Osubstn(X1,X2,X3) = c_Lambda_Osubst(X1,c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3),
cls_substn__subst__n_0 ).
cnf(i_0_609,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_substn_Osimps_I1_J_1 ).
cnf(i_0_610,axiom,
c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
cls_substn__subst__0_0 ).
cnf(i_0_611,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
cls_substn_Osimps_I1_J_2 ).
cnf(i_0_612,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonneg__eq__0__iff_2 ).
cnf(i_0_613,axiom,
( X1 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),X2,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X1)
| ~ c_Type_Otypings(X3,X6,X7)
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X2) ),
cls_var__app__types_0,
[final] ).
cnf(i_0_614,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otypings(X1,X6,X7)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
cls_var__app__types_1,
[final] ).
cnf(i_0_615,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X1,X7,X8,X9,X10) ),
cls_gb__semiring_Osemiring__rules_I15_J_0,
[final] ).
cnf(i_0_616,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X4)),hAPP(hAPP(X1,X3),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X6,X7,X8,X9,X10) ),
cls_gb__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_617,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X4)),hAPP(hAPP(X1,X3),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X1,X7,X8,X9,X10) ),
cls_gb__semiring_Osemiring__rules_I13_J_0,
[final] ).
cnf(i_0_618,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X1,X7,X8,X9,X10) ),
cls_gb__semiring_Osemiring__rules_I14_J_0,
[final] ).
cnf(i_0_619,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),hAPP(hAPP(X2,X5),X4)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X3),X5)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I1_J_0,
[final] ).
cnf(i_0_620,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5) = hAPP(hAPP(X2,hAPP(hAPP(X1,X3),X5)),hAPP(hAPP(X1,X4),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X2,X1,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I8_J_0,
[final] ).
cnf(i_0_621,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5) = hAPP(hAPP(X2,hAPP(hAPP(X1,X3),X5)),hAPP(hAPP(X1,X4),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X2,X1,X7,X8,X9) ),
cls_gb__semiring_Opwr__mul_0,
[final] ).
cnf(i_0_622,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),hAPP(hAPP(X2,X3),X5)) = hAPP(hAPP(X2,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X6,X1,X2,X7,X8,X9) ),
cls_gb__semiring_Omul__pwr_0,
[final] ).
cnf(i_0_623,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X5)) = hAPP(hAPP(X3,hAPP(hAPP(X1,X2),X4)),hAPP(hAPP(X1,X2),X5))
| ~ c_Groebner__Basis_Ogb__semiring(X3,X1,X6,X7,X8,X9) ),
cls_gb__semiring_Omul__d_0,
[final] ).
cnf(i_0_624,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X4)),X3)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_625,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X4)),X3)
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I16_J_0,
[final] ).
cnf(i_0_626,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X4) = hAPP(hAPP(X2,hAPP(hAPP(X1,X3),X5)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X6,X7,X5,X8) ),
cls_gb__semiring_Osemiring__rules_I2_J_0,
[final] ).
cnf(i_0_627,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_628,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I17_J_0,
[final] ).
cnf(i_0_629,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_630,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
cls_gb__semiring_Oadd__a_0,
[final] ).
cnf(i_0_631,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I18_J_0,
[final] ).
cnf(i_0_632,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4)
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
cls_gb__semiring_Omul__a_0,
[final] ).
cnf(i_0_633,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X2)) = hAPP(hAPP(X3,hAPP(hAPP(X1,X4),X5)),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X3,X6,X7,X5,X8) ),
cls_gb__semiring_Osemiring__rules_I3_J_0,
[final] ).
cnf(i_0_634,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X3) = hAPP(hAPP(X2,X3),c_Suc(X4))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X2,X6,X7,X8) ),
cls_gb__semiring_Osemiring__rules_I28_J_0,
[final] ).
cnf(i_0_635,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X5,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_636,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X6,X7,X8,X9) ),
cls_gb__semiring_Osemiring__rules_I19_J_0,
[final] ).
cnf(i_0_637,axiom,
( hAPP(hAPP(X1,X2),X2) = hAPP(hAPP(X3,hAPP(hAPP(X1,X4),X4)),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X3,X5,X6,X4,X7) ),
cls_gb__semiring_Osemiring__rules_I4_J_0,
[final] ).
cnf(i_0_638,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X2),X4)) = hAPP(hAPP(X3,X2),c_Suc(X4))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X1,X3,X6,X7,X8) ),
cls_gb__semiring_Osemiring__rules_I27_J_0,
[final] ).
cnf(i_0_639,axiom,
( hAPP(hAPP(X1,X2),c_Suc(X3)) = hAPP(hAPP(X4,X2),hAPP(hAPP(X1,X2),X3))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X4,X1,X6,X7,X8) ),
cls_gb__semiring_Opwr__Suc_0,
[final] ).
cnf(i_0_640,axiom,
( hAPP(hAPP(X1,X2),c_Suc(X3)) = hAPP(hAPP(X4,X2),hAPP(hAPP(X1,X2),X3))
| ~ c_Groebner__Basis_Ogb__semiring(X5,X4,X1,X6,X7,X8) ),
cls_gb__semiring_Osemiring__rules_I35_J_0,
[final] ).
cnf(i_0_641,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X6,X7,X8) ),
cls_gb__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_642,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X6,X7,X8) ),
cls_gb__semiring_Oadd__c_0,
[final] ).
cnf(i_0_643,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X7,X8) ),
cls_gb__semiring_Osemiring__rules_I7_J_0,
[final] ).
cnf(i_0_644,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X7,X8) ),
cls_gb__semiring_Omul__c_0,
[final] ).
cnf(i_0_645,axiom,
( hAPP(hAPP(X1,X2),c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X4,X5,X1,X6,X3,X7) ),
cls_gb__semiring_Opwr__0_0,
[final] ).
cnf(i_0_646,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X3,X6,X7) ),
cls_gb__semiring_Osemiring__rules_I6_J_0,
[final] ).
cnf(i_0_647,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X2,X6,X7) ),
cls_gb__semiring_Osemiring__rules_I9_J_0,
[final] ).
cnf(i_0_648,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X2,X6,X7) ),
cls_gb__semiring_Omul__0_0,
[final] ).
cnf(i_0_649,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X3,X7) ),
cls_gb__semiring_Osemiring__rules_I12_J_0,
[final] ).
cnf(i_0_650,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X2,X6,X7) ),
cls_gb__semiring_Osemiring__rules_I5_J_0,
[final] ).
cnf(i_0_651,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X1,X4,X5,X2,X6,X7) ),
cls_gb__semiring_Oadd__0_0,
[final] ).
cnf(i_0_652,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X3,X6,X7) ),
cls_gb__semiring_Osemiring__rules_I10_J_0,
[final] ).
cnf(i_0_653,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X2,X7) ),
cls_gb__semiring_Osemiring__rules_I11_J_0,
[final] ).
cnf(i_0_654,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ c_Groebner__Basis_Ogb__semiring(X4,X1,X5,X6,X2,X7) ),
cls_gb__semiring_Omul__1_0,
[final] ).
cnf(i_0_655,axiom,
c_Lambda_OdB_OdB__rec(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(hAPP(hAPP(X2,X4),X5),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X6)),c_Lambda_OdB_OdB__rec(X1,X2,X3,X5,X6)),
cls_dB_Orecs_I2_J_0,
[final] ).
cnf(i_0_656,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X3,X5),X6)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X6),t_a))) ),
cls_dB_Osplit_1,
[final] ).
cnf(i_0_657,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X3,X5),X6)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X6),t_a))) ),
cls_dB_Osplit__asm_1,
[final] ).
cnf(i_0_658,axiom,
( X1 = X2
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
cls_var__app__type__eq_0,
[final] ).
cnf(i_0_659,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X5)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a))) ),
cls_dB_Osplit_0,
[final] ).
cnf(i_0_660,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X5)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a))) ),
cls_dB_Osplit__asm_0,
[final] ).
cnf(i_0_661,axiom,
( hBOOL(hAPP(X1,hAPP(X4,X5)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OAbs(X5),t_a))) ),
cls_dB_Osplit__asm_2,
[final] ).
cnf(i_0_662,axiom,
( hBOOL(hAPP(X1,hAPP(X4,X5)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OAbs(X5),t_a))) ),
cls_dB_Osplit_2,
[final] ).
cnf(i_0_663,axiom,
( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
cls_var__app__typesE_0,
[final] ).
cnf(i_0_664,axiom,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
cls_list__app__typeD_0,
[final] ).
cnf(i_0_665,axiom,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
cls_list__app__typeE_0,
[final] ).
cnf(i_0_666,axiom,
( c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))
| ~ c_InductTermi_OIT(X2)
| ~ c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)) ),
cls_Beta_0,
[final] ).
cnf(i_0_667,axiom,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otypings(X1,X3,X5)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype)) ),
cls_list__app__typeI_0,
[final] ).
cnf(i_0_668,axiom,
( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB))
| ~ c_Lambda_Obeta(X1,X3) ),
cls_apps__preserves__beta_0,
[final] ).
cnf(i_0_669,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
cls_var__app__typesE_1,
[final] ).
cnf(i_0_670,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
cls_list__app__typeD_1,
[final] ).
cnf(i_0_671,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
cls_list__app__typeE_1,
[final] ).
cnf(i_0_672,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Abs__apps__eq__Abs__apps__conv_0,
[final] ).
cnf(i_0_673,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Var__apps__eq__Var__apps__conv_0,
[final] ).
cnf(i_0_674,axiom,
( X2 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Abs__apps__eq__Abs__apps__conv_1,
[final] ).
cnf(i_0_675,axiom,
( X2 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Var__apps__eq__Var__apps__conv_1,
[final] ).
cnf(i_0_676,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
cls_foldl__assoc_0,
[final] ).
cnf(i_0_677,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
cls_Var__apps__neq__Abs__apps_0,
[final] ).
cnf(i_0_678,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_apps__eq__tail__conv_0,
[final] ).
cnf(i_0_679,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_foldl__absorb0_0,
[final] ).
cnf(i_0_680,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_foldl__foldr1__lemma_0,
[final] ).
cnf(i_0_681,axiom,
c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(hAPP(X3,X4),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X5)),
cls_dB_Orecs_I3_J_0,
[final] ).
