%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL754-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:16:20 PM UTC 2026
% Result : Unsatisfiable 17.76s 2.98s
% Output : CNFRefutation 17.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of clauses : 99 ( 59 unt; 5 nHn; 37 RR)
% Number of literals : 139 ( 56 equ; 53 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 156 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_less__Suc__eq__le_1,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_1) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_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(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(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_mod__less__eq__dividend_0,axiom,
c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_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_mod__1_0,axiom,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_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_mod__if_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
cnf(cls_mod__if_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_1) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(cls_mod__by__0_0,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
cnf(clsarity_nat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(cls_not__less__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
cnf(cls_mod__mult__self1__is__0_0,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
cnf(cls_trans__less__add2_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_mod__mult__self2__is__0_0,axiom,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
cnf(cls_Lambda_0,axiom,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
cnf(cls_subst__Abs_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_lift_Osimps_I1_J_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(c_0_26,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(fof_simplification,[status(thm)],[cls_less__Suc__eq__le_1]) ).
cnf(c_0_27,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_26 ).
cnf(c_0_28,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
cls_Suc__eq__plus1_0 ).
cnf(c_0_29,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Oadd__0_0]) ).
cnf(c_0_30,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
c_0_29 ).
cnf(c_0_32,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_diff__self__eq__0_0 ).
cnf(c_0_33,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_34,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[cls_gr__implies__not0_0]) ).
cnf(c_0_35,plain,
( ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_36,axiom,
c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
cls_mod__less__eq__dividend_0 ).
cnf(c_0_37,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(fof_simplification,[status(thm)],[cls_nat__less__le_1]) ).
cnf(c_0_38,axiom,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_mod__1_0 ).
cnf(c_0_39,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
cls_minus__nat_Odiff__0_0 ).
cnf(c_0_40,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_34 ).
cnf(c_0_41,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 ),
inference(fof_simplification,[status(thm)],[cls_mod__if_0]) ).
cnf(c_0_42,plain,
c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) ),
cls_mod__if_1 ).
cnf(c_0_44,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_37 ).
cnf(c_0_45,plain,
c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[c_0_38,c_0_28]) ).
cnf(c_0_46,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
cls_plus__nat_Oadd__0_0 ).
cnf(c_0_47,plain,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_mod__by__0_0]) ).
cnf(c_0_48,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(rw,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_49,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),
inference(rw,[status(thm)],[c_0_32,c_0_32]) ).
cnf(c_0_50,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat),
inference(rw,[status(thm)],[c_0_40,c_0_32]) ).
cnf(c_0_51,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 ),
c_0_41 ).
cnf(c_0_52,plain,
c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_53,plain,
c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_32]) ).
cnf(c_0_54,plain,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
c_0_47 ).
cnf(c_0_55,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),tc_nat) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,axiom,
class_Divides_Osemiring__div(tc_nat),
clsarity_nat__Divides_Osemiring__div ).
cnf(c_0_57,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_58,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_natgb_Oadd__r0__iff_1 ).
cnf(c_0_59,plain,
( ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[cls_not__less__eq_1]) ).
cnf(c_0_60,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),X1,tc_nat) = X1,
inference(rw,[status(thm)],[c_0_46,c_0_32]) ).
cnf(c_0_61,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),
inference(spm,[status(thm)],[c_0_49,c_0_49]) ).
cnf(c_0_62,plain,
c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat) = c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_63,plain,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_mod__mult__self1__is__0_0]) ).
cnf(c_0_64,plain,
c_Divides_Odiv__class_Omod(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_43]),c_0_32]),c_0_32]),c_0_55]),c_0_32]),c_0_56])]),c_0_57]) ).
cnf(c_0_65,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(rw,[status(thm)],[c_0_58,c_0_32]) ).
cnf(c_0_66,plain,
( ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_59 ).
cnf(c_0_67,plain,
( ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[cls_trans__less__add2_0]) ).
cnf(c_0_68,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I3_J_0]) ).
cnf(c_0_69,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X2,tc_nat) = X2,
inference(spm,[status(thm)],[c_0_60,c_0_49]) ).
cnf(c_0_70,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,plain,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_63 ).
cnf(c_0_72,plain,
c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(rw,[status(thm)],[c_0_64,c_0_62]) ).
cnf(c_0_73,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),tc_nat) = X1,
inference(spm,[status(thm)],[c_0_65,c_0_49]) ).
