%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWV620-1 : 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 : n009.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 03:06:36 PM UTC 2026
% Result : Unsatisfiable 1.54s 0.65s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 36
% Syntax : Number of clauses : 116 ( 61 unt; 9 nHn; 95 RR)
% Number of literals : 213 ( 83 equ; 107 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 127 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_mult__numeral__1_0,axiom,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X2,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).
cnf(cls_real__add__minus__iff_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__minus__iff_0) ).
cnf(cls_eq__divide__2__times__iff_1,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(X2,X3,tc_RealDef_Oreal)
| X1 = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__2__times__iff_1) ).
cnf(cls_divide__Numeral1_0,axiom,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).
cnf(cls_real__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
cnf(cls_eq__number__of_0,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X3,X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
cnf(cls_comp__arith_I112_J_0,axiom,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
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(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
cnf(clsarity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).
cnf(cls_real__minus__half__eq_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__minus__half__eq_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
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_pi__neq__zero_0,axiom,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).
cnf(cls_rel__simps_I44_J_0,axiom,
( c_Int_OBit0(X1) != c_Int_OPls
| X1 = c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I44_J_0) ).
cnf(cls_rel__simps_I39_J_0,axiom,
c_Int_OPls != c_Int_OBit1(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).
cnf(cls_CHAINED_0,axiom,
( ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(cls_real__0__le__divide__iff_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X2,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_0) ).
cnf(cls_pi__ge__zero_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__ge__zero_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_real__sum__of__halves_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__of__halves_0) ).
cnf(cls_CHAINED_0_01,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_mult__imp__less__div__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
cnf(cls_real__less__def_2,axiom,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
cnf(cls_pi__half__ge__zero_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__ge__zero_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
cnf(cls_real__mult__order_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
cnf(cls_zero__less__divide__iff_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
cnf(cls_real0_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real0_0) ).
cnf(cls_not__real__of__nat__less__zero_0,axiom,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).
cnf(cls_pi__gt__zero_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__gt__zero_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
cnf(c_0_36,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_mult__numeral__1_0]) ).
cnf(c_0_37,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[cls_real__add__minus__iff_0]) ).
cnf(c_0_38,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(X2,X3,tc_RealDef_Oreal)
| X1 = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_eq__divide__2__times__iff_1]) ).
cnf(c_0_39,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_divide__Numeral1_0]) ).
cnf(c_0_40,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
cls_real__mult__commute_0 ).
cnf(c_0_41,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X2,X1) = X2 ),
c_0_36 ).
cnf(c_0_42,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber__ring ).
cnf(c_0_43,plain,
( c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X3,X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[cls_eq__number__of_0]) ).
cnf(c_0_44,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1) ),
inference(fof_simplification,[status(thm)],[cls_comp__arith_I112_J_0]) ).
cnf(c_0_45,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X2 ),
c_0_37 ).
cnf(c_0_46,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_47,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(X2,X3,tc_RealDef_Oreal)
| X1 = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
c_0_38 ).
cnf(c_0_48,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X1),X1) = X2 ),
c_0_39 ).
cnf(c_0_49,plain,
c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_50,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ofield ).
cnf(c_0_51,plain,
( c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X3,X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 = X3 ),
c_0_43 ).
cnf(c_0_52,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Oring__char__0 ).
cnf(c_0_53,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1) ),
c_0_44 ).
cnf(c_0_54,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X2 ),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__minus__half__eq_0 ).
cnf(c_0_56,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50]),c_0_42])])]) ).
cnf(c_0_57,plain,
( c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal) != c_Int_Onumber__class_Onumber__of(X2,tc_RealDef_Oreal)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_42])]) ).
cnf(c_0_58,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_53,c_0_42]) ).
cnf(c_0_59,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_56,c_0_49]) ).
cnf(c_0_61,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_62,plain,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_mult__eq__0__iff_2]) ).
cnf(c_0_63,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_64,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_pi__neq__zero_0]) ).
cnf(c_0_65,plain,
( c_Int_OBit0(X1) != c_Int_OPls
| X1 = c_Int_OPls ),
inference(fof_simplification,[status(thm)],[cls_rel__simps_I44_J_0]) ).
cnf(c_0_66,plain,
( c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = c_Int_OPls ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,plain,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,plain,
c_Int_OPls != c_Int_OBit1(X1),
inference(fof_simplification,[status(thm)],[cls_rel__simps_I39_J_0]) ).
