%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW177+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 : Tue Sep 29 01:29:46 PM UTC 2026
% Result : Theorem 14.68s 2.56s
% Output : Refutation 15.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 30
% Syntax : Number of formulae : 148 ( 76 unt; 12 def)
% Number of atoms : 262 ( 62 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 209 ( 95 ~; 91 |; 11 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-3 aty)
% Number of variables : 137 ( 0 sgn 137 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Olinorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Orderings_Oord__class_Omin(X3,X1,X0))
<=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
& c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).
fof(f444,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(f594,axiom,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X0 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(f675,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__gt__half__sum) ).
fof(f689,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
fof(f699,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f708,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f709,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f710,axiom,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f771,axiom,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f866,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(f901,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(f1102,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f1142,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1147,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f1198,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1199,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f1200,conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(f1201,negated_conjecture,
~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
inference(negated_conjecture,[status(cth)],[f1200]) ).
fof(f1248,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,X2,c_Orderings_Oord__class_Omin(X3,X1,X0))
<=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
& c_Orderings_Oord__class_Oless(X3,X2,X0) ) )
| ~ class_Orderings_Olinorder(X3) ),
inference(ennf_transformation,[],[f56]) ).
fof(f1639,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(ennf_transformation,[],[f444]) ).
fof(f1640,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(flattening,[],[f1639]) ).
fof(f1956,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f675]) ).
fof(f2129,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f901]) ).
fof(f2229,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
inference(ennf_transformation,[],[f1201]) ).
fof(f2289,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X3,X2,c_Orderings_Oord__class_Omin(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X0) )
& ( ( c_Orderings_Oord__class_Oless(X3,X2,X1)
& c_Orderings_Oord__class_Oless(X3,X2,X0) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Orderings_Oord__class_Omin(X3,X1,X0)) ) )
| ~ class_Orderings_Olinorder(X3) ),
inference(nnf_transformation,[],[f1248]) ).
fof(f2290,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X3,X2,c_Orderings_Oord__class_Omin(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X0) )
& ( ( c_Orderings_Oord__class_Oless(X3,X2,X1)
& c_Orderings_Oord__class_Oless(X3,X2,X0) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Orderings_Oord__class_Omin(X3,X1,X0)) ) )
| ~ class_Orderings_Olinorder(X3) ),
inference(flattening,[],[f2289]) ).
fof(f2466,plain,
! [X0,X1] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != X0 )
& ( X0 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f594]) ).
fof(f2737,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X3,X2,c_Orderings_Oord__class_Omin(X3,X1,X0))
| c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ class_Orderings_Olinorder(X3) ),
inference(cnf_transformation,[],[f2290]) ).
fof(f2738,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X3,X2,c_Orderings_Oord__class_Omin(X3,X1,X0))
| c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X3) ),
inference(cnf_transformation,[],[f2290]) ).
fof(f2739,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,c_Orderings_Oord__class_Omin(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ class_Orderings_Olinorder(X3) ),
inference(cnf_transformation,[],[f2290]) ).
fof(f3298,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(cnf_transformation,[],[f1640]) ).
fof(f3509,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)
| c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != X0 ),
inference(cnf_transformation,[],[f2466]) ).
fof(f3746,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f1956]) ).
fof(f3762,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X0,
inference(cnf_transformation,[],[f689]) ).
fof(f3773,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
inference(cnf_transformation,[],[f699]) ).
fof(f3784,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f708]) ).
fof(f3785,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f709]) ).
fof(f3786,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f710]) ).
fof(f3874,plain,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f771]) ).
fof(f4010,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),
inference(cnf_transformation,[],[f866]) ).
fof(f4047,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f2129]) ).
fof(f4281,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1102]) ).
fof(f4321,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1142]) ).
fof(f4326,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1147]) ).
fof(f4377,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
inference(cnf_transformation,[],[f1198]) ).
fof(f4378,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
inference(cnf_transformation,[],[f1199]) ).
fof(f4379,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
inference(cnf_transformation,[],[f2229]) ).