cnf(i_0_682,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_foldl__foldr1_0,
[final] ).
cnf(i_0_683,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
cls_foldr__conv__foldl_0,
[final] ).
cnf(i_0_684,axiom,
( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4),X3) ),
cls_typing__elims_I2_J_0,
[final] ).
cnf(i_0_685,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,hAPP(hAPP(c_Type_Otype_OFun,X4),X5),t_a))) ),
cls_type_Osplit_1,
[final] ).
cnf(i_0_686,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,hAPP(hAPP(c_Type_Otype_OFun,X4),X5),t_a))) ),
cls_type_Osplit__asm_1,
[final] ).
cnf(i_0_687,axiom,
c_Type_Otype_Otype__rec(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),X5) = hAPP(hAPP(hAPP(hAPP(X2,X3),X4),c_Type_Otype_Otype__rec(X1,X2,X3,X5)),c_Type_Otype_Otype__rec(X1,X2,X4,X5)),
cls_type_Orecs_I2_J_0,
[final] ).
cnf(i_0_688,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_App__eq__foldl__conv_0,
[final] ).
cnf(i_0_689,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
cls_Abs__App__neq__Var__apps_0,
[final] ).
cnf(i_0_690,axiom,
( c_Lambda_OdB_OAbs(X1) = X2
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Abs__eq__apps__conv_0,
[final] ).
cnf(i_0_691,axiom,
( c_Lambda_OdB_OVar(X1) = X2
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Var__eq__apps__conv_0,
[final] ).
cnf(i_0_692,axiom,
( X1 = c_Lambda_OdB_OAbs(X3)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
cls_apps__eq__Abs__conv_0,
[final] ).
cnf(i_0_693,axiom,
( X2 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
cls_apps__eq__Abs__conv_1,
[final] ).
cnf(i_0_694,axiom,
( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Abs__eq__apps__conv_1,
[final] ).
cnf(i_0_695,axiom,
( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Var__eq__apps__conv_1,
[final] ).
cnf(i_0_696,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X4)))
| ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,c_Type_Otype_OAtom(X4),t_a))) ),
cls_type_Osplit_0,
[final] ).
cnf(i_0_697,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X4)))
| ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,c_Type_Otype_OAtom(X4),t_a))) ),
cls_type_Osplit__asm_0,
[final] ).
cnf(i_0_698,axiom,
c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4) = c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4),
cls_shift__commute_0,
[final] ).
cnf(i_0_699,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_U____),
cls_conjecture_0,
[final] ).
cnf(i_0_700,axiom,
c_Lambda_OdB_OdB__case(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(X2,X4),X5),
cls_dB_Osimps_I11_J_0,
[final] ).
cnf(i_0_701,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_App__eq__foldl__conv_4,
[final] ).
cnf(i_0_702,plain,
c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_Lambda_Oliftn(X4,X3,c_HOL_Ozero__class_Ozero(tc_nat)),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,c_Lambda_Oliftn(X4,X3,c_HOL_Ozero__class_Ozero(tc_nat)),X4)),c_Lambda_Osubst(X2,c_Lambda_Oliftn(X4,X3,c_HOL_Ozero__class_Ozero(tc_nat)),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_607,c_0_608]),c_0_608]),c_0_608]),
[final] ).
cnf(i_0_703,axiom,
c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
cls_dB_Orecs_I1_J_0,
[final] ).
cnf(i_0_704,axiom,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X3,X4),
cls_dB_Osimps_I12_J_0,
[final] ).
cnf(i_0_705,axiom,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
cls_dB_Osimps_I10_J_0,
[final] ).
cnf(i_0_706,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
cls_apps__eq__Abs__conv_2,
[final] ).
cnf(i_0_707,axiom,
c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_Abs__eq__apps__conv_2,
[final] ).
cnf(i_0_708,axiom,
c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_Var__eq__apps__conv_2,
[final] ).
cnf(i_0_709,axiom,
c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
cls_foldr_Osimps_I1_J_0,
[final] ).
cnf(i_0_710,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
cls_foldl__Nil_0,
[final] ).
cnf(i_0_711,axiom,
( c_Type_Otyping(X1,c_Lambda_Osubst(X5,X2,X4),X6)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
cls_subst__lemma_0,
[final] ).
cnf(i_0_712,axiom,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,X2,X3))
| ~ c_Type_Otyping(X4,X2,X5)
| ~ c_InductTermi_OIT(X2)
| ~ c_Type_Otyping(c_Type_Oshift(X4,X3,X5,tc_Type_Otype),X1,X6)
| ~ c_InductTermi_OIT(X1) ),
cls_subst__type__IT_0,
[final] ).
cnf(i_0_713,axiom,
( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_Type_Otype),X2,X4) ),
cls_Abs_0,
[final] ).
cnf(i_0_714,axiom,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
cls_nat__diff__split__asm_1,
[final] ).
cnf(i_0_715,axiom,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
cls_nat__diff__split_1,
[final] ).
cnf(i_0_716,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X2,X1,X3),tc_Type_Otype),X3,c_Type_Osko__Type__Xtyping__elims__3__2(X2,X1,X3))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),X2) ),
cls_typing__elims_I3_J_1,
[final] ).
cnf(i_0_717,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
cls_CHAINED_0_01,
[final] ).
cnf(i_0_718,axiom,
( c_Type_Otyping(X1,X2,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2),X3) ),
cls_typing__elims_I2_J_1,
[final] ).
cnf(i_0_719,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_720,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
cls_abs__typeE_0,
[final] ).
cnf(i_0_721,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____),
cls_CHAINED_0,
[final] ).
cnf(i_0_722,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),c_Lambda_Olift(X4,X2),X5)
| ~ c_Type_Otyping(X1,X4,X5) ),
cls_lift__type_0,
[final] ).
cnf(i_0_723,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
cls_le__diff__iff_0,
[final] ).
cnf(i_0_724,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X3,X1,tc_nat) ),
cls_less__diff__iff_0,
[final] ).
cnf(i_0_725,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Suc(X4),X1),c_Power_Opower__class_Opower(X3,c_Suc(X4),X1),X1) ),
cls_power__le__imp__le__base_0,
[final] ).
cnf(i_0_726,axiom,
( hAPP(c_Type_Oshift(X1,X2,X3,X4),X5) = hAPP(X1,X5)
| ~ c_HOL_Oord__class_Oless(X5,X2,tc_nat) ),
cls_shift__gt_0,
[final] ).
cnf(i_0_727,axiom,
c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
cls_dB_Osize_I5_J_0,
[final] ).
cnf(i_0_728,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
cls_power__less__imp__less__base_0,
[final] ).
cnf(i_0_729,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_power__strict__mono_0,
[final] ).
cnf(i_0_730,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
cls_max__add__distrib__left_0,
[final] ).
cnf(i_0_731,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_732,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_le__diff__iff_1,
[final] ).
cnf(i_0_733,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_less__diff__iff_1,
[final] ).
cnf(i_0_734,axiom,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
cls_shift__eq_0,
[final] ).
cnf(i_0_735,axiom,
( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_diff__Suc__diff__eq2_0,
[final] ).
cnf(i_0_736,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),c_Suc(X2),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
cls_diff__Suc__diff__eq1_0,
[final] ).
cnf(i_0_737,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5),X1) ),
cls_le__add__right__mono_0,
[final] ).
cnf(i_0_738,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ),
cls_nat__diff__split_0,
[final] ).
cnf(i_0_739,axiom,
c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)),
cls_subst__App_0,
[final] ).
cnf(i_0_740,axiom,
c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)),
cls_liftn_Osimps_I2_J_0,
[final] ).
cnf(i_0_741,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_Nat_Odiff__diff__eq_0,
[final] ).
cnf(i_0_742,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat)),X2)
| ~ c_lessequals(X3,X1,tc_nat) ),
cls_diff__add__assoc2_0,
[final] ).
cnf(i_0_743,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X3) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_add__diff__assoc2_0,
[final] ).
cnf(i_0_744,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
cls_le__diff__conv2_0,
[final] ).
cnf(i_0_745,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
cls_add__le__cancel__right_0,
[final] ).
cnf(i_0_746,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
cls_add__le__cancel__left_0,
[final] ).
cnf(i_0_747,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
cls_add__less__cancel__right_0,
[final] ).
cnf(i_0_748,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
cls_add__less__cancel__left_0,
[final] ).
cnf(i_0_749,axiom,
( c_lessequals(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
cls_le__diff__conv2_1,
[final] ).
cnf(i_0_750,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_power__eq__imp__eq__base_0,
[final] ).
cnf(i_0_751,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_power__mono_0,
[final] ).
cnf(i_0_752,axiom,
( X1 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X1,X2,X3)),c_Type_Osko__Type__Xtyping__elims__3__2(X1,X2,X3))
| ~ c_Type_Otyping(X2,c_Lambda_OdB_OAbs(X3),X1) ),
cls_typing__elims_I3_J_0,
[final] ).
cnf(i_0_753,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__mono_0,
[final] ).
cnf(i_0_754,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__less__le__mono_0,
[final] ).
cnf(i_0_755,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__less__mono_0,
[final] ).
cnf(i_0_756,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__mono_0,
[final] ).
cnf(i_0_757,axiom,
( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
cls_max__diff__distrib__left_0,
[final] ).
cnf(i_0_758,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
cls_diff__less__mono2_0,
[final] ).
cnf(i_0_759,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_diff__less__mono_0,
[final] ).
cnf(i_0_760,axiom,
( c_lessequals(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
cls_le__add__diff_0,
[final] ).
cnf(i_0_761,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
cls_nat__add__left__cancel__le_0,
[final] ).
cnf(i_0_762,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
cls_nat__add__left__cancel__less_0,
[final] ).
cnf(i_0_763,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
[final] ).
cnf(i_0_764,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_765,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__assoc_0,
[final] ).
cnf(i_0_766,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_767,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0,
[final] ).
cnf(i_0_768,axiom,
( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
| ~ c_Type_Otyping(X1,X3,X5)
| ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X5),X4)) ),
cls_typing_OApp_0,
[final] ).
cnf(i_0_769,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat)
| ~ c_lessequals(X2,X4,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
cls_add__le__mono_0,
[final] ).
