%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG363-1 : 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 : n025.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 04:08:32 PM UTC 2026
% Result : Unsatisfiable 2.07s 2.04s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of clauses : 85 ( 52 unt; 9 nHn; 55 RR)
% Number of literals : 128 ( 31 equ; 42 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_sin__zero_0,axiom,
c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero_0) ).
cnf(cls_ln__one_0,axiom,
c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__one_0) ).
cnf(cls_sin__minus_0,axiom,
c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X1),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__minus_0) ).
cnf(cls_neg__0__equal__iff__equal_1,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),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(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_rp_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rp_0) ).
cnf(cls_abs__le__interval__iff_1,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
cnf(cls_real__le__refl_0,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
cnf(cls_abs__minus__add__cancel_0,axiom,
c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__add__cancel_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
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(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
cnf(cls_real__abs__def_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
cnf(cls_conjecture_0,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))),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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_th_0,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(X1)),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/sandbox2/benchmark/theBenchmark.p',cls_th_0) ).
cnf(cls_real__0__less__add__iff_1,axiom,
( 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_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__less__add__iff_1) ).
cnf(cls_real__le__trans_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_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_abs__cos__le__one_0,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(X1),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__cos__le__one_0) ).
cnf(cls_abs__le__interval__iff_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_0) ).
cnf(cls_cos__zero_0,axiom,
c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero_0) ).
cnf(cls_exp__gt__zero_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__gt__zero_0) ).
cnf(cls_exp__eq__one__iff_1,axiom,
c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__eq__one__iff_1) ).
cnf(cls_real__less__def_2,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
cnf(cls_neg__0__less__iff__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
cnf(c_0_28,axiom,
c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
cls_sin__zero_0 ).
cnf(c_0_29,axiom,
c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
cls_ln__one_0 ).
cnf(c_0_30,axiom,
c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X1),tc_RealDef_Oreal),
cls_sin__minus_0 ).
cnf(c_0_31,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_neg__0__equal__iff__equal_1 ).
cnf(c_0_32,plain,
c_Transcendental_Osin(c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))) = c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
cnf(c_0_33,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add ).
cnf(c_0_34,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0 ).
cnf(c_0_35,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_36,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
cls_rp_0 ).
cnf(c_0_37,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_abs__le__interval__iff_1 ).
cnf(c_0_38,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
cls_real__le__refl_0 ).
cnf(c_0_39,axiom,
c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_abs__minus__add__cancel_0 ).
cnf(c_0_40,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__0_0 ).
cnf(c_0_41,plain,
c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
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_30,c_0_31]),c_0_29]),c_0_32]),c_0_29]),c_0_32]),c_0_33])]) ).
cnf(c_0_42,plain,
c_HOL_Oplus__class_Oplus(X1,c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_29]),c_0_35])]) ).
cnf(c_0_43,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_linorder__not__le_1 ).
cnf(c_0_44,plain,
c_lessequals(c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),v_r,tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_36,c_0_29]) ).
cnf(c_0_45,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Olinorder ).
cnf(c_0_46,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__abs__def_1 ).
cnf(c_0_47,plain,
c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_29]),c_0_41]),c_0_42]),c_0_35])]) ).
cnf(c_0_49,plain,
~ c_HOL_Oord__class_Oless(v_r,c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_50,plain,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(X1,c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[c_0_46,c_0_29]) ).
cnf(c_0_51,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))),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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_conjecture_0 ).
cnf(c_0_52,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))),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_HOL_Oord__class_Oless(c_Transcendental_Oln(c_HOL_Oone__class_Oone(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(rw,[status(thm)],[c_0_51,c_0_29]) ).
cnf(c_0_55,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(X1)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_th_0 ).
cnf(c_0_56,axiom,
( 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_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_real__0__less__add__iff_1 ).
cnf(c_0_57,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
cls_real__le__trans_0 ).
cnf(c_0_58,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__less_0 ).
cnf(c_0_60,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_Transcendental_Oln(c_HOL_Oone__class_Oone(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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_61,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[c_0_56,c_0_29]) ).
cnf(c_0_62,plain,
( c_lessequals(X1,v_r,tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_59,c_0_45]) ).
cnf(c_0_64,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
( c_lessequals(X1,v_r,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,negated_conjecture,
( c_lessequals(X1,v_r,tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_57,c_0_66]) ).
cnf(c_0_68,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(X1),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_abs__cos__le__one_0 ).
cnf(c_0_69,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_abs__le__interval__iff_0 ).
cnf(c_0_70,negated_conjecture,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(X1),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,axiom,
c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
cls_cos__zero_0 ).
cnf(c_0_72,negated_conjecture,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_Transcendental_Ocos(X1),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,plain,
c_Transcendental_Ocos(c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_71,c_0_29]) ).
cnf(c_0_74,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_exp__gt__zero_0 ).
cnf(c_0_75,axiom,
c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
cls_exp__eq__one__iff_1 ).
cnf(c_0_76,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_2 ).
cnf(c_0_77,negated_conjecture,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,plain,
c_HOL_Oord__class_Oless(c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_74,c_0_29]) ).
cnf(c_0_79,plain,
c_Transcendental_Oexp(c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_75,c_0_29]) ).
cnf(c_0_80,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__0__less__iff__less_0 ).
cnf(c_0_81,negated_conjecture,
c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_64]) ).
cnf(c_0_82,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add ).
cnf(c_0_83,plain,
c_HOL_Oord__class_Oless(c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
$false,
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(spm,[status(thm)],[c_0_80,c_0_81]),c_0_29]),c_0_82]),c_0_29]),c_0_83])]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG363-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.13 % 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
% 0.15/0.34 % Computer : n025.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 10:33:28 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 2.07/2.04 % Version : CSE_E---1.7
% 2.07/2.04 % Problem : theBenchmark.p
% 2.07/2.04 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/2.04 % SZS output start CNFRefutation
% See solution above
% 2.07/2.05 % Total time : 1.428s
%------------------------------------------------------------------------------