cnf(c_0_69,plain,
( ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_0_70,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
c_0_61 ).
cnf(c_0_71,plain,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_62 ).
cnf(c_0_72,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors ).
cnf(c_0_73,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X2,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(fof_simplification,[status(thm)],[cls_real__0__le__divide__iff_0]) ).
cnf(c_0_74,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| X1 = X2 ),
c_0_63 ).
cnf(c_0_75,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
cls_pi__ge__zero_0 ).
cnf(c_0_76,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
c_0_64 ).
cnf(c_0_77,plain,
( c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_double__eq__0__iff_0]) ).
cnf(c_0_78,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
cls_real__sum__of__halves_0 ).
cnf(c_0_79,plain,
( c_Int_OBit0(X1) != c_Int_OPls
| X1 = c_Int_OPls ),
c_0_65 ).
cnf(c_0_80,plain,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Int_OBit0(c_Int_OBit1(c_Int_OPls)) = c_Int_OPls ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_81,plain,
c_Int_OPls != c_Int_OBit1(X1),
c_0_68 ).
cnf(c_0_82,plain,
( ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
c_0_69 ).
cnf(c_0_83,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
cls_CHAINED_0_01 ).
cnf(c_0_84,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_40]),c_0_40]) ).
cnf(c_0_85,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_mult__imp__less__div__pos_0]) ).
cnf(c_0_86,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_87,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__less__def_2]) ).
cnf(c_0_88,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X2,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) ),
c_0_73 ).
cnf(c_0_89,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_pi__half__ge__zero_0 ).
cnf(c_0_90,plain,
~ c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_91,plain,
( c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
c_0_77 ).
cnf(c_0_92,plain,
c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_78,c_0_60]) ).
cnf(c_0_93,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add ).
cnf(c_0_94,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_95,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_40]),c_0_40]),c_0_83]),c_0_40])]),c_0_84]) ).
cnf(c_0_96,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
c_0_85 ).
cnf(c_0_97,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field ).
cnf(c_0_98,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_40,c_0_86]) ).
cnf(c_0_99,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__mult__order_0]) ).
cnf(c_0_100,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
c_0_87 ).
cnf(c_0_101,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_102,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93])]),c_0_94]) ).
cnf(c_0_103,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_zero__less__divide__iff_3]) ).
cnf(c_0_104,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real0_0 ).
cnf(c_0_105,plain,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_not__real__of__nat__less__zero_0]) ).
cnf(c_0_106,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_98])]) ).
cnf(c_0_107,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
c_0_99 ).
cnf(c_0_108,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]) ).
cnf(c_0_109,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
cls_pi__gt__zero_0 ).
cnf(c_0_110,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
c_0_103 ).
cnf(c_0_111,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_104,c_0_40]) ).
cnf(c_0_112,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_113,plain,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
c_0_105 ).
cnf(c_0_114,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_109])]) ).
cnf(c_0_115,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_97])]),c_0_113]),c_0_114]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV620-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 09:14:42 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 1.54/0.65 % Version: 3.5.1
% 1.54/0.65 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.54/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.54/0.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.54/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.54/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.54/0.65 % Starting sh5l with 300s (1) cores
% 1.54/0.65 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1395808 completed with status 0
% 1.54/0.65 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.54/0.65 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.54/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.54/0.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.54/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.54/0.65 % No SInE strategy applied
% 1.54/0.65 % Search class: FGHSM-FSLM31-DFFFFFNN
% 1.54/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.54/0.65 % Starting SubtermCWHack with 136s (1) cores
% 1.54/0.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.54/0.65 % Starting C07_19_nc_SAT001_MinMin_p005000_rr with 354s (1) cores
% 1.54/0.65 % Starting U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.54/0.65 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 1.54/0.65 % C07_19_nc_SAT001_MinMin_p005000_rr with pid 1395816 completed with status 0
% 1.54/0.65 % Result found by C07_19_nc_SAT001_MinMin_p005000_rr
% 1.54/0.65 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.54/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.54/0.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.54/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.54/0.65 % No SInE strategy applied
% 1.54/0.65 % Search class: FGHSM-FSLM31-DFFFFFNN
% 1.54/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.54/0.65 % Starting SubtermCWHack with 136s (1) cores
% 1.54/0.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.54/0.65 % Starting C07_19_nc_SAT001_MinMin_p005000_rr with 354s (1) cores
% 1.54/0.65 % Preprocessing time : 0.007 s
% 1.54/0.65 % Presaturation interreduction done
% 1.54/0.65
% 1.54/0.65 % Proof found!