cnf(i_0_770,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_add__less__mono_0,
[final] ).
cnf(i_0_771,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) != c_Power_Opower__class_Opower(X4,c_Suc(X3),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_power__inject__base_0,
[final] ).
cnf(i_0_772,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
cls_less__diff__conv_0,
[final] ).
cnf(i_0_773,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
cls_le__diff__conv_0,
[final] ).
cnf(i_0_774,axiom,
c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
cls_dB_Osize_I2_J_0,
[final] ).
cnf(i_0_775,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
cls_add__cancel__21_0,
[final] ).
cnf(i_0_776,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
cls_diff__diff__right_0,
[final] ).
cnf(i_0_777,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
cls_le__diff__conv_1,
[final] ).
cnf(i_0_778,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
cls_less__diff__conv_1,
[final] ).
cnf(i_0_779,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))
| ~ c_lessequals(X3,X2,tc_nat) ),
cls_diff__add__assoc_0,
[final] ).
cnf(i_0_780,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
cls_add__diff__assoc_0,
[final] ).
cnf(i_0_781,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
cls_le__max__iff__disj_0,
[final] ).
cnf(i_0_782,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
cls_less__max__iff__disj_0,
[final] ).
cnf(i_0_783,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X1,tc_nat) = X2
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
cls_le__imp__diff__is__add_1,
[final] ).
cnf(i_0_784,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
cls_nat__add__assoc_0,
[final] ).
cnf(i_0_785,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonpos__nonpos_0,
[final] ).
cnf(i_0_786,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__neg__nonpos_0,
[final] ).
cnf(i_0_787,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonpos__neg_0,
[final] ).
cnf(i_0_788,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__neg__neg_0,
[final] ).
cnf(i_0_789,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__nonneg_0,
[final] ).
cnf(i_0_790,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__pos__nonneg_0,
[final] ).
cnf(i_0_791,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__pos_0,
[final] ).
cnf(i_0_792,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__pos__pos_0,
[final] ).
cnf(i_0_793,axiom,
c_Type_Otype_Otype__case(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),X5) = hAPP(hAPP(X2,X3),X4),
cls_type_Osimps_I6_J_0,
[final] ).
cnf(i_0_794,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_add__increasing2_0,
[final] ).
cnf(i_0_795,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__increasing_0,
[final] ).
cnf(i_0_796,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__strict__increasing_0,
[final] ).
cnf(i_0_797,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__strict__increasing2_0,
[final] ).
cnf(i_0_798,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__le__cancel__left_1,
[final] ).
cnf(i_0_799,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__left__mono_0,
[final] ).
cnf(i_0_800,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__cancel__right_1,
[final] ).
cnf(i_0_801,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__right__mono_0,
[final] ).
cnf(i_0_802,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__strict__left__mono_0,
[final] ).
cnf(i_0_803,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__less__cancel__left_1,
[final] ).
cnf(i_0_804,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__right__mono_0,
[final] ).
cnf(i_0_805,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__less__cancel__right_1,
[final] ).
cnf(i_0_806,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_pos__add__strict_0,
[final] ).
cnf(i_0_807,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
cls_diff__le__mono2_0,
[final] ).
cnf(i_0_808,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
cls_diff__le__mono_0,
[final] ).
cnf(i_0_809,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
cls_add__gr__0_0,
[final] ).
cnf(i_0_810,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__max_Ole__supI_0,
[final] ).
cnf(i_0_811,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__max_Osup__least_0,
[final] ).
cnf(i_0_812,axiom,
( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__max_Ole__sup__iff_2,
[final] ).
cnf(i_0_813,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_max__less__iff__conj_2,
[final] ).
cnf(i_0_814,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X2) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_le__add__diff__inverse2_0,
[final] ).
cnf(i_0_815,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X1)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__imp__diff__is__add_0,
[final] ).
cnf(i_0_816,axiom,
( X1 = X3
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_eq__diff__iff_0,
[final] ).
cnf(i_0_817,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_diff__less_0,
[final] ).
cnf(i_0_818,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
cls_Suc__diff__diff_0,
[final] ).
cnf(i_0_819,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__assoc_0,
[final] ).
cnf(i_0_820,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__left__commute_0,
[final] ).
cnf(i_0_821,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__iff__diff__le__0_1,
[final] ).
cnf(i_0_822,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__iff__diff__less__0_1,
[final] ).
cnf(i_0_823,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
cls_zero__le__double__add__iff__zero__le__single__add_0,
[final] ).
cnf(i_0_824,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
cls_zero__less__double__add__iff__zero__less__single__add_0,
[final] ).
cnf(i_0_825,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__le__zero__iff__single__add__le__zero_0,
[final] ).
cnf(i_0_826,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_even__less__0__iff_0,
[final] ).
cnf(i_0_827,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__less__zero__iff__single__less__zero_0,
[final] ).
cnf(i_0_828,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
cls_le__eqI_1,
[final] ).
cnf(i_0_829,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__eqI_0,
[final] ).
cnf(i_0_830,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
cls_less__eqI_1,
[final] ).
cnf(i_0_831,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__eqI_0,
[final] ).
cnf(i_0_832,axiom,
c_List_Odrop(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,X4),
cls_drop__replicate_0,
[final] ).
cnf(i_0_833,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
cls_nat__add__left__cancel__le_1,
[final] ).
cnf(i_0_834,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
cls_add__le__mono1_0,
[final] ).
cnf(i_0_835,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_nat__add__left__cancel__less_1,
[final] ).
cnf(i_0_836,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_add__less__mono1_0,
[final] ).
cnf(i_0_837,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
cls_min__max_Ole__supE_0,
[final] ).
cnf(i_0_838,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
cls_min__max_Ole__sup__iff_0,
[final] ).
cnf(i_0_839,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
cls_min__max_Ole__supE_1,
[final] ).
cnf(i_0_840,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
cls_min__max_Ole__sup__iff_1,
[final] ).
cnf(i_0_841,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
cls_max__less__iff__conj_0,
[final] ).
cnf(i_0_842,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
cls_max__less__iff__conj_1,
[final] ).
cnf(i_0_843,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__21_1,
[final] ).
cnf(i_0_844,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_845,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__left__commute_0,
[final] ).
cnf(i_0_846,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
cls_lem0_0,
[final] ).
cnf(i_0_847,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X1) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oring__1(X1)
| ~ c_lessequals(X3,X2,tc_nat) ),
cls_of__nat__diff_0,
[final] ).
cnf(i_0_848,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
cls_diff__commute_0,
[final] ).
cnf(i_0_849,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X2) = c_Orderings_Oord__class_Omax(X1,X2,tc_nat),
cls_nat__minus__add__max_0,
[final] ).
cnf(i_0_850,axiom,
c_List_Odrop(X1,c_List_Odrop(X2,X3,X4),X4) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4),
cls_drop__drop_0,
[final] ).
cnf(i_0_851,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
cls_zero__less__diff_0,
[final] ).
cnf(i_0_852,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
cls_diff__diff__left_0,
[final] ).
cnf(i_0_853,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__eq__0__iff_0,
[final] ).
cnf(i_0_854,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__eq__0__iff_1,
[final] ).
cnf(i_0_855,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
cls_diff__cancel_0,
[final] ).
cnf(i_0_856,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
cls_diff__cancel2_0,
[final] ).
cnf(i_0_857,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(rw,[status(thm)],[i_0_609,c_0_608]),
[final] ).
cnf(i_0_858,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
cls_less__add__eq__less_0,
[final] ).
cnf(i_0_859,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
cls_add__leE_0,
[final] ).
cnf(i_0_860,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),X2,tc_nat) ),
cls_add__leE_1,
[final] ).
cnf(i_0_861,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
cls_add__lessD1_0,
[final] ).
cnf(i_0_862,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__add__cancel_0,
[final] ).
cnf(i_0_863,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
cls_nat__add__left__commute_0,
[final] ).
cnf(i_0_864,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__power_0,
[final] ).
cnf(i_0_865,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__power_0,
[final] ).
cnf(i_0_866,axiom,
c_Type_Otype_Otype__case(X1,X2,c_Type_Otype_OAtom(X3),X4) = hAPP(X1,X3),
cls_type_Osimps_I5_J_0,
[final] ).
cnf(i_0_867,axiom,
c_Type_Otype_Otype__rec(X1,X2,c_Type_Otype_OAtom(X3),X4) = hAPP(X1,X3),
cls_type_Orecs_I1_J_0,
[final] ).
cnf(i_0_868,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__le__zero__iff__single__add__le__zero_1,
[final] ).
cnf(i_0_869,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_even__less__0__iff_1,
[final] ).
cnf(i_0_870,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__less__zero__iff__single__less__zero_1,
[final] ).
cnf(i_0_871,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__double__add__iff__zero__le__single__add_1,
[final] ).
cnf(i_0_872,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__double__add__iff__zero__less__single__add_1,
[final] ).
cnf(i_0_873,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__diff__le__0_0,
[final] ).
cnf(i_0_874,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__iff__diff__less__0_0,
[final] ).
cnf(i_0_875,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_diff__Suc__less_0,
[final] ).
cnf(i_0_876,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Ole__supI1_0,
[final] ).
cnf(i_0_877,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__max__iff__disj_1,
[final] ).
cnf(i_0_878,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_min__max_Ole__supI2_0,
[final] ).
cnf(i_0_879,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__max__iff__disj_2,
[final] ).
cnf(i_0_880,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__max__iff__disj_1,
[final] ).
cnf(i_0_881,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_min__max_Oless__supI1_0,
[final] ).
cnf(i_0_882,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_less__max__iff__disj_2,
[final] ).
cnf(i_0_883,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_min__max_Oless__supI2_0,
[final] ).
cnf(i_0_884,axiom,
( c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_Suc__diff__le_0,
[final] ).
cnf(i_0_885,axiom,
( c_Lambda_Obeta(c_Lambda_Osubst(X1,X2,X3),c_Lambda_Osubst(X4,X2,X3))
| ~ c_Lambda_Obeta(X1,X4) ),
cls_subst__preserves__beta_0,
[final] ).
cnf(i_0_886,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
cls_zero__less__diff_1,
[final] ).
cnf(i_0_887,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X2
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_diff__diff__cancel_0,
[final] ).
