%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU079+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:47:12 PM UTC 2026
% Result : Theorem 7.10s 1.88s
% Output : Refutation 9.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 129 ( 26 unt; 7 def)
% Number of atoms : 579 ( 67 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 766 ( 316 ~; 327 |; 85 &)
% ( 23 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 9 con; 0-4 aty)
% Number of variables : 366 ( 0 sgn 316 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f10,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f11,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f12,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f40,conjecture,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0))) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f60,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f61,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f66,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f67,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f66]) ).
fof(f81,plain,
? [X0,X1] :
( ? [X2] :
( ~ subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0)))
& subset(relation_rng(X1),relation_dom(X2))
& relation(X2) )
& relation(X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
? [X0,X1] :
( ? [X2] :
( ~ subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0)))
& subset(relation_rng(X1),relation_dom(X2))
& relation(X2) )
& relation(X1) ),
inference(flattening,[],[f81]) ).
fof(f92,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f60]) ).
fof(f93,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X3),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X8,X6),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| ~ in(X4,X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
& in(sK1(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
& in(sK2(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f93]) ).
fof(f95,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f61]) ).
fof(f96,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X6,X8),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(sK3(X0,X1,X2),X4),X0)
| ~ in(X4,X1) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X0)
& in(sK4(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(X6,sK5(X0,X1,X6)),X0)
& in(sK5(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X5,sK4(X0,X1,X2)),skolemize(X8,sK5(X0,X1,X6))],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f99,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f99]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f102]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f64]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK10(X0,X1)),X0)
| ~ in(sK10(X0,X1),X1) )
& ( in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0)
| in(sK10(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK12(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X2,sK10(X0,X1)),skolemize(X4,sK11(X0,X1)),skolemize(X7,sK12(X0,X5))],[f105]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ( ( ! [X5] :
( ~ in(ordered_pair(sK13(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK14(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK13(X0,X1,X2),sK15(X0,X1,X2)),X0)
& in(ordered_pair(sK15(X0,X1,X2),sK14(X0,X1,X2)),X1) )
| in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK16(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK16(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X3,sK13(X0,X1,X2)),skolemize(X4,sK14(X0,X1,X2)),skolemize(X6,sK15(X0,X1,X2)),skolemize(X10,sK16(X0,X1,X7,X8))],[f108]) ).
fof(f121,plain,
( ~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))
& subset(relation_rng(sK29),relation_dom(sK30))
& relation(sK30)
& relation(sK29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30]),skolemize(X0,sK28),skolemize(X1,sK29),skolemize(X2,sK30)],[f82]) ).
fof(f131,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f135,plain,
! [X2,X0,X1,X6] :
( in(sK5(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f136,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK5(X0,X1,X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f137,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f141,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f142,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f143,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f144,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f149,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f152,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f155,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f159,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f201,plain,
relation(sK29),
inference(cnf_transformation,[],[f121]) ).
fof(f202,plain,
relation(sK30),
inference(cnf_transformation,[],[f121]) ).
fof(f203,plain,
subset(relation_rng(sK29),relation_dom(sK30)),
inference(cnf_transformation,[],[f121]) ).
fof(f204,plain,
~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),
inference(cnf_transformation,[],[f121]) ).
fof(f216,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f131,f152]) ).
fof(f220,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f137,f152]) ).
fof(f221,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f136,f152]) ).
fof(f225,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f144,f152]) ).
fof(f228,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f149,f152]) ).
fof(f233,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f155,f152,f152,f152]) ).
fof(f237,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,relation_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f216]) ).
fof(f240,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,relation_inverse_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f220]) ).
fof(f241,plain,
! [X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f221]) ).
fof(f242,plain,
! [X0,X1,X6] :
( in(sK5(X0,X1,X6),X1)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f135]) ).
fof(f244,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f225]) ).
fof(f245,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f228]) ).
fof(f247,plain,
! [X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f233]) ).
fof(f250,definition,
sF31 = relation_inverse_image(sK29,sK28),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f251,plain,
relation_inverse_image(sK29,sK28) = sF31,
inference(reorient_equations,[],[f250]) ).
fof(f252,definition,
sF32 = relation_composition(sK29,sK30),
introduced(definition,[new_symbols(definition,[sF32])],[function_definition]) ).
fof(f253,plain,
relation_composition(sK29,sK30) = sF32,
inference(reorient_equations,[],[f252]) ).
fof(f254,definition,
sF33 = relation_image(sK30,sK28),
introduced(definition,[new_symbols(definition,[sF33])],[function_definition]) ).
fof(f255,plain,
relation_image(sK30,sK28) = sF33,
inference(reorient_equations,[],[f254]) ).