fof(f4604,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(definition_unfolding,[],[f3746,f3786,f3874]) ).
fof(f4612,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = X0,
inference(definition_unfolding,[],[f3762,f3786,f3874,f3786,f3874]) ).
fof(f4649,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_d2) ),
inference(definition_unfolding,[],[f4379,f3786,f3874,f3786,f3874,f3786,f3874]) ).
fof(f4766,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(equality_resolution,[],[f3509]) ).
fof(f4837,definition,
sF29 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f4838,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = sF29,
inference(reorient_equations,[],[f4837]) ).
fof(f4839,definition,
sF30 = c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f4840,plain,
c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2) = sF30,
inference(reorient_equations,[],[f4839]) ).
fof(f4841,definition,
sF31 = c_Groups_Oone__class_Oone(tc_Int_Oint),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f4842,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = sF31,
inference(reorient_equations,[],[f4841]) ).
fof(f4843,definition,
sF32 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF31,c_Int_OPls),
introduced(definition,[new_symbols(definition,[sF32])],[function_definition]) ).
fof(f4844,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF31,c_Int_OPls) = sF32,
inference(reorient_equations,[],[f4843]) ).
fof(f4845,definition,
sF33 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF32,c_Int_OPls),
introduced(definition,[new_symbols(definition,[sF33])],[function_definition]) ).
fof(f4846,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF32,c_Int_OPls) = sF33,
inference(reorient_equations,[],[f4845]) ).
fof(f4847,definition,
sF34 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF33,sF33),
introduced(definition,[new_symbols(definition,[sF34])],[function_definition]) ).
fof(f4848,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF33,sF33) = sF34,
inference(reorient_equations,[],[f4847]) ).
fof(f4849,definition,
sF35 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF34),
introduced(definition,[new_symbols(definition,[sF35])],[function_definition]) ).
fof(f4850,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF34) = sF35,
inference(reorient_equations,[],[f4849]) ).
fof(f4851,definition,
sF36 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF30,sF35),
introduced(definition,[new_symbols(definition,[sF36])],[function_definition]) ).
fof(f4852,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF30,sF35) = sF36,
inference(reorient_equations,[],[f4851]) ).
fof(f4853,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,sF36)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d2) ),
inference(definition_folding,[],[f4649,f4852,f4850,f4848,f4846,f4844,f4842,f4846,f4844,f4842,f4840,f4852,f4850,f4848,f4846,f4844,f4842,f4846,f4844,f4842,f4840,f4852,f4850,f4848,f4846,f4844,f4842,f4846,f4844,f4842,f4840,f4838]) ).
fof(f4861,definition,
( spl37_1
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d2) ),
introduced(definition,[new_symbols(definition,[spl37_1])],[avatar_definition]) ).
fof(f4862,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d2)
| ~ spl37_1 ),
inference(avatar_component_clause,[],[f4861]) ).
fof(f4863,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d2)
| spl37_1 ),
inference(avatar_component_clause,[],[f4861]) ).
fof(f4865,definition,
( spl37_2
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d1) ),
introduced(definition,[new_symbols(definition,[spl37_2])],[avatar_definition]) ).
fof(f4867,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d1)
| spl37_2 ),
inference(avatar_component_clause,[],[f4865]) ).
fof(f4869,definition,
( spl37_3
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,sF36) ),
introduced(definition,[new_symbols(definition,[spl37_3])],[avatar_definition]) ).
fof(f4871,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,sF36)
| spl37_3 ),
inference(avatar_component_clause,[],[f4869]) ).
fof(f4872,plain,
( ~ spl37_1
| ~ spl37_2
| ~ spl37_3 ),
inference(avatar_split_clause,[],[f4853,f4869,f4865,f4861]) ).
fof(f4879,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = X0,
inference(forward_demodulation,[],[f4612,f3773]) ).
fof(f4887,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f4604,f3773]) ).
fof(f4900,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1),
inference(forward_demodulation,[],[f4766,f4010]) ).
