%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG374-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 : Fri Sep 25 12:54:08 PM UTC 2026
% Result : Unsatisfiable 18.12s 4.94s
% Output : CNFRefutation 18.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 85 ( 38 unt; 6 def)
% Number of atoms : 189 ( 42 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 125 ( 65 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 7 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 96 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
fof(f340,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__diff__def_0) ).
fof(f368,axiom,
! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1
| ~ class_OrderedGroup_Ogroup__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f444,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
fof(f462,axiom,
! [X0] :
( ~ c_lessequals(c_RealDef_Oreal(X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| X0 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__nat__le__zero__cancel__iff_0) ).
fof(f463,plain,
! [X0] :
( ~ c_lessequals(c_RealDef_Oreal(X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
inference(reorient_equations,[],[f462]) ).
fof(f492,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f501,axiom,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
fof(f541,axiom,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__local__Xs1__1(v_p,v_r,X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_s1_1) ).
fof(f542,axiom,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__local__Xs1__1(v_p,v_r,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_s1_2) ).
fof(f586,axiom,
! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f669,axiom,
! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f690,axiom,
! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1
| ~ class_OrderedGroup_Ogroup__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
fof(f704,negated_conjecture,
! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f737,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f742,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
fof(f744,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) ).
fof(f747,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
fof(f758,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f764,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
tcf(c_1001,plain,
! [X0: $i,X1: $i] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f340]) ).
tcf(c_1023,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 )
| ~ class_OrderedGroup_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f368]) ).
tcf(c_1079,plain,
! [X0: $i] : c_Suc(X0) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[],[f444]) ).
tcf(c_1095,plain,
! [X0: $i] :
( ( c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ c_lessequals(c_RealDef_Oreal(X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f463]) ).
tcf(c_1122,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(cnf_transformation,[],[f492]) ).
tcf(c_1131,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_1168,plain,
! [X0: $i] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__local__Xs1__1(v_p,v_r,X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f541]) ).
tcf(c_1169,plain,
! [X0: $i] :
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__local__Xs1__1(v_p,v_r,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f542]) ).
tcf(c_1211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f586]) ).
tcf(c_1280,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f669]) ).
tcf(c_1295,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ~ class_OrderedGroup_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f690]) ).
tcf(c_1309,negated_conjecture,
! [X0: $i] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f704]) ).
tcf(c_1342,plain,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f737]) ).
tcf(c_1347,plain,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f742]) ).
tcf(c_1349,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f744]) ).
tcf(c_1352,plain,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f747]) ).
tcf(c_1363,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f758]) ).
tcf(c_1369,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f764]) ).
tcf(c_2000,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 )
| ~ class_OrderedGroup_Ogroup__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_1023]) ).
tcf(c_2010,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ~ class_OrderedGroup_Ogroup__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_1295]) ).
tcf(c_2024,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_1211]) ).
tcf(c_9773,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_2024,c_1349]) ).
tcf(c_9774,plain,
! [X0: $i,X1: $i] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_9773]) ).
tcf(c_10158,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1122,c_1342]) ).
tcf(c_10159,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_10158]) ).
tcf(c_10204,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1280,c_1369]) ).
tcf(c_10205,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_10204]) ).
tcf(c_11349,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_2010,c_1363]) ).
tcf(c_11350,plain,
! [X0: $i] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0,
inference(unflattening,[status(thm)],[c_11349]) ).
tcf(c_11373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_2000,c_1363]) ).
tcf(c_11374,plain,
! [X0: $i,X1: $i] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0,
inference(unflattening,[status(thm)],[c_11373]) ).
tcf(c_13582,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1131,c_1352]) ).
tcf(c_13583,plain,
! [X0: $i] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_13582]) ).
tcf(c_30144,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal) ),
inference(prop_impl_just,[status(thm)],[c_10205]) ).
tcf(c_30145,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(renaming,[status(thm)],[c_30144]) ).
tcf(c_30176,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(prop_impl_just,[status(thm)],[c_10159]) ).
tcf(c_30262,plain,
! [X0: $i] :
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(prop_impl_just,[status(thm)],[c_1347,c_13583]) ).
tcf(c_30263,plain,
! [X0: $i] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(renaming,[status(thm)],[c_30262]) ).
tcf(c_35250,definition,
iPr_def_10 = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_35251,definition,
iPr_def_11 = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_35252,definition,
iPr_def_12 = c_Suc(v_n____),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_35253,definition,
iPr_def_13 = c_RealDef_Oreal(iPr_def_12,tc_nat),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_35254,definition,
iPr_def_14 = c_HOL_Oinverse__class_Odivide(iPr_def_11,iPr_def_13,tc_RealDef_Oreal),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_35255,definition,
iPr_def_15 = c_HOL_Oplus__class_Oplus(iPr_def_10,iPr_def_14,tc_RealDef_Oreal),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_35256,negated_conjecture,
! [X0: $i] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),iPr_def_15,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm)],[c_1309,c_35252,c_35253,c_35251,c_35254,c_35250,c_35255]) ).
tcf(c_42604,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != iPr_def_12,
inference(superposition,[status(thm)],[c_35252,c_1079]) ).
tcf(c_42947,plain,
c_HOL_Ouminus__class_Ouminus(iPr_def_10,tc_RealDef_Oreal) = v_s____,
inference(superposition,[status(thm)],[c_35250,c_11350]) ).
tcf(c_42950,plain,
c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) = iPr_def_10,
inference(superposition,[status(thm)],[c_42947,c_11350]) ).
tcf(c_43204,plain,
! [X0: $i] : c_HOL_Ominus__class_Ominus(X0,iPr_def_10,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,v_s____,tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_42947,c_1001]) ).
