%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 11:55:58 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of clauses : 94 ( 35 unt; 10 nHn; 52 RR)
% Number of literals : 159 ( 27 equ; 63 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 133 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_real__le__trans_0,axiom,
( ~ c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
cnf(cls_r_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,X1),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r_0) ).
cnf(cls_abs__le__interval__iff_0,axiom,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_0) ).
cnf(cls_abs__Re__le__cmod_0,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X1),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__Re__le__cmod_0) ).
cnf(cls_complex__Re__le__cmod_0,axiom,
c_lessequals(c_Complex_ORe(X1),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__Re__le__cmod_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_abs__le__interval__iff_1,axiom,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_real__le__refl_0,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
cnf(cls_real__le__antisym_0,axiom,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
cnf(cls_real__abs__def_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_0) ).
cnf(cls_real__le__eq__diff_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__eq__diff_1) ).
cnf(cls_real__diff__def_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__diff__def_0) ).
cnf(cls_real__le__linear_0,axiom,
( c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_real__0__less__add__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__less__add__iff_1) ).
cnf(cls_real__abs__def_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_real__sum__gt__zero__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__gt__zero__less_0) ).
cnf(cls_real__add__le__0__iff_1,axiom,
( ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__le__0__iff_1) ).
cnf(cls_abs__add__one__not__less__self_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__not__less__self_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_22,plain,
( ~ c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__le__trans_0]) ).
cnf(c_0_23,plain,
( ~ c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
c_0_22 ).
cnf(c_0_24,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,X1),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
cls_r_0 ).
cnf(c_0_25,plain,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_abs__le__interval__iff_0]) ).
cnf(c_0_26,plain,
( ~ c_lessequals(X1,c_RealVector_Onorm__class_Onorm(hAPP(v_s,X2),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X1,v_r,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X1),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_abs__Re__le__cmod_0 ).
cnf(c_0_28,axiom,
c_lessequals(c_Complex_ORe(X1),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_complex__Re__le__cmod_0 ).
cnf(c_0_29,plain,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
c_0_25 ).
cnf(c_0_30,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,X1)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
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 ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Oadd__0_0]) ).
cnf(c_0_32,plain,
( ~ c_lessequals(X1,c_Complex_ORe(X2),tc_RealDef_Oreal)
| c_lessequals(X1,c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_33,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_Complex_ORe(hAPP(v_s,X1)),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_abs__le__interval__iff_1]) ).
cnf(c_0_35,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_31 ).
cnf(c_0_36,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_37,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
cls_real__le__refl_0 ).
cnf(c_0_38,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[cls_real__le__antisym_0]) ).
cnf(c_0_39,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,X1),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
c_0_34 ).
cnf(c_0_41,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__abs__def_0]) ).
cnf(c_0_42,plain,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__le__eq__diff_1]) ).
cnf(c_0_43,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__diff__def_0 ).
cnf(c_0_45,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_46,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| X1 = X2 ),
c_0_38 ).
cnf(c_0_47,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_48,plain,
c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_49,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal) ),
c_0_41 ).
cnf(c_0_50,plain,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
c_0_42 ).
cnf(c_0_51,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_53,axiom,
( c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__le__linear_0 ).
cnf(c_0_54,plain,
( ~ c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = v_r ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,plain,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
( c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_23,c_0_48]) ).
cnf(c_0_59,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I6_J_0]) ).
cnf(c_0_60,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = v_r ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__0__less__add__iff_1]) ).
cnf(c_0_62,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_63,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1 ),
cls_real__abs__def_1 ).
cnf(c_0_64,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
c_0_59 ).
cnf(c_0_65,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Oadd__c_0]) ).
cnf(c_0_66,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(v_r,c_Complex_ORe(hAPP(v_s,X1)),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_67,plain,
c_lessequals(c_Complex_ORe(hAPP(v_s,X1)),v_r,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_68,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__sum__gt__zero__less_0]) ).
cnf(c_0_69,plain,
( ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__add__le__0__iff_1]) ).
cnf(c_0_70,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
c_0_61 ).
cnf(c_0_71,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_36]) ).
cnf(c_0_73,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_abs__add__one__not__less__self_0]) ).
cnf(c_0_74,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
c_0_65 ).
cnf(c_0_75,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Complex_ORe(hAPP(v_s,X1)) = v_r ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_66]),c_0_67])]) ).
cnf(c_0_76,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
c_0_68 ).
cnf(c_0_77,plain,
( ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
c_0_69 ).
cnf(c_0_78,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_79,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
c_0_73 ).
cnf(c_0_80,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_74,c_0_36]) ).
cnf(c_0_81,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_30,c_0_75]) ).
cnf(c_0_82,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[c_0_76,c_0_44]) ).
cnf(c_0_83,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_72]) ).
cnf(c_0_84,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_81]),c_0_48])]),c_0_63]) ).
cnf(c_0_86,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_80]) ).
cnf(c_0_88,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_50,c_0_86]) ).
cnf(c_0_89,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_90,plain,
c_lessequals(v_r,c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_91,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
c_0_89 ).