% 1.54/0.65 % SZS status Unsatisfiable
% 1.54/0.65 % SZS output start CNFRefutation
% See solution above
% 1.54/0.65 % Parsed axioms : 877
% 1.54/0.65 % Removed by relevancy pruning/SinE : 0
% 1.54/0.65 % Initial clauses : 877
% 1.54/0.65 % Removed in clause preprocessing : 0
% 1.54/0.65 % Initial clauses in saturation : 877
% 1.54/0.65 % Processed clauses : 3856
% 1.54/0.65 % ...of these trivial : 79
% 1.54/0.65 % ...subsumed : 2069
% 1.54/0.65 % ...remaining for further processing : 1708
% 1.54/0.65 % Other redundant clauses eliminated : 95
% 1.54/0.65 % Clauses deleted for lack of memory : 0
% 1.54/0.65 % Backward-subsumed : 18
% 1.54/0.65 % Backward-rewritten : 12
% 1.54/0.65 % Generated clauses : 9107
% 1.54/0.65 % ...of the previous two non-redundant : 7656
% 1.54/0.65 % ...aggressively subsumed : 0
% 1.54/0.65 % Contextual simplify-reflections : 0
% 1.54/0.65 % Paramodulations : 8999
% 1.54/0.65 % Factorizations : 2
% 1.54/0.65 % NegExts : 0
% 1.54/0.65 % Equation resolutions : 105
% 1.54/0.65 % Disequality decompositions : 0
% 1.54/0.65 % Total rewrite steps : 7355
% 1.54/0.65 % ...of those cached : 7020
% 1.54/0.65 % Propositional unsat checks : 0
% 1.54/0.65 % Propositional check models : 0
% 1.54/0.65 % Propositional check unsatisfiable : 0
% 1.54/0.65 % Propositional clauses : 0
% 1.54/0.65 % Propositional clauses after purity: 0
% 1.54/0.65 % Propositional unsat core size : 0
% 1.54/0.65 % Propositional preprocessing time : 0.000
% 1.54/0.65 % Propositional encoding time : 0.000
% 1.54/0.65 % Propositional solver time : 0.000
% 1.54/0.65 % Success case prop preproc time : 0.000
% 1.54/0.65 % Success case prop encoding time : 0.000
% 1.54/0.65 % Success case prop solver time : 0.000
% 1.54/0.65 % Current number of processed clauses : 982
% 1.54/0.65 % Positive orientable unit clauses : 296
% 1.54/0.65 % Positive unorientable unit clauses: 3
% 1.54/0.65 % Negative unit clauses : 136
% 1.54/0.65 % Non-unit-clauses : 547
% 1.54/0.65 % Current number of unprocessed clauses: 5289
% 1.54/0.65 % ...number of literals in the above : 14764
% 1.54/0.65 % Current number of archived formulas : 0
% 1.54/0.65 % Current number of archived clauses : 726
% 1.54/0.65 % Clause-clause subsumption calls (NU) : 94852
% 1.54/0.65 % Rec. Clause-clause subsumption calls : 46238
% 1.54/0.65 % Non-unit clause-clause subsumptions : 902
% 1.54/0.65 % Unit Clause-clause subsumption calls : 3610
% 1.54/0.65 % Rewrite failures with RHS unbound : 0
% 1.54/0.65 % BW rewrite match attempts : 190
% 1.54/0.65 % BW rewrite match successes : 25
% 1.54/0.65 % Condensation attempts : 0
% 1.54/0.65 % Condensation successes : 0
% 1.54/0.65 % Termbank termtop insertions : 191369
% 1.54/0.65 % Search garbage collected termcells : 1926
% 1.54/0.65
% 1.54/0.65 % -------------------------------------------------
% 1.54/0.65 % User time : 0.178 s
% 1.54/0.65 % System time : 0.013 s
% 1.54/0.65 % Total time : 0.191 s
% 1.54/0.65 % Maximum resident set size: 5284 pages
% 1.54/0.65
% 1.54/0.65 % -------------------------------------------------
% 1.54/0.65 % User time : 0.774 s
% 1.54/0.65 % System time : 0.059 s
% 1.54/0.65 % Total time : 0.833 s
% 1.54/0.65 % Maximum resident set size: 5120 pages
% 1.54/0.65 % E exiting
%------------------------------------------------------------------------------