%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV620-1 : 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 : n010.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 03:23:54 PM UTC 2026
% Result : Unsatisfiable 10.01s 30.85s
% Output : CNFRefutation 10.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 76 ( 40 unt; 0 def)
% Number of atoms : 174 ( 31 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 195 ( 97 ~; 98 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
fof(f137,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f151,axiom,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).
fof(f152,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Opi,
inference(reorient_equations,[],[f151]) ).
fof(f258,axiom,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_0) ).
fof(f375,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,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_zero__less__divide__iff_4) ).
fof(f376,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
fof(f437,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f504,axiom,
! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X3,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(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_less__divide__eq_2) ).
fof(f553,axiom,
! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X1,X0),X0)
| c_Int_Onumber__class_Onumber__of(X1,X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Int_Onumber(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).
fof(f554,plain,
! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X1,X0),X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Int_Onumber__class_Onumber__of(X1,X0)
| ~ class_Int_Onumber(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(reorient_equations,[],[f553]) ).
fof(f558,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ 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),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
fof(f562,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).
fof(f564,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__gt__zero_0) ).
fof(f623,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/sandbox2/benchmark/theBenchmark.p',cls_pi__half__ge__zero_0) ).
fof(f731,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__ge__zero_0) ).
fof(f791,axiom,
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) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__half__neq__zero_0) ).
fof(f792,plain,
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),
inference(reorient_equations,[],[f791]) ).
fof(f799,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/sandbox2/benchmark/theBenchmark.p',cls_real0_0) ).
fof(f809,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f864,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
fof(f871,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/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f872,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f874,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f969,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(f977,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(f992,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f1001,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber) ).
tcf(c_926,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(cnf_transformation,[],[f874]) ).
tcf(c_1029,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1001]) ).
tcf(c_1030,plain,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f977]) ).
tcf(c_1031,plain,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f969]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f864]) ).
tcf(c_1035,plain,
! [X0: $i] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f809]) ).
tcf(c_1054,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ 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),X0,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f558]) ).
tcf(c_1064,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f437]) ).
tcf(c_1068,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,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_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_1082,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| ( X0 = X1 )
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_1090,plain,
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) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f792]) ).
tcf(c_1092,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f731]) ).
tcf(c_1094,plain,
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),
inference(cnf_transformation,[],[f623]) ).
tcf(c_1096,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f564]) ).
tcf(c_1097,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Opi,
inference(cnf_transformation,[],[f152]) ).
tcf(c_1102,plain,
! [X0: $i] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f562]) ).
tcf(c_1108,plain,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
inference(cnf_transformation,[],[f872]) ).
tcf(c_1109,plain,
( 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_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) ),
inference(cnf_transformation,[],[f871]) ).
tcf(c_1110,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_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),
inference(cnf_transformation,[],[f799]) ).
tcf(c_1160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
inference(cnf_transformation,[],[f376]) ).
tcf(c_1168,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
inference(cnf_transformation,[],[f375]) ).
tcf(c_1261,plain,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f992]) ).
tcf(c_1277,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X0,X1),X1) = c_HOL_Ozero__class_Ozero(X1) )
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ( c_Int_Onumber__class_Onumber__of(X0,X1) != c_HOL_Ozero__class_Ozero(X1) ) ),
inference(cnf_transformation,[],[f554]) ).
tcf(c_1728,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1168,c_1167]) ).
tcf(c_1729,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
inference(renaming,[status(thm)],[c_1728]) ).
tcf(c_1738,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_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),
inference(global_subsumption_just,[status(thm)],[c_1109,c_1108,c_926,c_1109]) ).
tcf(c_5281,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(demodulation,[status(thm)],[c_1738,c_1032]) ).
tcf(c_5530,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(demodulation,[status(thm)],[c_1110,c_1032]) ).
tcf(c_9166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X0,X1),X1) = c_HOL_Ozero__class_Ozero(X1) )
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ( X1 != tc_RealDef_Oreal )
| ( c_Int_Onumber__class_Onumber__of(X0,X1) != c_HOL_Ozero__class_Ozero(X1) ) ),
inference(resolution_lifted,[status(thm)],[c_1277,c_1029]) ).
tcf(c_9167,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ( c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unflattening,[status(thm)],[c_9166]) ).
tcf(c_9169,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(global_subsumption_just,[status(thm)],[c_9167,c_1261,c_1031,c_9167]) ).
tcf(c_11616,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1729,c_1030]) ).
tcf(c_11617,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ 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),X0,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_11616]) ).
tcf(c_11998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1160,c_1030]) ).
tcf(c_11999,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_11998]) ).
tcf(c_12001,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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(X0,c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(global_subsumption_just,[status(thm)],[c_11999,c_1031,c_11999]) ).
tcf(c_21204,plain,
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Opi )
| ~ c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_1092,c_1064]) ).