cnf(c_0_74,plain,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[c_0_66,c_0_28]) ).
cnf(c_0_75,plain,
( ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
c_0_67 ).
cnf(c_0_76,plain,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_mod__mult__self2__is__0_0]) ).
cnf(c_0_77,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1) ),
c_0_68 ).
cnf(c_0_78,plain,
c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),X1,tc_nat) = X1,
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_79,plain,
c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_32]),c_0_70]),c_0_56])]) ).
cnf(c_0_80,plain,
c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(rw,[status(thm)],[c_0_73,c_0_70]) ).
cnf(c_0_81,plain,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1)) ),
inference(fof_simplification,[status(thm)],[cls_Lambda_0]) ).
cnf(c_0_82,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
cls_subst__Abs_0 ).
cnf(c_0_83,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,plain,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_76 ).
cnf(c_0_85,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_80]),c_0_33])]) ).
cnf(c_0_86,plain,
( ~ c_InductTermi_OIT(X1)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1)) ),
c_0_81 ).
cnf(c_0_87,plain,
c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) = c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3),
inference(rw,[status(thm)],[c_0_82,c_0_32]) ).
cnf(c_0_88,negated_conjecture,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2)),
cls_conjecture_1 ).
cnf(c_0_89,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
cls_lift_Osimps_I1_J_1 ).
cnf(c_0_90,plain,
~ c_HOL_Oord__class_Oless(X1,c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_83,c_0_52]) ).
cnf(c_0_91,plain,
c_Divides_Odiv__class_Omod(X1,X1,tc_nat) = c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_32]),c_0_70]),c_0_56])]) ).
cnf(c_0_92,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_93,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
| c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_70]) ).
cnf(c_0_94,negated_conjecture,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2),X3)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,plain,
~ c_HOL_Oord__class_Oless(X1,c_Divides_Odiv__class_Omod(X2,X2,tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
c_0_92 ).
cnf(c_0_97,negated_conjecture,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X1),X2)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
cnf(c_0_98,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL754-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.60 % Computer : n015.cluster.edu
% 0.12/0.60 % Model : x86_64 x86_64
% 0.12/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.60 % Memory : 8046.5625MB
% 0.12/0.60 % OS : Linux 6.8.0-71-generic
% 0.12/0.60 % CPULimit : 300
% 0.12/0.60 % WCLimit : 300
% 0.12/0.60 % DateTime : Mon Sep 21 01:05:09 UTC 2026
% 0.12/0.60 % CPUTime :
% 0.12/0.60 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.65 Running first-order theorem proving
% 0.14/0.65 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.76/2.98 % Version: 3.5.1
% 17.76/2.98 % Preprocessing class: FSLSSMSSSSSNFFN.
% 17.76/2.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.76/2.98 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 17.76/2.98 % Starting new_bool_3 with 300s (1) cores
% 17.76/2.98 % Starting new_bool_1 with 300s (1) cores
% 17.76/2.98 % Starting sh5l with 300s (1) cores
% 17.76/2.98 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 216869 completed with status 0
% 17.76/2.98 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 17.76/2.98 % Preprocessing class: FSLSSMSSSSSNFFN.
% 17.76/2.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.76/2.98 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 17.76/2.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.76/2.98 % No SInE strategy applied
% 17.76/2.98 % Search class: FGHSM-FSLM32-MFFFFFNN
% 17.76/2.98 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 17.76/2.98 % Starting SubtermCWHack with 136s (1) cores
% 17.76/2.98 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 17.76/2.98 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 17.76/2.98 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 17.76/2.98 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 17.76/2.98 % U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with pid 216878 completed with status 0
% 17.76/2.98 % Result found by U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN
% 17.76/2.98 % Preprocessing class: FSLSSMSSSSSNFFN.
% 17.76/2.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.76/2.98 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 17.76/2.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.76/2.98 % No SInE strategy applied
% 17.76/2.98 % Search class: FGHSM-FSLM32-MFFFFFNN
% 17.76/2.98 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 17.76/2.98 % Starting SubtermCWHack with 136s (1) cores
% 17.76/2.98 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 17.76/2.98 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 17.76/2.98 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 17.76/2.98 % Preprocessing time : 0.011 s
% 17.76/2.98 % Presaturation interreduction done
% 17.76/2.98
% 17.76/2.98 % Proof found!