cnf(i_0_888,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1)),c_Nat_Osemiring__1__class_Oof__nat(X3,X1))
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__add_0,
[final] ).
cnf(i_0_889,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_less__imp__diff__less_0,
[final] ).
cnf(i_0_890,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
cls_less__iff__Suc__add_1,
[final] ).
cnf(i_0_891,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
cls_less__add__Suc1_0,
[final] ).
cnf(i_0_892,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
cls_less__add__Suc2_0,
[final] ).
cnf(i_0_893,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_add__gr__0_1,
[final] ).
cnf(i_0_894,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_add__gr__0_2,
[final] ).
cnf(i_0_895,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__add__diff__inverse_0,
[final] ).
cnf(i_0_896,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__trans_0,
[final] ).
cnf(i_0_897,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I6_J_0,
[final] ).
cnf(i_0_898,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__le__trans_0,
[final] ).
cnf(i_0_899,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__le__less__trans_0,
[final] ).
cnf(i_0_900,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__trans_0,
[final] ).
cnf(i_0_901,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I8_J_0,
[final] ).
cnf(i_0_902,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I7_J_0,
[final] ).
cnf(i_0_903,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I10_J_0,
[final] ).
cnf(i_0_904,plain,
c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X1,c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(rw,[status(thm)],[i_0_610,c_0_608]),
[final] ).
cnf(i_0_905,plain,
( X1 = X3
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3) = c_Lambda_OdB_OVar(X1)
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
inference(rw,[status(thm)],[i_0_611,c_0_608]),
[final] ).
cnf(i_0_906,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
cls_of__nat__le__iff_0,
[final] ).
cnf(i_0_907,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
cls_of__nat__less__iff_0,
[final] ).
cnf(i_0_908,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_less__trans__Suc_0,
[final] ).
cnf(i_0_909,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_termination__basic__simps_I3_J_0,
[final] ).
cnf(i_0_910,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_trans__le__add1_0,
[final] ).
cnf(i_0_911,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
cls_termination__basic__simps_I4_J_0,
[final] ).
cnf(i_0_912,axiom,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
cls_trans__le__add2_0,
[final] ).
cnf(i_0_913,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_trans__less__add1_0,
[final] ).
cnf(i_0_914,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_termination__basic__simps_I1_J_0,
[final] ).
cnf(i_0_915,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_trans__less__add2_0,
[final] ).
cnf(i_0_916,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_termination__basic__simps_I2_J_0,
[final] ).
cnf(i_0_917,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
cls_not__add__less1_0,
[final] ).
cnf(i_0_918,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
cls_not__add__less2_0,
[final] ).
cnf(i_0_919,axiom,
c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))),
cls_beta_0,
[final] ).
cnf(i_0_920,axiom,
( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = c_Orderings_Oord__class_Omax(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__left__idem_0,
[final] ).
cnf(i_0_921,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_Suc__pred_0,
[final] ).
cnf(i_0_922,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
cls_le__trans_0,
[final] ).
cnf(i_0_923,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_HOL_Oord__class_Oless(X3,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
cls_infinite__descent0_2,
[final] ).
cnf(i_0_924,axiom,
( c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_liftn_Osimps_I1_J_1,
[final] ).
cnf(i_0_925,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
cls_add__diff__inverse_0,
[final] ).
cnf(i_0_926,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_less__le__not__le_2,
[final] ).
cnf(i_0_927,axiom,
c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)),
cls_lift_Osimps_I2_J_0,
[final] ).
cnf(i_0_928,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
cls_of__nat__0__less__iff_0,
[final] ).
cnf(i_0_929,axiom,
( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X2,X3,tc_nat) ),
cls_of__nat__le__iff_1,
[final] ).
cnf(i_0_930,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_of__nat__less__iff_1,
[final] ).
cnf(i_0_931,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
cls_upt_Oinduct_1,
[final] ).
cnf(i_0_932,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1))))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
cls_nat_Oinduct_1,
[final] ).
cnf(i_0_933,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
cls_nat__less__cases_0,
[final] ).
cnf(i_0_934,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(cn,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_935,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_of__nat__0__less__iff_1,
[final] ).
cnf(i_0_936,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_order__antisym__conv_0,
[final] ).
cnf(i_0_937,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__antisym_0,
[final] ).
cnf(i_0_938,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__eq__iff_2,
[final] ).
cnf(i_0_939,axiom,
c_Lambda_Oliftn(c_Suc(X1),X2,X3) = c_Lambda_Olift(c_Lambda_Oliftn(X1,X2,X3),X3),
cls_liftn__lift_0,
[final] ).
cnf(i_0_940,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_class__ringb_Oadd__cancel_0,
[final] ).
cnf(i_0_941,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
cls_eq__eqI_1,
[final] ).
cnf(i_0_942,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
cls_eq__eqI_0,
[final] ).
cnf(i_0_943,axiom,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3))
| ~ c_Lambda_Obeta(X2,X3) ),
cls_appR_0,
[final] ).
cnf(i_0_944,axiom,
( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
| ~ c_Lambda_Obeta(X1,X3) ),
cls_appL_0,
[final] ).
cnf(i_0_945,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__antisym__conv2_1,
[final] ).
cnf(i_0_946,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_linorder__not__less_1,
[final] ).
cnf(i_0_947,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_linorder__not__le_1,
[final] ).
cnf(i_0_948,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_not__less__iff__gr__or__eq_1,
[final] ).
cnf(i_0_949,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_less__le__not__le_1,
[final] ).
cnf(i_0_950,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_H_0,
[final] ).
cnf(i_0_951,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_0,
[final] ).
cnf(i_0_952,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_xt1_I9_J_0,
[final] ).
cnf(i_0_953,axiom,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
cls_le__less__Suc__eq_0,
[final] ).
cnf(i_0_954,axiom,
( X2 = X5
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
cls_replicate__eq__replicate_1,
[final] ).
cnf(i_0_955,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
cls_not__less__eq__eq_1,
[final] ).
cnf(i_0_956,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
cls_not__less__eq_1,
[final] ).
cnf(i_0_957,axiom,
( X2 = X1
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_diffs0__imp__equal_0,
[final] ).
cnf(i_0_958,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
cls_add__right__cancel_0,
[final] ).
cnf(i_0_959,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__left__cancel_0,
[final] ).
cnf(i_0_960,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__imp__eq_0,
[final] ).
cnf(i_0_961,axiom,
( X1 = X4
| c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
cls_replicate__eq__replicate_0,
[final] ).
cnf(i_0_962,axiom,
c_Orderings_Oord__class_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X1,X2,tc_nat)),
cls_max__Suc__Suc_0,
[final] ).
cnf(i_0_963,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__antisym_0,
[final] ).
cnf(i_0_964,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_le__maxI1_0,
[final] ).
cnf(i_0_965,axiom,
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X2,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_le__maxI2_0,
[final] ).
cnf(i_0_966,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__diff__cancel_0,
[final] ).
cnf(i_0_967,axiom,
( c_Type_Otyping(X1,X2,X3)
| ~ c_Lambda_Obeta(X4,X2)
| ~ c_Type_Otyping(X1,X4,X3) ),
cls_subject__reduction_0,
[final] ).
cnf(i_0_968,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
cls_diff__less__Suc_0,
[final] ).
cnf(i_0_969,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
cls_diff__le__self_0,
[final] ).
cnf(i_0_970,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
cls_Suc__le__mono_0,
[final] ).
cnf(i_0_971,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
cls_Suc__less__eq_0,
[final] ).
cnf(i_0_972,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
cls_infinite__descent0_1,
[final] ).
cnf(i_0_973,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
cls_add__Suc_0,
[final] ).
cnf(i_0_974,axiom,
( X1 = c_Suc(X2)
| c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
cls_le__SucE_0,
[final] ).
cnf(i_0_975,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv2_0,
[final] ).
cnf(i_0_976,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv1_0,
[final] ).
cnf(i_0_977,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__neq__le__trans_0,
[final] ).
cnf(i_0_978,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__neq__trans_0,
[final] ).
cnf(i_0_979,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__less__le_2,
[final] ).
cnf(i_0_980,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__less_0,
[final] ).
cnf(i_0_981,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I12_J_0,
[final] ).
cnf(i_0_982,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I11_J_0,
[final] ).
cnf(i_0_983,axiom,
( hBOOL(hAPP(X1,X2))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X1),tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
cls_infinite__descent0_0,
[final] ).
cnf(i_0_984,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Omax(X2,X3,X1) != X3 ),
cls_min__max_Ole__iff__sup_1,
[final] ).
cnf(i_0_985,axiom,
( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_Suc__le__mono_1,
[final] ).
cnf(i_0_986,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_Suc__mono_0,
[final] ).
cnf(i_0_987,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_less__Suc__eq__0__disj_3,
[final] ).
cnf(i_0_988,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_min__max_Osup__absorb1_0,
[final] ).
cnf(i_0_989,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Ole__iff__sup_0,
[final] ).
cnf(i_0_990,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
cls_not__less__less__Suc__eq_0,
[final] ).
cnf(i_0_991,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
cls_less__SucE_0,
[final] ).
cnf(i_0_992,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
cls_less__antisym_0,
[final] ).
cnf(i_0_993,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_Suc__lessI_0,
[final] ).
cnf(i_0_994,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_subst__lt_0,
[final] ).
cnf(i_0_995,axiom,
( c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3) = c_Lambda_OdB_OVar(X2)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_liftn_Osimps_I1_J_0,
[final] ).
cnf(i_0_996,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_order__less__imp__le_0,
[final] ).
cnf(i_0_997,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_order__le__less_1,
[final] ).
cnf(i_0_998,axiom,
( X1 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
cls_nat__add__right__cancel_0,
[final] ).
cnf(i_0_999,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
cls_nat__add__left__cancel_0,
[final] ).
cnf(i_0_1000,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
cls_natgb_Oadd__cancel_0,
[final] ).
cnf(i_0_1001,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
cls_Suc__leD_0,
[final] ).
cnf(i_0_1002,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
cls_less__eq__Suc__le_1,
[final] ).
cnf(i_0_1003,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
cls_Suc__le__eq_0,
[final] ).
cnf(i_0_1004,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
cls_Suc__lessD_0,
[final] ).