fof(f5078,plain,
sF31 = sF32,
inference(forward_demodulation,[],[f4844,f3785]) ).
fof(f5079,plain,
sF32 = sF33,
inference(forward_demodulation,[],[f4846,f3785]) ).
fof(f5083,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))) = X0,
inference(forward_demodulation,[],[f4879,f3773]) ).
fof(f5091,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f4887,f3773]) ).
fof(f5104,plain,
! [X1] : sF29 = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1),
inference(forward_demodulation,[],[f4900,f4838]) ).
fof(f5274,plain,
sF31 = sF33,
inference(forward_demodulation,[],[f5079,f5078]) ).
fof(f5278,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = X0,
inference(forward_demodulation,[],[f5083,f3784]) ).
fof(f5286,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f5091,f3784]) ).
fof(f5420,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = X0,
inference(forward_demodulation,[],[f5278,f3784]) ).
fof(f5428,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f5286,f3784]) ).
fof(f5561,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls)))))) = X0,
inference(forward_demodulation,[],[f5420,f3773]) ).
fof(f5569,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls))))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f5428,f3773]) ).
fof(f5673,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))) = X0,
inference(forward_demodulation,[],[f5561,f3784]) ).
fof(f5681,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f5569,f3784]) ).
fof(f5785,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = X0,
inference(forward_demodulation,[],[f5673,f3785]) ).
fof(f5793,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f5681,f3785]) ).
fof(f5896,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF31,sF31))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF31,sF31)))) = X0,
inference(forward_demodulation,[],[f5785,f4842]) ).
fof(f5904,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF31,sF31))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f5793,f4842]) ).
fof(f6006,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF33,sF33))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF33,sF33)))) = X0,
inference(forward_demodulation,[],[f5896,f5274]) ).
fof(f6014,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF33,sF33))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f5904,f5274]) ).
fof(f6116,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF34)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF34))) = X0,
inference(forward_demodulation,[],[f6006,f4848]) ).
fof(f6124,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF34)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f6014,f4848]) ).
fof(f6226,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,sF35),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,sF35)) = X0,
inference(forward_demodulation,[],[f6116,f4850]) ).
fof(f6234,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),sF35),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f6124,f4850]) ).
fof(f6782,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF30)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_d1)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(superposition,[],[f2738,f4840]) ).
fof(f6783,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF30)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_d1) ),
inference(forward_subsumption_resolution,[],[f6782,f4321]) ).
fof(f6784,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF30)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_d2)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(superposition,[],[f2737,f4840]) ).
fof(f6785,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF30)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_d2) ),
inference(forward_subsumption_resolution,[],[f6784,f4321]) ).
fof(f6786,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,v_d1),
inference(superposition,[],[f4377,f4838]) ).
fof(f6787,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,v_d2),
inference(superposition,[],[f4378,f4838]) ).
fof(f6790,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF30)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_d2)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(superposition,[],[f2739,f4840]) ).
fof(f6793,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_d1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF30) ),
inference(forward_subsumption_resolution,[],[f6790,f4321]) ).
fof(f6794,plain,
sF30 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF36,sF36),
inference(superposition,[],[f6226,f4852]) ).
fof(f6991,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,sF36),sF30)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF36)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(superposition,[],[f3298,f6794]) ).
fof(f6994,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,sF36),sF30)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF36) ),
inference(forward_subsumption_resolution,[],[f6991,f4281]) ).
fof(f7051,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,v_d1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,sF30) ),
inference(resolution,[],[f6793,f6787]) ).
fof(f7066,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,sF30),
inference(forward_subsumption_resolution,[],[f7051,f6786]) ).
fof(f7169,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,sF30),sF35),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF30) ),
inference(resolution,[],[f6234,f6785]) ).
fof(f7170,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,sF30),sF35),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sF30) ),
inference(resolution,[],[f6234,f6783]) ).
fof(f7209,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,sF30)
| ~ spl37_1 ),
inference(resolution,[],[f4862,f6793]) ).
fof(f7211,definition,
( spl37_33
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,sF30) ),
introduced(definition,[new_symbols(definition,[spl37_33])],[avatar_definition]) ).