% 17.76/2.98 % SZS status Unsatisfiable
% 17.76/2.98 % SZS output start CNFRefutation
% See solution above
% 17.76/2.98 % Parsed axioms : 718
% 17.76/2.98 % Removed by relevancy pruning/SinE : 0
% 17.76/2.98 % Initial clauses : 718
% 17.76/2.98 % Removed in clause preprocessing : 2
% 17.76/2.98 % Initial clauses in saturation : 716
% 17.76/2.98 % Processed clauses : 12791
% 17.76/2.98 % ...of these trivial : 395
% 17.76/2.98 % ...subsumed : 9930
% 17.76/2.98 % ...remaining for further processing : 2466
% 17.76/2.98 % Other redundant clauses eliminated : 1236
% 17.76/2.98 % Clauses deleted for lack of memory : 0
% 17.76/2.98 % Backward-subsumed : 83
% 17.76/2.98 % Backward-rewritten : 122
% 17.76/2.98 % Generated clauses : 125412
% 17.76/2.98 % ...of the previous two non-redundant : 108194
% 17.76/2.98 % ...aggressively subsumed : 0
% 17.76/2.98 % Contextual simplify-reflections : 1
% 17.76/2.98 % Paramodulations : 124149
% 17.76/2.98 % Factorizations : 6
% 17.76/2.98 % NegExts : 0
% 17.76/2.98 % Equation resolutions : 1257
% 17.76/2.98 % Disequality decompositions : 0
% 17.76/2.98 % Total rewrite steps : 105035
% 17.76/2.98 % ...of those cached : 102619
% 17.76/2.98 % Propositional unsat checks : 0
% 17.76/2.98 % Propositional check models : 0
% 17.76/2.98 % Propositional check unsatisfiable : 0
% 17.76/2.98 % Propositional clauses : 0
% 17.76/2.98 % Propositional clauses after purity: 0
% 17.76/2.98 % Propositional unsat core size : 0
% 17.76/2.98 % Propositional preprocessing time : 0.000
% 17.76/2.98 % Propositional encoding time : 0.000
% 17.76/2.98 % Propositional solver time : 0.000
% 17.76/2.98 % Success case prop preproc time : 0.000
% 17.76/2.98 % Success case prop encoding time : 0.000
% 17.76/2.98 % Success case prop solver time : 0.000
% 17.76/2.98 % Current number of processed clauses : 1687
% 17.76/2.98 % Positive orientable unit clauses : 220
% 17.76/2.98 % Positive unorientable unit clauses: 20
% 17.76/2.98 % Negative unit clauses : 508
% 17.76/2.98 % Non-unit-clauses : 939
% 17.76/2.98 % Current number of unprocessed clauses: 95472
% 17.76/2.98 % ...number of literals in the above : 309783
% 17.76/2.98 % Current number of archived formulas : 0
% 17.76/2.98 % Current number of archived clauses : 781
% 17.76/2.98 % Clause-clause subsumption calls (NU) : 129774
% 17.76/2.98 % Rec. Clause-clause subsumption calls : 77463
% 17.76/2.98 % Non-unit clause-clause subsumptions : 1758
% 17.76/2.98 % Unit Clause-clause subsumption calls : 72179
% 17.76/2.98 % Rewrite failures with RHS unbound : 0
% 17.76/2.98 % BW rewrite match attempts : 816
% 17.76/2.98 % BW rewrite match successes : 236
% 17.76/2.98 % Condensation attempts : 0
% 17.76/2.98 % Condensation successes : 0
% 17.76/2.98 % Termbank termtop insertions : 1878325
% 17.76/2.98 % Search garbage collected termcells : 1388
% 17.76/2.98
% 17.76/2.98 % -------------------------------------------------
% 17.76/2.98 % User time : 2.145 s
% 17.76/2.98 % System time : 0.097 s
% 17.76/2.98 % Total time : 2.241 s
% 17.76/2.98 % Maximum resident set size: 4884 pages
% 17.76/2.98
% 17.76/2.98 % -------------------------------------------------
% 17.76/2.98 % User time : 10.840 s
% 17.76/2.98 % System time : 0.437 s
% 17.76/2.98 % Total time : 11.277 s
% 17.76/2.98 % Maximum resident set size: 5376 pages
% 17.76/2.98 % E exiting
%------------------------------------------------------------------------------