cnf(i_0_1005,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
cls_less__Suc__eq__le_0,
[final] ).
cnf(i_0_1006,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
cls_add__Suc__right_0,
[final] ).
cnf(i_0_1007,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_diff__add__0_0,
[final] ).
cnf(i_0_1008,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
cls_diff__add__inverse_0,
[final] ).
cnf(i_0_1009,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
cls_diff__add__inverse2_0,
[final] ).
cnf(i_0_1010,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_of__nat__less__0__iff_0,
[final] ).
cnf(i_0_1011,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_less__eq__Suc__le_0,
[final] ).
cnf(i_0_1012,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_Suc__leI_0,
[final] ).
cnf(i_0_1013,axiom,
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__SucI_0,
[final] ).
cnf(i_0_1014,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X1,tc_nat) ),
cls_le__less__Suc__eq_1,
[final] ).
cnf(i_0_1015,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_less__Suc__eq__le_1,
[final] ).
cnf(i_0_1016,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_less__SucI_0,
[final] ).
cnf(i_0_1017,axiom,
c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat),
cls_le__iff__add_1,
[final] ).
cnf(i_0_1018,axiom,
c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat),
cls_le__add1_0,
[final] ).
cnf(i_0_1019,axiom,
c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat),
cls_le__add2_0,
[final] ).
cnf(i_0_1020,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_diff__is__0__eq_0,
[final] ).
cnf(i_0_1021,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__neq__implies__less_0,
[final] ).
cnf(i_0_1022,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__eq__less__or__eq_0,
[final] ).
cnf(i_0_1023,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_nat__less__le_2,
[final] ).
cnf(i_0_1024,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_diff__is__0__eq_1,
[final] ).
cnf(i_0_1025,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_nat__less__le_0,
[final] ).
cnf(i_0_1026,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_termination__basic__simps_I5_J_0,
[final] ).
cnf(i_0_1027,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
cls_upt_Oinduct_0,
[final] ).
cnf(i_0_1028,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
| ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
cls_nat_Oinduct_0,
[final] ).
cnf(i_0_1029,axiom,
( c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))
| ~ c_InductTermi_OIT(X1) ),
cls_subst__Var__IT_0,
[final] ).
cnf(i_0_1030,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_power__eq__0__iff_0,
[final] ).
cnf(i_0_1031,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_power__eq__0__iff_1,
[final] ).
cnf(i_0_1032,axiom,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X2))
| c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3) ),
cls_type__induct_0,
[final] ).
cnf(i_0_1033,axiom,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X3))
| c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3) ),
cls_type__induct_1,
[final] ).
cnf(i_0_1034,axiom,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
cls_dB_Osize_I6_J_0,
[final] ).
cnf(i_0_1035,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
cls_subst__Var_2,
[final] ).
cnf(i_0_1036,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_linorder__neqE__ordered__idom_0,
[final] ).
cnf(i_0_1037,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv3_0,
[final] ).
cnf(i_0_1038,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__less__linear_0,
[final] ).
cnf(i_0_1039,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__neqE_0,
[final] ).
cnf(i_0_1040,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__less__iff__gr__or__eq_0,
[final] ).
cnf(i_0_1041,axiom,
( X1 = X3
| hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
cls_type_Osimps_I2_J_0,
[final] ).
cnf(i_0_1042,axiom,
( X1 = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
cls_dB_Osimps_I2_J_0,
[final] ).
cnf(i_0_1043,axiom,
( X2 = X4
| hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
cls_type_Osimps_I2_J_1,
[final] ).
cnf(i_0_1044,axiom,
( X2 = X4
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
cls_dB_Osimps_I2_J_1,
[final] ).
cnf(i_0_1045,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
cls_diff__Suc__Suc_0,
[final] ).
cnf(i_0_1046,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_1047,axiom,
( c_HOL_Oord__class_Oless(X2,X2,X1)
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv1_1,
[final] ).
cnf(i_0_1048,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__le_0,
[final] ).
cnf(i_0_1049,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__leE_0,
[final] ).
cnf(i_0_1050,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__less_0,
[final] ).
cnf(i_0_1051,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = c_Orderings_Oord__class_Omax(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__commute_0,
[final] ).
cnf(i_0_1052,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2 ),
cls_subst__Var_1,
[final] ).
cnf(i_0_1053,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2),
cls_replicate__eq__replicate_2,
[final] ).
cnf(i_0_1054,axiom,
c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
cls_App_I1_J_0,
[final] ).
cnf(i_0_1055,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
cls_not__less__eq__eq_0,
[final] ).
cnf(i_0_1056,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
cls_not__less__less__Suc__eq_1,
[final] ).
cnf(i_0_1057,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
cls_not__less__eq_0,
[final] ).
cnf(i_0_1058,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__c_0,
[final] ).
cnf(i_0_1059,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_1060,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__commute_0,
[final] ).
cnf(i_0_1061,axiom,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
cls_typing__elims_I1_J_0,
[final] ).
cnf(i_0_1062,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
cls_add__Suc__shift_0,
[final] ).
cnf(i_0_1063,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
cls_linorder__neqE__nat_0,
[final] ).
cnf(i_0_1064,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
cls_nat__neq__iff_0,
[final] ).
cnf(i_0_1065,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_class__ringb_Osubr0__iff_0,
[final] ).
cnf(i_0_1066,axiom,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_lift_Osimps_I1_J_0,
[final] ).
cnf(i_0_1067,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
cls_less__Suc0_0,
[final] ).
cnf(i_0_1068,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
cls_nat__le__linear_0,
[final] ).
cnf(i_0_1069,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_field__power__not__zero_0,
[final] ).
cnf(i_0_1070,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
cls_class__ringb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_1071,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__iff__diff__eq__0_1,
[final] ).
cnf(i_0_1072,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_right__minus__eq_0,
[final] ).
cnf(i_0_1073,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_double__eq__0__iff_0,
[final] ).
cnf(i_0_1074,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_1,
[final] ).
cnf(i_0_1075,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_one__is__add_1,
[final] ).
cnf(i_0_1076,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Type_Osko__Type__Xtype__induct__1__1(X1))) ),
cls_type__induct_2,
[final] ).
cnf(i_0_1077,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1) ),
cls_power__eq__0__iff_2,
[final] ).
cnf(i_0_1078,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_0,
[final] ).
cnf(i_0_1079,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_3,
[final] ).
cnf(i_0_1080,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_one__is__add_0,
[final] ).
cnf(i_0_1081,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_one__is__add_3,
[final] ).
cnf(i_0_1082,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
cls_replicate__empty_0,
[final] ).
cnf(i_0_1083,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Olist_ONil(X1) != c_List_Oreplicate(X2,X3,X1) ),
cls_empty__replicate_0,
[final] ).
cnf(i_0_1084,axiom,
( c_InductTermi_OIT(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2)))
| ~ c_InductTermi_OIT(X1) ),
cls_app__Var__IT_0,
[final] ).
cnf(i_0_1085,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__le__imp__of__nat_0,
[final] ).
cnf(i_0_1086,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_of__nat__0__le__iff_0,
[final] ).
cnf(i_0_1087,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_1088,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_1089,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_1090,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_neq0__conv_1,
[final] ).
cnf(i_0_1091,axiom,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
cls_Suc__n__not__le__n_0,
[final] ).
cnf(i_0_1092,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
cls_le__0__eq_0,
[final] ).
cnf(i_0_1093,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
cls_nat__add__commute_0,
[final] ).
cnf(i_0_1094,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_2,
[final] ).
cnf(i_0_1095,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_one__is__add_2,
[final] ).
cnf(i_0_1096,axiom,
( c_Lambda_Obeta(c_Lambda_Olift(X1,X2),c_Lambda_Olift(X3,X2))
| ~ c_Lambda_Obeta(X1,X3) ),
cls_lift__preserves__beta_0,
[final] ).
cnf(i_0_1097,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_not__less0_0,
[final] ).
cnf(i_0_1098,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_gr__implies__not0_0,
[final] ).
cnf(i_0_1099,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
cls_ATP__Linkup_Ofequal__imp__equal_0,
[final] ).
cnf(i_0_1100,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
cls_typing_OVar_0,
[final] ).
cnf(i_0_1101,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0__Suc_0,
[final] ).
cnf(i_0_1102,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_less__not__refl_0,
[final] ).
cnf(i_0_1103,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_nat__less__le_1,
[final] ).
cnf(i_0_1104,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0__left_1,
[final] ).
cnf(i_0_1105,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_double__eq__0__iff_1,
[final] ).
cnf(i_0_1106,axiom,
c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
cls_subst__lift_0,
[final] ).
cnf(i_0_1107,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
cls_add__is__1_4,
[final] ).
cnf(i_0_1108,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
cls_one__is__add_4,
[final] ).
cnf(i_0_1109,axiom,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
cls_dB_Osize_I3_J_0,
[final] ).
cnf(i_0_1110,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_add__is__0_0,
[final] ).
cnf(i_0_1111,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_add__is__0_1,
[final] ).
cnf(i_0_1112,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
cls_add__eq__self__zero_0,
[final] ).
cnf(i_0_1113,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_natgb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_1114,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_1115,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Osubr0__iff_1,
[final] ).
cnf(i_0_1116,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_add__0__left_0,
[final] ).
cnf(i_0_1117,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I5_J_0,
[final] ).
cnf(i_0_1118,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__0_0,
[final] ).
cnf(i_0_1119,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1_0,
[final] ).
cnf(i_0_1120,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
cls_add__is__1_5,
[final] ).
cnf(i_0_1121,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
cls_one__is__add_5,
[final] ).
cnf(i_0_1122,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__0__right_0,
[final] ).
cnf(i_0_1123,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
cls_less__Suc0_1,
[final] ).
cnf(i_0_1124,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0,
[final] ).
cnf(i_0_1125,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_monoid__add__class_Oadd__0__right_0,
[final] ).
cnf(i_0_1126,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0,
[final] ).
cnf(i_0_1127,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1__right_0,
[final] ).
cnf(i_0_1128,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_eq__iff__diff__eq__0_0,
[final] ).
cnf(i_0_1129,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus__eq_1,
[final] ).
cnf(i_0_1130,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__self_0,
[final] ).