fof(f7213,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,sF30)
| ~ spl37_33 ),
inference(avatar_component_clause,[],[f7211]) ).
fof(f7214,plain,
( spl37_33
| ~ spl37_2
| ~ spl37_1 ),
inference(avatar_split_clause,[],[f7209,f4861,f4865,f7211]) ).
fof(f13516,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X1) = X0,
inference(resolution,[],[f4326,f4047]) ).
fof(f13518,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF29,X0) = X0,
inference(superposition,[],[f13516,f5104]) ).
fof(f13607,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF30,sF35),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,sF30) ),
inference(superposition,[],[f7169,f13518]) ).
fof(f13608,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF30,sF35),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,sF30) ),
inference(superposition,[],[f7170,f13518]) ).
fof(f13613,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,sF30)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,sF36) ),
inference(superposition,[],[f6994,f13518]) ).
fof(f13643,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF30,sF35),v_d1),
inference(forward_subsumption_resolution,[],[f13608,f7066]) ).
fof(f13644,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF30,sF35),v_d2),
inference(forward_subsumption_resolution,[],[f13607,f7066]) ).
fof(f13660,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d1),
inference(forward_demodulation,[],[f13643,f4852]) ).
fof(f13774,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF36,v_d2),
inference(forward_demodulation,[],[f13644,f4852]) ).
fof(f13832,plain,
( $false
| spl37_1 ),
inference(forward_subsumption_resolution,[],[f13774,f4863]) ).
fof(f13833,plain,
spl37_1,
inference(avatar_contradiction_clause,[],[f13832]) ).
fof(f13947,plain,
( $false
| spl37_2 ),
inference(forward_subsumption_resolution,[],[f13660,f4867]) ).
fof(f13948,plain,
spl37_2,
inference(avatar_contradiction_clause,[],[f13947]) ).
fof(f14016,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF29,sF36)
| ~ spl37_33 ),
inference(forward_subsumption_resolution,[],[f13613,f7213]) ).
fof(f14017,plain,
( $false
| spl37_3
| ~ spl37_33 ),
inference(forward_subsumption_resolution,[],[f14016,f4871]) ).
fof(f14018,plain,
( spl37_3
| ~ spl37_33 ),
inference(avatar_contradiction_clause,[],[f14017]) ).
cnf(s1,plain,
( ~ spl37_1
| ~ spl37_2
| ~ spl37_3 ),
inference(sat_conversion,[],[f4872]) ).
cnf(s16,plain,
( ~ spl37_1
| ~ spl37_2
| spl37_33 ),
inference(sat_conversion,[],[f7214]) ).
cnf(s167,plain,
spl37_1,
inference(sat_conversion,[],[f13833]) ).
cnf(s174,plain,
spl37_2,
inference(sat_conversion,[],[f13948]) ).
cnf(s190,plain,
( spl37_3
| ~ spl37_33 ),
inference(sat_conversion,[],[f14018]) ).
cnf(s198,plain,
spl37_33,
inference(rat,[],[s16,s174,s167]) ).
cnf(s199,plain,
spl37_3,
inference(rat,[],[s190,s198]) ).
cnf(s201,plain,
$false,
inference(rat,[],[s1,s199,s174,s167]) ).
fof(f14019,plain,
$false,
inference(avatar_sat_refutation,[],[s201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW177+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 13:15:47 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.62/2.25 % (2619028)Detected formulas, will run a generic FOF schedule.
% 12.62/2.25 % (2619039)dis-21_1_sil=8000:lcm=predicate:random_seed=2892783388:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 12.62/2.25 % (2619035)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1911952048:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.62/2.25 % (2619034)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3839658681:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.62/2.25 % (2619033)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1889266010:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.62/2.25 % (2619038)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3653997040:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.62/2.25 % (2619036)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1758884630:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.62/2.25 % (2619037)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4169560793:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.62/2.25 % (2619039)Instruction limit reached!