tcf(c_21214,plain,
~ c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_21204,c_1097]) ).
tcf(c_24374,plain,
( c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| 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(superposition,[status(thm)],[c_1094,c_1068]) ).
tcf(c_24380,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(forward_subsumption_resolution,[status(thm)],[c_24374,c_21214]) ).
tcf(c_24542,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(instantiation,[status(thm)],[c_1035]) ).
tcf(c_24546,plain,
( ( 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) = 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_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(instantiation,[status(thm)],[c_9169]) ).
tcf(c_24629,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)
| ( 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(superposition,[status(thm)],[c_24380,c_1082]) ).
tcf(c_30239,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)
| ~ 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(instantiation,[status(thm)],[c_11617]) ).
tcf(c_32854,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| 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_RealDef_Oreal(v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ 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(instantiation,[status(thm)],[c_12001]) ).
tcf(c_60162,plain,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(instantiation,[status(thm)],[c_1102]) ).
tcf(c_279935,plain,
( 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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ 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(instantiation,[status(thm)],[c_1054]) ).
tcf(c_279936,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_279935,c_60162,c_32854,c_30239,c_24629,c_24546,c_24542,c_5530,c_5281,c_1090,c_1096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV620-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.42 % Computer : n010.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Thu Sep 24 20:44:59 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 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
% 0.17/0.50
% 0.17/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.50
% 0.17/0.51 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 10.01/30.85 % SZS status Started for theBenchmark.p
% 10.01/30.85 % SZS status Unsatisfiable for theBenchmark.p
% 10.01/30.85
% 10.01/30.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.01/30.85
% 10.01/30.85 % ------ iProver source info
% 10.01/30.85
% 10.01/30.85 % git: date: 2026-07-19 20:42:38 +0200
% 10.01/30.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.01/30.85 % git: non_committed_changes: false
% 10.01/30.85
% 10.01/30.85 % ------ Parsing...% successful
% 10.01/30.85
% 10.01/30.85
% 10.01/30.85 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.01/30.85
% 10.01/30.85 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e %
% 10.01/30.85
% 10.01/30.85 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.01/30.85
% 10.01/30.85 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.01/30.85 % ------ Proving...
% 10.01/30.85 % ------ Problem Properties
% 10.01/30.85
% 10.01/30.85 %
% 10.01/30.85 % clauses 500
% 10.01/30.85 % conjectures 0
% 10.01/30.85 % EPR 14
% 10.01/30.85 % Horn 385
% 10.01/30.85 % unary 149
% 10.01/30.85 % binary 151
% 10.01/30.85 % lits 1101
% 10.01/30.85 % lits eq 390
% 10.01/30.85 % fd_pure 0
% 10.01/30.85 % fd_pseudo 0
% 10.01/30.85 % fd_cond 37
% 10.01/30.85 % fd_pseudo_cond 28
% 10.01/30.85 % AC symbols 0
% 10.01/30.85
% 10.01/30.85 % ------ Schedule dynamic 5 is on
% 10.01/30.85
% 10.01/30.85 % ------ no conjectures: strip conj schedule
% 10.01/30.85
% 10.01/30.85 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 10.01/30.85
% 10.01/30.85
% 10.01/30.85 % ------
% 10.01/30.85 % Current options:
% 10.01/30.85 % ------
% 10.01/30.85
% 10.01/30.85
% 10.01/30.85 %
% 10.01/30.85
% 10.01/30.85 % ------ Proving...
% 10.01/30.85 % Proof_search_loop: time out after: 2219 full_loop iterations
% 10.01/30.85
% 10.01/30.85 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" stripped conjectures Time Limit: 15.
% 10.01/30.85
% 10.01/30.85
% 10.01/30.85 % ------
% 10.01/30.85 % Current options:
% 10.01/30.85 % ------
% 10.01/30.85
% 10.01/30.85
% 10.01/30.85 %
% 10.01/30.85
% 10.01/30.85 % ------ Proving...
% 10.01/30.85 % Proof_search_loop: time out after: 3214 full_loop iterations
% 10.01/30.85
% 10.01/30.85 % ------ Option_1: Negative Selections stripped conjectures Time Limit: 35.
% 10.01/30.85
% 10.01/30.85
% 10.01/30.85 % ------
% 10.01/30.85 % Current options:
% 10.01/30.85 % ------
% 10.01/30.85
% 10.01/30.85
% 10.01/30.85 %
% 10.01/30.85
% 10.01/30.85 % ------ Proving...
% 10.01/30.85 %
% 10.01/30.85
% 10.01/30.85 % SZS status Unsatisfiable for theBenchmark.p
% 10.01/30.85
% 10.01/30.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.01/30.85
% 10.01/30.85
%------------------------------------------------------------------------------