cnf(i_0_1131,axiom,
c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
cls_le__Suc__eq_2,
[final] ).
cnf(i_0_1132,axiom,
c_List_Odrop(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
cls_drop__Nil_0,
[final] ).
cnf(i_0_1133,axiom,
hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != c_Type_Otype_OAtom(X3),
cls_type_Osimps_I4_J_0,
[final] ).
cnf(i_0_1134,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
cls_dB_Osimps_I8_J_0,
[final] ).
cnf(i_0_1135,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
cls_dB_Osimps_I5_J_0,
[final] ).
cnf(i_0_1136,axiom,
c_Type_Otype_OAtom(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3),
cls_type_Osimps_I3_J_0,
[final] ).
cnf(i_0_1137,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
cls_dB_Osimps_I9_J_0,
[final] ).
cnf(i_0_1138,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
cls_dB_Osimps_I4_J_0,
[final] ).
cnf(i_0_1139,axiom,
( c_Orderings_Oord__class_Omax(X2,X2,X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__idem_0,
[final] ).
cnf(i_0_1140,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_gr0__conv__Suc_1,
[final] ).
cnf(i_0_1141,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_zero__less__Suc_0,
[final] ).
cnf(i_0_1142,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_1143,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_1144,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
cls_replicate__empty_1,
[final] ).
cnf(i_0_1145,axiom,
c_List_Olist_ONil(X1) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X1),
cls_empty__replicate_1,
[final] ).
cnf(i_0_1146,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
cls_subst__eq_0,
[final] ).
cnf(i_0_1147,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_gr0I_0,
[final] ).
cnf(i_0_1148,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_le__0__eq_1,
[final] ).
cnf(i_0_1149,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_less__Suc__eq_2,
[final] ).
cnf(i_0_1150,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_lessI_0,
[final] ).
cnf(i_0_1151,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_diff__0__eq__0_0,
[final] ).
cnf(i_0_1152,axiom,
c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
cls_drop__0_0,
[final] ).
cnf(i_0_1153,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
cls_liftn__0_0,
[final] ).
cnf(i_0_1154,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_add__is__0_2,
[final] ).
cnf(i_0_1155,axiom,
c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
cls_max__0L_0,
[final] ).
cnf(i_0_1156,axiom,
c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
cls_max__0R_0,
[final] ).
cnf(i_0_1157,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
cls_minus__nat_Odiff__0_0,
[final] ).
cnf(i_0_1158,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
cls_le0_0,
[final] ).
cnf(i_0_1159,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_diff__self__eq__0_0,
[final] ).
cnf(i_0_1160,axiom,
c_fequal(X1,X1,X2),
cls_ATP__Linkup_Oequal__imp__fequal_0,
[final] ).
cnf(i_0_1161,axiom,
( X2 = X3
| ~ class_Nat_Osemiring__char__0(X1)
| c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
cls_of__nat__eq__iff_0,
[final] ).
cnf(i_0_1162,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
cls_plus__nat_Oadd__0_0,
[final] ).
cnf(i_0_1163,axiom,
c_lessequals(X1,X1,tc_nat),
cls_eq__imp__le_0,
[final] ).
cnf(i_0_1164,axiom,
c_lessequals(X1,X1,tc_nat),
cls_le__refl_0,
[final] ).
cnf(i_0_1165,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
cls_Nat_Oadd__0__right_0,
[final] ).
cnf(i_0_1166,axiom,
X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
cls_natgb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_1167,axiom,
c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
cls_App_I3_J_0,
[final] ).
cnf(i_0_1168,axiom,
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
| ~ c_Lambda_Obeta(X1,X2) ),
cls_abs_0,
[final] ).
cnf(i_0_1169,axiom,
( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
| ~ c_InductTermi_OIT(X1) ),
cls_lift__IT_0,
[final] ).
cnf(i_0_1170,axiom,
( class_Orderings_Obot(tc_fun(X1,X2))
| ~ class_Orderings_Obot(X2) ),
clsarity_fun__Orderings_Obot,
[final] ).
cnf(i_0_1171,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
clsarity_fun__Orderings_Opreorder,
[final] ).
cnf(i_0_1172,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
clsarity_fun__Orderings_Oorder,
[final] ).
cnf(i_0_1173,axiom,
~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
cls_beta__cases_I1_J_0,
[final] ).
cnf(i_0_1174,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__0_0,
[final] ).
cnf(i_0_1175,axiom,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_dB_Osize_I4_J_0,
[final] ).
cnf(i_0_1176,axiom,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
cls_Lambda_0,
[final] ).
cnf(i_0_1177,axiom,
( X1 = X2
| c_Type_Otype_OAtom(X1) != c_Type_Otype_OAtom(X2) ),
cls_type_Osimps_I1_J_0,
[final] ).
cnf(i_0_1178,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
cls_dB_Osimps_I3_J_0,
[final] ).
cnf(i_0_1179,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
cls_dB_Osimps_I1_J_0,
[final] ).
cnf(i_0_1180,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_nat_Oinject_0,
[final] ).
cnf(i_0_1181,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_Suc__inject_0,
[final] ).
cnf(i_0_1182,axiom,
c_Nat_Osize__class_Osize(X1,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_size__char_0,
[final] ).
cnf(i_0_1183,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
cls_dB_Osimps_I7_J_0,
[final] ).
cnf(i_0_1184,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
cls_dB_Osimps_I6_J_0,
[final] ).
cnf(i_0_1185,axiom,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_dB_Osize_I1_J_0,
[final] ).
cnf(i_0_1186,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
cls_nat_Osimps_I2_J_0,
[final] ).
cnf(i_0_1187,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
cls_Zero__neq__Suc_0,
[final] ).
cnf(i_0_1188,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
cls_nat_Osimps_I3_J_0,
[final] ).
cnf(i_0_1189,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
cls_Suc__neq__Zero_0,
[final] ).
cnf(i_0_1190,axiom,
c_InductTermi_OIT(c_Lambda_OdB_OVar(X1)),
cls_Var__IT_0,
[final] ).
cnf(i_0_1191,axiom,
c_Suc(X1) != X1,
cls_Suc__n__not__n_0,
[final] ).
cnf(i_0_1192,axiom,
X1 != c_Suc(X1),
cls_n__not__Suc__n_0,
[final] ).
cnf(i_0_1193,axiom,
c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_bot__nat__def_0,
[final] ).
cnf(i_0_1194,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__1,
[final] ).
cnf(i_0_1195,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
clsarity_nat__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_1196,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
clsarity_nat__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_1197,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
clsarity_nat__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_1198,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_1199,axiom,
c_InductTermi_OIT(v_ta____),
cls_App_I4_J_0,
[final] ).
cnf(i_0_1200,axiom,
c_InductTermi_OIT(v_s____),
cls_App_I2_J_0,
[final] ).
cnf(i_0_1201,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_1202,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_1203,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
clsarity_nat__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_1204,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_1205,axiom,
class_Nat_Osemiring__char__0(tc_nat),
clsarity_nat__Nat_Osemiring__char__0,
[final] ).
cnf(i_0_1206,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Osemigroup__add,
[final] ).
cnf(i_0_1207,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1208,axiom,
class_Orderings_Obot(tc_nat),
clsarity_nat__Orderings_Obot,
[final] ).
cnf(i_0_1209,axiom,
class_Power_Opower(tc_nat),
clsarity_nat__Power_Opower,
[final] ).
cnf(i_0_1210,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_1211,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder,
[final] ).
cnf(i_0_1212,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_1213,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_1214,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_1215,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_1216,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_1217,axiom,
class_Orderings_Opreorder(tc_nat),
clsarity_nat__Orderings_Opreorder,
[final] ).
cnf(i_0_1218,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder,
[final] ).
cnf(i_0_1219,axiom,
X1 = X1 ).
cnf(i_0_1220,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1221,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1222,axiom,
( X1 != X2
| c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1223,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1224,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1225,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1226,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1227,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X1,X3,X4,X5,X6) = c_Lambda_OdB_OdB__case(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1228,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X3,X1,X4,X5,X6) = c_Lambda_OdB_OdB__case(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1229,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X3,X4,X1,X5,X6) = c_Lambda_OdB_OdB__case(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1230,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X3,X4,X5,X1,X6) = c_Lambda_OdB_OdB__case(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1231,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X3,X4,X5,X6,X1) = c_Lambda_OdB_OdB__case(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1232,axiom,
( X1 != X2
| c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).
cnf(i_0_1233,axiom,
( X1 != X2
| c_Lambda_Osubst(X1,X3,X4) = c_Lambda_Osubst(X2,X3,X4) ) ).
cnf(i_0_1234,axiom,
( X1 != X2
| c_Lambda_Osubst(X3,X1,X4) = c_Lambda_Osubst(X3,X2,X4) ) ).
cnf(i_0_1235,axiom,
( X1 != X2
| c_Lambda_Osubst(X3,X4,X1) = c_Lambda_Osubst(X3,X4,X2) ) ).
cnf(i_0_1236,axiom,
( X1 != X2
| c_Type_Otype_Otype__case(X1,X3,X4,X5) = c_Type_Otype_Otype__case(X2,X3,X4,X5) ) ).
cnf(i_0_1237,axiom,
( X1 != X2
| c_Type_Otype_Otype__case(X3,X1,X4,X5) = c_Type_Otype_Otype__case(X3,X2,X4,X5) ) ).
cnf(i_0_1238,axiom,
( X1 != X2
| c_Type_Otype_Otype__case(X3,X4,X1,X5) = c_Type_Otype_Otype__case(X3,X4,X2,X5) ) ).
cnf(i_0_1239,axiom,
( X1 != X2
| c_Type_Otype_Otype__case(X3,X4,X5,X1) = c_Type_Otype_Otype__case(X3,X4,X5,X2) ) ).
cnf(i_0_1240,axiom,
( X1 != X2
| c_Type_Otype_Otype__rec(X1,X3,X4,X5) = c_Type_Otype_Otype__rec(X2,X3,X4,X5) ) ).
cnf(i_0_1241,axiom,
( X1 != X2
| c_Type_Otype_Otype__rec(X3,X1,X4,X5) = c_Type_Otype_Otype__rec(X3,X2,X4,X5) ) ).
