%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV611-1 : 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 03:23:53 PM UTC 2026
% Result : Unsatisfiable 96.30s 34.47s
% Output : CNFRefutation 96.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 66 ( 32 unt; 0 def)
% Number of atoms : 152 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 166 ( 80 ~; 86 |; 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 : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
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(f157,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
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(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(f506,axiom,
! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X0),X1,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(c_HOL_Ozero__class_Ozero(X0),X1,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__less__eq_2) ).
fof(f507,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X1,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,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_zero__less__divide__iff_3) ).
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(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(f812,axiom,
c_HOL_Oord__class_Oless(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_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__half__less__two_0) ).
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(f996,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
tcf(c_1040,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Opi,
inference(cnf_transformation,[],[f152]) ).
tcf(c_1045,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_1125,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_1239,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_1283,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_1343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X0,X1,X2),X3,X2) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_1344,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,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),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_1376,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_1380,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_1382,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_1429,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_1522,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f731]) ).
tcf(c_1583,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_1594,plain,
c_HOL_Oord__class_Oless(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_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f812]) ).
tcf(c_1631,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_1638,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_1639,plain,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
inference(cnf_transformation,[],[f872]) ).
tcf(c_1641,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_1736,plain,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f969]) ).
tcf(c_1744,plain,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f977]) ).
tcf(c_1763,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f996]) ).
tcf(c_2799,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_1638,c_1639,c_1641,c_1638]) ).
tcf(c_6556,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_2799,c_1631]) ).
tcf(c_6557,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_1583,c_1631]) ).
tcf(c_9010,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_1045,c_1763]) ).
tcf(c_9011,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_9010]) ).
tcf(c_15969,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1344,c_1744]) ).
tcf(c_15970,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ 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) ),
inference(unflattening,[status(thm)],[c_15969]) ).
tcf(c_15971,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(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),c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(global_subsumption_just,[status(thm)],[c_15970,c_1736,c_15970]) ).
tcf(c_16041,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_1239,c_1744]) ).
tcf(c_16042,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_16041]) ).
tcf(c_16778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1343,c_1744]) ).
tcf(c_16779,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X1,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(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_16778]) ).
tcf(c_16781,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X1,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(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
inference(global_subsumption_just,[status(thm)],[c_16779,c_1736,c_16779]) ).
tcf(c_38325,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_1522,c_1283]) ).
tcf(c_39210,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_16042]) ).
tcf(c_41311,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_HOL_Oord__class_Oless(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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(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_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_16781]) ).
tcf(c_41885,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_1429,c_1125]) ).
tcf(c_42825,plain,
! [X0: $i] :
( 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(X0,c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(instantiation,[status(thm)],[c_15971]) ).
tcf(c_44865,plain,
( ~ c_HOL_Oord__class_Oless(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),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(instantiation,[status(thm)],[c_9011]) ).
tcf(c_46516,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_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_42825]) ).
tcf(c_47016,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_1376]) ).
tcf(c_51810,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_1380]) ).
tcf(c_51811,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_51810,c_47016,c_46516,c_44865,c_41885,c_41311,c_39210,c_38325,c_6557,c_6556,c_1594,c_1040,c_1382]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV611-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/20.44 % Computer : n010.cluster.edu
% 0.15/20.44 % Model : x86_64 x86_64
% 0.15/20.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/20.44 % Memory : 8046.5625MB
% 0.15/20.44 % OS : Linux 6.8.0-71-generic
% 0.15/20.44 % CPULimit : 300
% 0.15/20.44 % WCLimit : 300
% 0.15/20.44 % DateTime : Thu Sep 24 20:43:35 UTC 2026
% 0.15/20.44 % CPUTime :
% 0.15/20.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/20.48 Running first-order theorem proving
% 0.15/20.48 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
% 0.15/20.49
% 0.15/20.49 % ======== iProver multi-core TPTP/SMT =========
% 0.15/20.49
% 0.15/20.49 % Detected problem language: tptp
% 0.18/20.50 % Proving...
% 96.30/34.47 % SZS status Started for theBenchmark.p
% 96.30/34.47 % SZS status Unsatisfiable for theBenchmark.p
% 96.30/34.47
% 96.30/34.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 96.30/34.47
% 96.30/34.47 % ------ iProver source info
% 96.30/34.47
% 96.30/34.47 % git: date: 2026-07-19 20:42:38 +0200
% 96.30/34.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 96.30/34.47 % git: non_committed_changes: false
% 96.30/34.47
% 96.30/34.47 % ------ Parsing...% successful
% 96.30/34.47
% 96.30/34.47
% 96.30/34.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 96.30/34.47
% 96.30/34.47 % ------ Preprocessing... sup_sim: 8 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 %
% 96.30/34.47
% 96.30/34.47 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 96.30/34.47
% 96.30/34.47 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e sf_s rm: 0 0s sf_e sf_s rm: 0 0s sf_e
% 96.30/34.47 % ------ Proving...
% 96.30/34.47 % ------ Problem Properties
% 96.30/34.47
% 96.30/34.47 %
% 96.30/34.47 % clauses 873
% 96.30/34.47 % conjectures 0
% 96.30/34.47 % EPR 59
% 96.30/34.47 % Horn 749
% 96.30/34.47 % unary 282
% 96.30/34.47 % binary 250
% 96.30/34.47 % lits 1895
% 96.30/34.47 % lits eq 624
% 96.30/34.47 % fd_pure 0
% 96.30/34.47 % fd_pseudo 0
% 96.30/34.47 % fd_cond 58
% 96.30/34.47 % fd_pseudo_cond 66
% 96.30/34.47 % AC symbols 0
% 96.30/34.47
% 96.30/34.47 % ------ Input Options Time Limit: Unbounded
% 96.30/34.47
% 96.30/34.47
% 96.30/34.47 % ------
% 96.30/34.47 % Current options:
% 96.30/34.47 % ------
% 96.30/34.47
% 96.30/34.47
% 96.30/34.47 %
% 96.30/34.47
% 96.30/34.47 % ------ Proving...
% 96.30/34.47 %
% 96.30/34.47
% 96.30/34.47 % SZS status Unsatisfiable for theBenchmark.p
% 96.30/34.47
% 96.30/34.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 96.30/34.47
% 96.30/34.47
%------------------------------------------------------------------------------