% 12.62/2.25 % (2619039)------------------------------
% 12.62/2.25 % (2619039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.62/2.25 % (2619039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.25 % (2619039)CaDiCaL version: 2.1.3
% 12.62/2.25 % (2619039)Termination reason: Instruction limit
% 12.62/2.25 % (2619039)Termination phase: Saturation
% 12.62/2.25 % (2619039)Time elapsed: 0.036 s
% 12.62/2.25 % (2619039)Peak memory usage: 90 MB
% 12.62/2.25 % (2619039)Instructions burned: 132 (million)
% 12.62/2.25 % (2619036)Instruction limit reached!
% 12.62/2.25 % (2619036)------------------------------
% 12.62/2.25 % (2619036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.62/2.25 % (2619036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.25 % (2619036)CaDiCaL version: 2.1.3
% 12.62/2.25 % (2619036)Termination reason: Instruction limit
% 12.62/2.25 % (2619036)Termination phase: Saturation
% 12.62/2.25 % (2619036)Time elapsed: 0.065 s
% 12.62/2.25 % (2619036)Peak memory usage: 90 MB
% 12.62/2.25 % (2619036)Instructions burned: 110 (million)
% 12.62/2.25 % (2619037)Instruction limit reached!
% 12.62/2.25 % (2619037)------------------------------
% 12.62/2.25 % (2619037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.62/2.25 % (2619037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.25 % (2619037)CaDiCaL version: 2.1.3
% 12.62/2.25 % (2619037)Termination reason: Instruction limit
% 12.62/2.25 % (2619037)Termination phase: Saturation
% 12.62/2.25 % (2619037)Time elapsed: 0.071 s
% 12.62/2.25 % (2619037)Peak memory usage: 89 MB
% 12.62/2.25 % (2619037)Instructions burned: 120 (million)
% 12.62/2.25 % (2619038)Instruction limit reached!
% 12.62/2.25 % (2619038)------------------------------
% 12.62/2.25 % (2619038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.62/2.25 % (2619038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.25 % (2619038)CaDiCaL version: 2.1.3
% 12.62/2.25 % (2619038)Termination reason: Instruction limit
% 12.62/2.25 % (2619038)Termination phase: Saturation
% 12.62/2.25 % (2619038)Time elapsed: 0.078 s
% 12.62/2.25 % (2619038)Peak memory usage: 91 MB
% 12.62/2.25 % (2619038)Instructions burned: 139 (million)
% 12.62/2.25 % (2619047)lrs+10_1_sil=8000:sp=occurrence:random_seed=2360171362:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 12.62/2.25 % (2619047)Instruction limit reached!
% 12.62/2.25 % (2619047)------------------------------
% 12.62/2.25 % (2619047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.62/2.25 % (2619047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.25 % (2619047)CaDiCaL version: 2.1.3
% 12.62/2.25 % (2619047)Termination reason: Instruction limit
% 12.62/2.25 % (2619047)Termination phase: Saturation
% 12.62/2.25 % (2619047)Time elapsed: 0.096 s
% 12.62/2.25 % (2619047)Peak memory usage: 92 MB
% 12.62/2.25 % (2619047)Instructions burned: 285 (million)
% 14.68/2.56 % (2619048)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1891980193:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 14.68/2.56 % (2619049)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1929939336:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 14.68/2.56 % (2619050)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1796407975:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 14.68/2.56 % (2619048)Instruction limit reached!
% 14.68/2.56 % (2619048)------------------------------
% 14.68/2.56 % (2619048)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619048)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619048)Termination reason: Instruction limit
% 14.68/2.56 % (2619048)Termination phase: Saturation
% 14.68/2.56 % (2619048)Time elapsed: 0.083 s
% 14.68/2.56 % (2619048)Peak memory usage: 91 MB
% 14.68/2.56 % (2619048)Instructions burned: 159 (million)
% 14.68/2.56 % (2619054)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1041997360:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 14.68/2.56 % (2619050)Instruction limit reached!