cnf(i_0_1242,axiom,
( X1 != X2
| c_Type_Otype_Otype__rec(X3,X4,X1,X5) = c_Type_Otype_Otype__rec(X3,X4,X2,X5) ) ).
cnf(i_0_1243,axiom,
( X1 != X2
| c_Type_Otype_Otype__rec(X3,X4,X5,X1) = c_Type_Otype_Otype__rec(X3,X4,X5,X2) ) ).
cnf(i_0_1244,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_1245,axiom,
( X1 != X2
| c_Type_Otype_OAtom(X1) = c_Type_Otype_OAtom(X2) ) ).
cnf(i_0_1246,axiom,
( X1 != X2
| c_Type_Oshift(X1,X3,X4,X5) = c_Type_Oshift(X2,X3,X4,X5) ) ).
cnf(i_0_1247,axiom,
( X1 != X2
| c_Type_Oshift(X3,X1,X4,X5) = c_Type_Oshift(X3,X2,X4,X5) ) ).
cnf(i_0_1248,axiom,
( X1 != X2
| c_Type_Oshift(X3,X4,X1,X5) = c_Type_Oshift(X3,X4,X2,X5) ) ).
cnf(i_0_1249,axiom,
( X1 != X2
| c_Type_Oshift(X3,X4,X5,X1) = c_Type_Oshift(X3,X4,X5,X2) ) ).
cnf(i_0_1250,axiom,
( X1 != X2
| c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).
cnf(i_0_1251,axiom,
( X1 != X2
| c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).
cnf(i_0_1252,axiom,
( X1 != X2
| c_Lambda_Oliftn(X1,X3,X4) = c_Lambda_Oliftn(X2,X3,X4) ) ).
cnf(i_0_1253,axiom,
( X1 != X2
| c_Lambda_Oliftn(X3,X1,X4) = c_Lambda_Oliftn(X3,X2,X4) ) ).
cnf(i_0_1254,axiom,
( X1 != X2
| c_Lambda_Oliftn(X3,X4,X1) = c_Lambda_Oliftn(X3,X4,X2) ) ).
cnf(i_0_1255,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_1256,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_1257,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_1258,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_1259,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_1260,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_1261,axiom,
( X1 != X2
| c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1262,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1263,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1264,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1265,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1266,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1267,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1268,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1,X3,X4) = c_Orderings_Oord__class_Omax(X2,X3,X4) ) ).
cnf(i_0_1269,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X3,X1,X4) = c_Orderings_Oord__class_Omax(X3,X2,X4) ) ).
cnf(i_0_1270,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X3,X4,X1) = c_Orderings_Oord__class_Omax(X3,X4,X2) ) ).
cnf(i_0_1271,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__size(X1) = c_Lambda_OdB_OdB__size(X2) ) ).
cnf(i_0_1272,axiom,
( X1 != X2
| c_List_Odrop(X1,X3,X4) = c_List_Odrop(X2,X3,X4) ) ).
cnf(i_0_1273,axiom,
( X1 != X2
| c_List_Odrop(X3,X1,X4) = c_List_Odrop(X3,X2,X4) ) ).
cnf(i_0_1274,axiom,
( X1 != X2
| c_List_Odrop(X3,X4,X1) = c_List_Odrop(X3,X4,X2) ) ).
cnf(i_0_1275,axiom,
( X1 != X2
| c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).
cnf(i_0_1276,axiom,
( X1 != X2
| c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).
cnf(i_0_1277,axiom,
( X1 != X2
| c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).
cnf(i_0_1278,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).
cnf(i_0_1279,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).
cnf(i_0_1280,axiom,
( X1 != X2
| c_Type_Osko__Type__Xtype__induct__1__1(X1) = c_Type_Osko__Type__Xtype__induct__1__1(X2) ) ).
cnf(i_0_1281,axiom,
( X1 != X2
| c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).
cnf(i_0_1282,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1283,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1284,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1285,axiom,
( X1 != X2
| c_Suc(X1) = c_Suc(X2) ) ).
cnf(i_0_1286,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1287,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X1,X3,X4,X5,X6) = c_Lambda_OdB_OdB__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1288,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X3,X1,X4,X5,X6) = c_Lambda_OdB_OdB__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1289,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X3,X4,X1,X5,X6) = c_Lambda_OdB_OdB__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1290,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X3,X4,X5,X1,X6) = c_Lambda_OdB_OdB__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1291,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X3,X4,X5,X6,X1) = c_Lambda_OdB_OdB__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1292,axiom,
( X1 != X2
| ~ c_Type_Otyping(X1,X3,X4)
| c_Type_Otyping(X2,X3,X4) ) ).
cnf(i_0_1293,axiom,
( X1 != X2
| ~ c_Type_Otyping(X3,X1,X4)
| c_Type_Otyping(X3,X2,X4) ) ).
cnf(i_0_1294,axiom,
( X1 != X2
| ~ c_Type_Otyping(X3,X4,X1)
| c_Type_Otyping(X3,X4,X2) ) ).
cnf(i_0_1295,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1296,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1297,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1298,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1299,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1300,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1301,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1302,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_1303,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1304,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1305,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1306,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1307,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1308,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1309,axiom,
( X1 != X2
| ~ c_Type_Otypings(X1,X3,X4)
| c_Type_Otypings(X2,X3,X4) ) ).
cnf(i_0_1310,axiom,
( X1 != X2
| ~ c_Type_Otypings(X3,X1,X4)
| c_Type_Otypings(X3,X2,X4) ) ).
cnf(i_0_1311,axiom,
( X1 != X2
| ~ c_Type_Otypings(X3,X4,X1)
| c_Type_Otypings(X3,X4,X2) ) ).
cnf(i_0_1312,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1313,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_1314,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1315,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1316,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1(X1)
| class_Ring__and__Field_Oring__1(X2) ) ).
cnf(i_0_1317,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1318,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_1319,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1320,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1321,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1322,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X1,X3,X4,X5,X6,X7)
| c_Groebner__Basis_Ogb__semiring(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_1323,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X1,X4,X5,X6,X7)
| c_Groebner__Basis_Ogb__semiring(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_1324,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X4,X1,X5,X6,X7)
| c_Groebner__Basis_Ogb__semiring(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_1325,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X1,X6,X7)
| c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_1326,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X6,X1,X7)
| c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_1327,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X6,X7,X1)
| c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_1328,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1329,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1330,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1331,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_1332,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1333,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1334,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_1335,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_1336,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_1337,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_1338,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_1339,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_1340,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1341,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_1342,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_1343,axiom,
( X1 != X2
| ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(X2) ) ).
cnf(i_0_1344,axiom,
( X1 != X2
| ~ c_Lambda_Obeta(X1,X3)
| c_Lambda_Obeta(X2,X3) ) ).
cnf(i_0_1345,axiom,
( X1 != X2
| ~ c_Lambda_Obeta(X3,X1)
| c_Lambda_Obeta(X3,X2) ) ).
cnf(i_0_1346,axiom,
( X1 != X2
| ~ class_OrderedGroup_Osemigroup__add(X1)
| class_OrderedGroup_Osemigroup__add(X2) ) ).
cnf(i_0_1347,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_1348,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_1219_001,axiom,
X1 = X1 ).
cnf(i_0_1220_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1221_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1222_004,axiom,
( X1 != X2
| c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1223_005,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1224_006,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1225_007,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1226_008,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1227_009,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X1,X3,X4,X5,X6) = c_Lambda_OdB_OdB__case(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1228_010,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X3,X1,X4,X5,X6) = c_Lambda_OdB_OdB__case(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1229_011,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X3,X4,X1,X5,X6) = c_Lambda_OdB_OdB__case(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1230_012,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X3,X4,X5,X1,X6) = c_Lambda_OdB_OdB__case(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1231_013,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__case(X3,X4,X5,X6,X1) = c_Lambda_OdB_OdB__case(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1232_014,axiom,
( X1 != X2
| c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).
cnf(i_0_1233_015,axiom,
( X1 != X2
| c_Lambda_Osubst(X1,X3,X4) = c_Lambda_Osubst(X2,X3,X4) ) ).
cnf(i_0_1234_016,axiom,
( X1 != X2
| c_Lambda_Osubst(X3,X1,X4) = c_Lambda_Osubst(X3,X2,X4) ) ).
cnf(i_0_1235_017,axiom,
( X1 != X2
| c_Lambda_Osubst(X3,X4,X1) = c_Lambda_Osubst(X3,X4,X2) ) ).
cnf(i_0_1236_018,axiom,
( X1 != X2
| c_Type_Otype_Otype__case(X1,X3,X4,X5) = c_Type_Otype_Otype__case(X2,X3,X4,X5) ) ).
cnf(i_0_1237_019,axiom,
( X1 != X2
| c_Type_Otype_Otype__case(X3,X1,X4,X5) = c_Type_Otype_Otype__case(X3,X2,X4,X5) ) ).
cnf(i_0_1238_020,axiom,
( X1 != X2
| c_Type_Otype_Otype__case(X3,X4,X1,X5) = c_Type_Otype_Otype__case(X3,X4,X2,X5) ) ).
cnf(i_0_1239_021,axiom,
( X1 != X2
| c_Type_Otype_Otype__case(X3,X4,X5,X1) = c_Type_Otype_Otype__case(X3,X4,X5,X2) ) ).
cnf(i_0_1240_022,axiom,
( X1 != X2
| c_Type_Otype_Otype__rec(X1,X3,X4,X5) = c_Type_Otype_Otype__rec(X2,X3,X4,X5) ) ).
cnf(i_0_1241_023,axiom,
( X1 != X2
| c_Type_Otype_Otype__rec(X3,X1,X4,X5) = c_Type_Otype_Otype__rec(X3,X2,X4,X5) ) ).
cnf(i_0_1242_024,axiom,
( X1 != X2
| c_Type_Otype_Otype__rec(X3,X4,X1,X5) = c_Type_Otype_Otype__rec(X3,X4,X2,X5) ) ).
cnf(i_0_1243_025,axiom,
( X1 != X2
| c_Type_Otype_Otype__rec(X3,X4,X5,X1) = c_Type_Otype_Otype__rec(X3,X4,X5,X2) ) ).
cnf(i_0_1244_026,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_1245_027,axiom,
( X1 != X2
| c_Type_Otype_OAtom(X1) = c_Type_Otype_OAtom(X2) ) ).