cnf(c_0_92,plain,
( ~ c_lessequals(X1,v_r,tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_23,c_0_90]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 13:17:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.18/0.51 % Version: 3.5.1
% 0.18/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.51 % Starting sh5l with 300s (1) cores
% 0.18/0.51 % new_bool_3 with pid 847675 completed with status 0
% 0.18/0.51 % Result found by new_bool_3
% 0.18/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.51 % Search class: FGHSM-FFLM32-MFFFFFNN
% 0.18/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.18/0.51 % SubtermCWHack with pid 847680 completed with status 0
% 0.18/0.51 % Result found by SubtermCWHack
% 0.18/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.51 % Search class: FGHSM-FFLM32-MFFFFFNN
% 0.18/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.18/0.51 % Preprocessing time : 0.002 s
% 0.18/0.51
% 0.18/0.51 % Proof found!
% 0.18/0.51 % SZS status Unsatisfiable
% 0.18/0.51 % SZS output start CNFRefutation
% See solution above
% 0.18/0.51 % Parsed axioms : 800
% 0.18/0.51 % Removed by relevancy pruning/SinE : 646
% 0.18/0.51 % Initial clauses : 154
% 0.18/0.51 % Removed in clause preprocessing : 0
% 0.18/0.51 % Initial clauses in saturation : 154
% 0.18/0.51 % Processed clauses : 919
% 0.18/0.51 % ...of these trivial : 87
% 0.18/0.51 % ...subsumed : 370
% 0.18/0.51 % ...remaining for further processing : 462
% 0.18/0.51 % Other redundant clauses eliminated : 3
% 0.18/0.51 % Clauses deleted for lack of memory : 0
% 0.18/0.51 % Backward-subsumed : 8
% 0.18/0.51 % Backward-rewritten : 22
% 0.18/0.51 % Generated clauses : 5102
% 0.18/0.51 % ...of the previous two non-redundant : 3467
% 0.18/0.51 % ...aggressively subsumed : 0
% 0.18/0.51 % Contextual simplify-reflections : 2
% 0.18/0.51 % Paramodulations : 5087
% 0.18/0.51 % Factorizations : 10
% 0.18/0.51 % NegExts : 0
% 0.18/0.51 % Equation resolutions : 5
% 0.18/0.51 % Disequality decompositions : 0
% 0.18/0.51 % Total rewrite steps : 5034
% 0.18/0.51 % ...of those cached : 4570
% 0.18/0.51 % Propositional unsat checks : 0
% 0.18/0.51 % Propositional check models : 0
% 0.18/0.51 % Propositional check unsatisfiable : 0
% 0.18/0.51 % Propositional clauses : 0
% 0.18/0.51 % Propositional clauses after purity: 0
% 0.18/0.51 % Propositional unsat core size : 0
% 0.18/0.51 % Propositional preprocessing time : 0.000
% 0.18/0.51 % Propositional encoding time : 0.000
% 0.18/0.51 % Propositional solver time : 0.000
% 0.18/0.51 % Success case prop preproc time : 0.000
% 0.18/0.51 % Success case prop encoding time : 0.000
% 0.18/0.51 % Success case prop solver time : 0.000
% 0.18/0.51 % Current number of processed clauses : 432
% 0.18/0.51 % Positive orientable unit clauses : 178
% 0.18/0.51 % Positive unorientable unit clauses: 7
% 0.18/0.51 % Negative unit clauses : 26
% 0.18/0.51 % Non-unit-clauses : 221
% 0.18/0.51 % Current number of unprocessed clauses: 2691
% 0.18/0.51 % ...number of literals in the above : 5558
% 0.18/0.51 % Current number of archived formulas : 0
% 0.18/0.51 % Current number of archived clauses : 30
% 0.18/0.51 % Clause-clause subsumption calls (NU) : 2506
% 0.18/0.51 % Rec. Clause-clause subsumption calls : 2206
% 0.18/0.51 % Non-unit clause-clause subsumptions : 266
% 0.18/0.51 % Unit Clause-clause subsumption calls : 84
% 0.18/0.51 % Rewrite failures with RHS unbound : 0
% 0.18/0.51 % BW rewrite match attempts : 226
% 0.18/0.51 % BW rewrite match successes : 32
% 0.18/0.51 % Condensation attempts : 0
% 0.18/0.51 % Condensation successes : 0
% 0.18/0.51 % Termbank termtop insertions : 78454
% 0.18/0.51 % Search garbage collected termcells : 2225
% 0.18/0.51
% 0.18/0.51 % -------------------------------------------------
% 0.18/0.51 % User time : 0.051 s
% 0.18/0.51 % System time : 0.005 s
% 0.18/0.51 % Total time : 0.056 s
% 0.18/0.51 % Maximum resident set size: 4424 pages
% 0.18/0.51
% 0.18/0.51 % -------------------------------------------------
% 0.18/0.51 % User time : 0.071 s
% 0.18/0.51 % System time : 0.010 s
% 0.18/0.51 % Total time : 0.081 s
% 0.18/0.51 % Maximum resident set size: 5376 pages
% 0.18/0.51 % E exiting
%------------------------------------------------------------------------------