% 14.68/2.56 % (2619050)------------------------------
% 14.68/2.56 % (2619050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619050)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619050)Termination reason: Instruction limit
% 14.68/2.56 % (2619050)Termination phase: Saturation
% 14.68/2.56 % (2619050)Time elapsed: 0.145 s
% 14.68/2.56 % (2619050)Peak memory usage: 92 MB
% 14.68/2.56 % (2619050)Instructions burned: 249 (million)
% 14.68/2.56 % (2619054)Instruction limit reached!
% 14.68/2.56 % (2619054)------------------------------
% 14.68/2.56 % (2619054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619054)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619054)Termination reason: Instruction limit
% 14.68/2.56 % (2619054)Termination phase: Saturation
% 14.68/2.56 % (2619054)Time elapsed: 0.083 s
% 14.68/2.56 % (2619054)Peak memory usage: 91 MB
% 14.68/2.56 % (2619054)Instructions burned: 297 (million)
% 14.68/2.56 % (2619049)Instruction limit reached!
% 14.68/2.56 % (2619049)------------------------------
% 14.68/2.56 % (2619049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619049)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619049)Termination reason: Instruction limit
% 14.68/2.56 % (2619049)Termination phase: Saturation
% 14.68/2.56 % (2619049)Time elapsed: 0.211 s
% 14.68/2.56 % (2619049)Peak memory usage: 92 MB
% 14.68/2.56 % (2619049)Instructions burned: 325 (million)
% 14.68/2.56 % (2619056)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=16832860:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 14.68/2.56 % (2619059)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=786989110:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 14.68/2.56 % (2619058)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1358702293:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 14.68/2.56 % (2619059)Instruction limit reached!
% 14.68/2.56 % (2619059)------------------------------
% 14.68/2.56 % (2619059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619059)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619059)Termination reason: Instruction limit
% 14.68/2.56 % (2619059)Termination phase: Saturation
% 14.68/2.56 % (2619059)Time elapsed: 0.030 s
% 14.68/2.56 % (2619059)Peak memory usage: 90 MB
% 14.68/2.56 % (2619059)Instructions burned: 127 (million)
% 14.68/2.56 % (2619060)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1712390912:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 14.68/2.56 % (2619058)Instruction limit reached!
% 14.68/2.56 % (2619058)------------------------------
% 14.68/2.56 % (2619058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619058)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619058)Termination reason: Instruction limit
% 14.68/2.56 % (2619058)Termination phase: Saturation
% 14.68/2.56 % (2619058)Time elapsed: 0.057 s
% 14.68/2.56 % (2619058)Peak memory usage: 90 MB
% 14.68/2.56 % (2619058)Instructions burned: 114 (million)
% 14.68/2.56 % (2619060)Instruction limit reached!
% 14.68/2.56 % (2619060)------------------------------
% 14.68/2.56 % (2619060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619060)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619060)Termination reason: Instruction limit
% 14.68/2.56 % (2619060)Termination phase: Saturation
% 14.68/2.56 % (2619060)Time elapsed: 0.057 s
% 14.68/2.56 % (2619060)Peak memory usage: 90 MB
% 14.68/2.56 % (2619060)Instructions burned: 115 (million)
% 14.68/2.56 % (2619064)lrs+10_1_sil=8000:sp=occurrence:random_seed=601239931:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 14.68/2.56 % (2619066)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3213981178:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 14.68/2.56 % (2619067)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2817929872:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 14.68/2.56 % (2619064)Instruction limit reached!
% 14.68/2.56 % (2619064)------------------------------
% 14.68/2.56 % (2619064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619064)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619064)Termination reason: Instruction limit
% 14.68/2.56 % (2619064)Termination phase: Saturation
% 14.68/2.56 % (2619064)Time elapsed: 0.297 s
% 14.68/2.56 % (2619064)Peak memory usage: 95 MB
% 14.68/2.56 % (2619064)Instructions burned: 908 (million)
% 14.68/2.56 % (2619066)Instruction limit reached!