cnf(i_0_1246_028,axiom,
( X1 != X2
| c_Type_Oshift(X1,X3,X4,X5) = c_Type_Oshift(X2,X3,X4,X5) ) ).
cnf(i_0_1247_029,axiom,
( X1 != X2
| c_Type_Oshift(X3,X1,X4,X5) = c_Type_Oshift(X3,X2,X4,X5) ) ).
cnf(i_0_1248_030,axiom,
( X1 != X2
| c_Type_Oshift(X3,X4,X1,X5) = c_Type_Oshift(X3,X4,X2,X5) ) ).
cnf(i_0_1249_031,axiom,
( X1 != X2
| c_Type_Oshift(X3,X4,X5,X1) = c_Type_Oshift(X3,X4,X5,X2) ) ).
cnf(i_0_1250_032,axiom,
( X1 != X2
| c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).
cnf(i_0_1251_033,axiom,
( X1 != X2
| c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).
cnf(i_0_1252_034,axiom,
( X1 != X2
| c_Lambda_Oliftn(X1,X3,X4) = c_Lambda_Oliftn(X2,X3,X4) ) ).
cnf(i_0_1253_035,axiom,
( X1 != X2
| c_Lambda_Oliftn(X3,X1,X4) = c_Lambda_Oliftn(X3,X2,X4) ) ).
cnf(i_0_1254_036,axiom,
( X1 != X2
| c_Lambda_Oliftn(X3,X4,X1) = c_Lambda_Oliftn(X3,X4,X2) ) ).
cnf(i_0_1255_037,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_1256_038,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_1257_039,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_1258_040,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_1259_041,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_1260_042,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_1261_043,axiom,
( X1 != X2
| c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1262_044,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1263_045,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1264_046,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1265_047,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1266_048,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1267_049,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1268_050,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1,X3,X4) = c_Orderings_Oord__class_Omax(X2,X3,X4) ) ).
cnf(i_0_1269_051,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X3,X1,X4) = c_Orderings_Oord__class_Omax(X3,X2,X4) ) ).
cnf(i_0_1270_052,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X3,X4,X1) = c_Orderings_Oord__class_Omax(X3,X4,X2) ) ).
cnf(i_0_1271_053,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__size(X1) = c_Lambda_OdB_OdB__size(X2) ) ).
cnf(i_0_1272_054,axiom,
( X1 != X2
| c_List_Odrop(X1,X3,X4) = c_List_Odrop(X2,X3,X4) ) ).
cnf(i_0_1273_055,axiom,
( X1 != X2
| c_List_Odrop(X3,X1,X4) = c_List_Odrop(X3,X2,X4) ) ).
cnf(i_0_1274_056,axiom,
( X1 != X2
| c_List_Odrop(X3,X4,X1) = c_List_Odrop(X3,X4,X2) ) ).
cnf(i_0_1275_057,axiom,
( X1 != X2
| c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).
cnf(i_0_1276_058,axiom,
( X1 != X2
| c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).
cnf(i_0_1277_059,axiom,
( X1 != X2
| c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).
cnf(i_0_1278_060,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).
cnf(i_0_1279_061,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).
cnf(i_0_1280_062,axiom,
( X1 != X2
| c_Type_Osko__Type__Xtype__induct__1__1(X1) = c_Type_Osko__Type__Xtype__induct__1__1(X2) ) ).
cnf(i_0_1281_063,axiom,
( X1 != X2
| c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).
cnf(i_0_1282_064,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1283_065,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1284_066,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1285_067,axiom,
( X1 != X2
| c_Suc(X1) = c_Suc(X2) ) ).
cnf(i_0_1286_068,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1287_069,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X1,X3,X4,X5,X6) = c_Lambda_OdB_OdB__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1288_070,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X3,X1,X4,X5,X6) = c_Lambda_OdB_OdB__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1289_071,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X3,X4,X1,X5,X6) = c_Lambda_OdB_OdB__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1290_072,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X3,X4,X5,X1,X6) = c_Lambda_OdB_OdB__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1291_073,axiom,
( X1 != X2
| c_Lambda_OdB_OdB__rec(X3,X4,X5,X6,X1) = c_Lambda_OdB_OdB__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1292_074,axiom,
( X1 != X2
| ~ c_Type_Otyping(X1,X3,X4)
| c_Type_Otyping(X2,X3,X4) ) ).
cnf(i_0_1293_075,axiom,
( X1 != X2
| ~ c_Type_Otyping(X3,X1,X4)
| c_Type_Otyping(X3,X2,X4) ) ).
cnf(i_0_1294_076,axiom,
( X1 != X2
| ~ c_Type_Otyping(X3,X4,X1)
| c_Type_Otyping(X3,X4,X2) ) ).
cnf(i_0_1295_077,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1296_078,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1297_079,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1298_080,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1299_081,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1300_082,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1301_083,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1302_084,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_1303_085,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1304_086,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1305_087,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1306_088,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1307_089,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1308_090,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1309_091,axiom,
( X1 != X2
| ~ c_Type_Otypings(X1,X3,X4)
| c_Type_Otypings(X2,X3,X4) ) ).
cnf(i_0_1310_092,axiom,
( X1 != X2
| ~ c_Type_Otypings(X3,X1,X4)
| c_Type_Otypings(X3,X2,X4) ) ).
cnf(i_0_1311_093,axiom,
( X1 != X2
| ~ c_Type_Otypings(X3,X4,X1)
| c_Type_Otypings(X3,X4,X2) ) ).
cnf(i_0_1312_094,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1313_095,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_1314_096,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1315_097,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1316_098,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1(X1)
| class_Ring__and__Field_Oring__1(X2) ) ).
cnf(i_0_1317_099,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1318_100,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_1319_101,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1320_102,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1321_103,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1322_104,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X1,X3,X4,X5,X6,X7)
| c_Groebner__Basis_Ogb__semiring(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_1323_105,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X1,X4,X5,X6,X7)
| c_Groebner__Basis_Ogb__semiring(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_1324_106,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X4,X1,X5,X6,X7)
| c_Groebner__Basis_Ogb__semiring(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_1325_107,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X1,X6,X7)
| c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_1326_108,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X6,X1,X7)
| c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_1327_109,axiom,
( X1 != X2
| ~ c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X6,X7,X1)
| c_Groebner__Basis_Ogb__semiring(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_1328_110,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1329_111,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1330_112,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1331_113,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_1332_114,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1333_115,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1334_116,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_1335_117,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_1336_118,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_1337_119,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_1338_120,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_1339_121,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_1340_122,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1341_123,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_1342_124,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_1343_125,axiom,
( X1 != X2
| ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(X2) ) ).
cnf(i_0_1344_126,axiom,
( X1 != X2
| ~ c_Lambda_Obeta(X1,X3)
| c_Lambda_Obeta(X2,X3) ) ).
cnf(i_0_1345_127,axiom,
( X1 != X2
| ~ c_Lambda_Obeta(X3,X1)
| c_Lambda_Obeta(X3,X2) ) ).
cnf(i_0_1346_128,axiom,
( X1 != X2
| ~ class_OrderedGroup_Osemigroup__add(X1)
| class_OrderedGroup_Osemigroup__add(X2) ) ).
cnf(i_0_1347_129,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_1348_130,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_1349,plain,
X1 = X1,
inference(equality_inference,[],[672]) ).
cnf(i_0_1350,plain,
X1 = X1,
inference(equality_inference,[],[673]) ).
cnf(i_0_1351,plain,
X1 = X1,
inference(equality_inference,[],[674]) ).
cnf(i_0_1352,plain,
X1 = X1,
inference(equality_inference,[],[675]) ).
cnf(i_0_1353,plain,
X1 = X1,
inference(equality_inference,[],[678]) ).
cnf(i_0_1354,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(equality_inference,[],[750]) ).
cnf(i_0_1355,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(equality_inference,[],[771]) ).
cnf(i_0_1356,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
inference(equality_inference,[],[775]) ).
cnf(i_0_1357,plain,
( X1 = X1
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(equality_inference,[],[816]) ).
cnf(i_0_1358,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[940]) ).
cnf(i_0_1359,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[941]) ).
cnf(i_0_1360,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[942]) ).
cnf(i_0_1361,plain,
( X1 = X1
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(equality_inference,[],[954]) ).
cnf(i_0_1362,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[958]) ).
cnf(i_0_1363,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[959]) ).
cnf(i_0_1364,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[960]) ).
cnf(i_0_1365,plain,
X1 = X1,
inference(equality_inference,[],[961]) ).
cnf(i_0_1366,plain,
X1 = X1,
inference(equality_inference,[],[998]) ).
cnf(i_0_1367,plain,
X1 = X1,
inference(equality_inference,[],[1000]) ).
cnf(i_0_1368,plain,
X1 = X1,
inference(equality_inference,[],[1041]) ).
cnf(i_0_1369,plain,
X1 = X1,
inference(equality_inference,[],[1042]) ).
cnf(i_0_1370,plain,
X1 = X1,
inference(equality_inference,[],[1043]) ).
cnf(i_0_1371,plain,
X1 = X1,
inference(equality_inference,[],[1044]) ).
cnf(i_0_1372,plain,
( X1 = X1
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(equality_inference,[],[1161]) ).
cnf(i_0_1373,plain,
X1 = X1,
inference(equality_inference,[],[1177]) ).
cnf(i_0_1374,plain,
X1 = X1,
inference(equality_inference,[],[1178]) ).
cnf(i_0_1375,plain,
X1 = X1,
inference(equality_inference,[],[1179]) ).
cnf(i_0_1376,plain,
X1 = X1,
inference(equality_inference,[],[1181]) ).
cnf(i_0_1377,plain,
$false,
inference(scs_inference,[],[i_0_699,i_0_721,i_0_717,i_0_768]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL852-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n023.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 23:13:53 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.37/5.69 % Version : CSE_E---1.7
% 0.37/5.69 % Problem : theBenchmark.p
% 0.37/5.69 % SZS status Unsatisfiable for theBenchmark.p
% 0.37/5.69 % SZS output start CNFRefutation
% See solution above
% 5.57/5.76 % Total time : 5.349s
%------------------------------------------------------------------------------