tcf(c_43928,plain,
( ( c_HOL_Ozero__class_Ozero(tc_nat) = iPr_def_12 )
| ~ c_lessequals(iPr_def_13,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_35253,c_1095]) ).
tcf(c_43930,plain,
~ c_lessequals(iPr_def_13,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_43928,c_42604]) ).
tcf(c_44300,plain,
! [X0: $i] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(iPr_def_11,X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(light_normalisation,[status(thm)],[c_30263,c_35251]) ).
tcf(c_44309,plain,
( c_lessequals(iPr_def_13,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(iPr_def_14,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_35254,c_44300]) ).
tcf(c_44311,plain,
~ c_lessequals(iPr_def_14,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_44309,c_43930]) ).
tcf(c_47524,plain,
! [X0: $i,X1: $i] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X1,
inference(superposition,[status(thm)],[c_9774,c_11374]) ).
tcf(c_48616,plain,
! [X0: $i] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__local__Xs1__1(v_p,v_r,X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(iPr_def_10,X0,tc_RealDef_Oreal) ),
inference(light_normalisation,[status(thm)],[c_1168,c_42950]) ).
tcf(c_50126,plain,
! [X0: $i] :
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__local__Xs1__1(v_p,v_r,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(iPr_def_10,X0,tc_RealDef_Oreal) ),
inference(light_normalisation,[status(thm)],[c_1169,c_42950]) ).
tcf(c_50137,plain,
( ~ c_HOL_Oord__class_Oless(iPr_def_10,iPr_def_15,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__local__Xs1__1(v_p,v_r,iPr_def_15),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_50126,c_35256]) ).
tcf(c_50289,plain,
~ c_HOL_Oord__class_Oless(iPr_def_10,iPr_def_15,tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_50137,c_48616]) ).
tcf(c_52904,plain,
c_HOL_Ominus__class_Ominus(iPr_def_15,iPr_def_10,tc_RealDef_Oreal) = iPr_def_14,
inference(superposition,[status(thm)],[c_35255,c_47524]) ).
tcf(c_52967,plain,
c_HOL_Oplus__class_Oplus(iPr_def_15,v_s____,tc_RealDef_Oreal) = iPr_def_14,
inference(demodulation,[status(thm)],[c_52904,c_43204]) ).
tcf(c_52973,plain,
( c_lessequals(iPr_def_14,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(iPr_def_15,c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_52967,c_30176]) ).
tcf(c_53007,plain,
( c_lessequals(iPr_def_14,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(iPr_def_15,iPr_def_10,tc_RealDef_Oreal) ),
inference(light_normalisation,[status(thm)],[c_52973,c_42950]) ).
tcf(c_53008,plain,
~ c_lessequals(iPr_def_15,iPr_def_10,tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_53007,c_44311]) ).
tcf(c_53051,plain,
c_HOL_Oord__class_Oless(iPr_def_10,iPr_def_15,tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_30145,c_53008]) ).
tcf(c_53052,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_53051,c_50289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG374-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.43 % Computer : n019.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 05:30:19 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.51
% 0.26/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.51
% 0.26/0.51 % Detected problem language: tptp
% 0.26/0.52 % Proving...
% 18.12/4.94 % SZS status Started for theBenchmark.p
% 18.12/4.94 % SZS status Unsatisfiable for theBenchmark.p
% 18.12/4.94
% 18.12/4.94 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.12/4.94
% 18.12/4.94 % ------ iProver source info
% 18.12/4.94
% 18.12/4.94 % git: date: 2026-07-19 20:42:38 +0200
% 18.12/4.94 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.12/4.94 % git: non_committed_changes: false
% 18.12/4.94
% 18.12/4.94 % ------ Parsing...% successful
% 18.12/4.94
% 18.12/4.94
% 18.12/4.94 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.12/4.94
% 18.12/4.94 % ------ Preprocessing... sup_sim: 14 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e sup_sim: 61 sf_s rm: 40 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 42 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 42 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 42 0s sf_e pe_s pe_e %
% 18.12/4.94
% 18.12/4.94 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.12/4.94
% 18.12/4.94 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.12/4.94 % ------ Proving...
% 18.12/4.94 % ------ Problem Properties
% 18.12/4.94
% 18.12/4.94 %
% 18.12/4.94 % clauses 525
% 18.12/4.94 % conjectures 1
% 18.12/4.94 % EPR 16
% 18.12/4.94 % Horn 454
% 18.12/4.94 % unary 184
% 18.12/4.94 % binary 212
% 18.12/4.94 % lits 1027
% 18.12/4.94 % lits eq 279
% 18.12/4.94 % fd_pure 0
% 18.12/4.94 % fd_pseudo 0
% 18.12/4.94 % fd_cond 38
% 18.12/4.94 % fd_pseudo_cond 36
% 18.12/4.94 % AC symbols 0
% 18.12/4.94
% 18.12/4.94 % ------ Schedule dynamic 5 is on
% 18.12/4.94
% 18.12/4.94 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.12/4.94
% 18.12/4.94
% 18.12/4.94 % ------
% 18.12/4.94 % Current options:
% 18.12/4.94 % ------
% 18.12/4.94
% 18.12/4.94
% 18.12/4.94 %
% 18.12/4.94
% 18.12/4.94 % ------ Proving...
% 18.12/4.94 %
% 18.12/4.94
% 18.12/4.94 % SZS status Unsatisfiable for theBenchmark.p
% 18.12/4.94
% 18.12/4.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.12/4.94
% 18.12/4.94
%------------------------------------------------------------------------------