% 14.68/2.56 % (2619066)------------------------------
% 14.68/2.56 % (2619066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619066)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619066)Termination reason: Instruction limit
% 14.68/2.56 % (2619066)Termination phase: Saturation
% 14.68/2.56 % (2619066)Time elapsed: 0.238 s
% 14.68/2.56 % (2619066)Peak memory usage: 94 MB
% 14.68/2.56 % (2619066)Instructions burned: 438 (million)
% 14.68/2.56 % (2619071)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2159467868:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 14.68/2.56 % (2619071)Instruction limit reached!
% 14.68/2.56 % (2619071)------------------------------
% 14.68/2.56 % (2619071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619071)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619071)Termination reason: Instruction limit
% 14.68/2.56 % (2619071)Termination phase: Saturation
% 14.68/2.56 % (2619071)Time elapsed: 0.038 s
% 14.68/2.56 % (2619071)Peak memory usage: 92 MB
% 14.68/2.56 % (2619071)Instructions burned: 135 (million)
% 14.68/2.56 % (2619072)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=487317720:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 14.68/2.56 % (2619074)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3014627721:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 14.68/2.56 % (2619072)Instruction limit reached!
% 14.68/2.56 % (2619072)------------------------------
% 14.68/2.56 % (2619072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619072)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619072)Termination reason: Instruction limit
% 14.68/2.56 % (2619072)Termination phase: Saturation
% 14.68/2.56 % (2619072)Time elapsed: 0.325 s
% 14.68/2.56 % (2619072)Peak memory usage: 94 MB
% 14.68/2.56 % (2619072)Instructions burned: 592 (million)
% 14.68/2.56 % (2619077)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=445585611:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/125Mi)
% 14.68/2.56 % (2619033)First to succeed.
% 14.68/2.56 % (2619033)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2619028"
% 14.68/2.56 % (2619077)Instruction limit reached!
% 14.68/2.56 % (2619077)------------------------------
% 14.68/2.56 % (2619077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619077)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619077)Termination reason: Instruction limit
% 14.68/2.56 % (2619077)Termination phase: Saturation
% 14.68/2.56 % (2619077)Time elapsed: 0.072 s
% 14.68/2.56 % (2619077)Peak memory usage: 91 MB
% 14.68/2.56 % (2619077)Instructions burned: 126 (million)
% 14.68/2.56 % (2619056)Instruction limit reached!
% 14.68/2.56 % (2619056)------------------------------
% 14.68/2.56 % (2619056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/2.56 % (2619056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/2.56 % (2619056)CaDiCaL version: 2.1.3
% 14.68/2.56 % (2619056)Termination reason: Instruction limit
% 14.68/2.56 % (2619056)Termination phase: Saturation
% 14.68/2.56 % (2619056)Time elapsed: 1.422 s
% 14.68/2.56 % (2619056)Peak memory usage: 150 MB
% 14.68/2.56 % (2619056)Instructions burned: 2351 (million)
% 14.68/2.56 % (2619079)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3631167022:i=134:gtgl=5:slsql=off:gtg=exists_sym_2980 on theBenchmark for (2980ds/134Mi)
% 14.68/2.56 % (2619033)Refutation found. Thanks to Tanya!
% 14.68/2.56 % SZS status Theorem for theBenchmark
% 14.68/2.56 % SZS output start Proof for theBenchmark
% See solution above
% 15.46/2.76 % (2619033)------------------------------
% 15.46/2.76 % (2619033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.46/2.76 % (2619033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.46/2.76 % (2619033)CaDiCaL version: 2.1.3
% 15.46/2.76 % (2619033)Termination reason: Refutation
% 15.46/2.76 % (2619033)Time elapsed: 1.679 s
% 15.46/2.76 % (2619033)Peak memory usage: 148 MB
% 15.46/2.76 % (2619033)Instructions burned: 2670 (million)
% 15.46/2.76 % (2619033)------------------------------
% 15.46/2.76 % (2619033)------------------------------
% 15.46/2.76 % (2619028)Success in time 2.148 s
% 15.46/2.76 % Vampire exiting
%------------------------------------------------------------------------------