fof(f256,definition,
sF34 = relation_inverse_image(sF32,sF33),
introduced(definition,[new_symbols(definition,[sF34])],[function_definition]) ).
fof(f257,plain,
relation_inverse_image(sF32,sF33) = sF34,
inference(reorient_equations,[],[f256]) ).
fof(f258,plain,
~ subset(sF31,sF34),
inference(definition_folding,[],[f204,f257,f255,f253,f251]) ).
fof(f259,definition,
sF35 = relation_rng(sK29),
introduced(definition,[new_symbols(definition,[sF35])],[function_definition]) ).
fof(f260,plain,
relation_rng(sK29) = sF35,
inference(reorient_equations,[],[f259]) ).
fof(f261,definition,
sF36 = relation_dom(sK30),
introduced(definition,[new_symbols(definition,[sF36])],[function_definition]) ).
fof(f262,plain,
relation_dom(sK30) = sF36,
inference(reorient_equations,[],[f261]) ).
fof(f263,plain,
subset(sF35,sF36),
inference(definition_folding,[],[f203,f262,f260]) ).
fof(f266,plain,
! [X0,X1,X8,X9,X7] :
( ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f247,f159]) ).
fof(f269,plain,
! [X0] :
( ~ in(X0,sF35)
| in(X0,sF36) ),
inference(resolution,[],[f141,f263]) ).
fof(f278,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),relation_rng(X0))
| ~ relation(X0)
| ~ in(X2,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(resolution,[],[f245,f241]) ).
fof(f281,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),relation_rng(X0))
| ~ relation(X0)
| ~ in(X2,relation_inverse_image(X0,X1)) ),
inference(duplicate_literal_removal,[],[f278]) ).
fof(f311,definition,
( spl37_4
<=> relation(sF32) ),
introduced(definition,[new_symbols(definition,[spl37_4])],[avatar_definition]) ).
fof(f312,plain,
( relation(sF32)
| ~ spl37_4 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f313,plain,
( ~ relation(sF32)
| spl37_4 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f381,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X3)
| in(unordered_pair(unordered_pair(X2,sK9(X1,X0)),singleton(X2)),relation_composition(X3,X1))
| ~ relation(X1)
| ~ relation(X3) ),
inference(resolution,[],[f244,f266]) ).
fof(f384,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(sK9(X1,X0),relation_image(X1,X2))
| ~ in(X0,X2)
| ~ relation(X1) ),
inference(resolution,[],[f244,f237]) ).
fof(f390,plain,
! [X2,X0,X1] :
( in(sK9(X1,X0),relation_image(X1,X2))
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| ~ in(X0,X2) ),
inference(duplicate_literal_removal,[],[f384]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X2,sK9(X1,X0)),singleton(X2)),relation_composition(X3,X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X3)
| ~ in(X0,relation_dom(X1))
| ~ relation(X3) ),
inference(duplicate_literal_removal,[],[f381]) ).
fof(f446,plain,
! [X0,X1] :
( in(sK5(sK29,X0,X1),sF35)
| ~ relation(sK29)
| ~ in(X1,relation_inverse_image(sK29,X0)) ),
inference(superposition,[],[f281,f260]) ).
fof(f448,plain,
! [X0,X1] :
( in(sK5(sK29,X0,X1),sF35)
| ~ in(X1,relation_inverse_image(sK29,X0)) ),
inference(forward_subsumption_resolution,[],[f446,f201]) ).
fof(f620,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK29,X1))
| in(sK5(sK29,X1,X0),sF36) ),
inference(resolution,[],[f448,f269]) ).
fof(f823,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK9(sK30,X1)),singleton(X0)),sF32)
| ~ relation(sK30)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK29)
| ~ in(X1,relation_dom(sK30))
| ~ relation(sK29) ),
inference(superposition,[],[f393,f253]) ).
fof(f830,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK9(sK30,X1)),singleton(X0)),sF32)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK29)
| ~ in(X1,relation_dom(sK30))
| ~ relation(sK29) ),
inference(forward_subsumption_resolution,[],[f823,f202]) ).
fof(f840,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK9(sK30,X1)),singleton(X0)),sF32)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK29)
| ~ in(X1,relation_dom(sK30)) ),
inference(forward_subsumption_resolution,[],[f830,f201]) ).
fof(f841,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK9(sK30,X1)),singleton(X0)),sF32)
| ~ in(X1,sF36)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK29) ),
inference(forward_demodulation,[],[f840,f262]) ).
fof(f848,plain,
! [X2,X0,X1] :
( ~ in(X0,sF36)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK29)
| in(X1,relation_inverse_image(sF32,X2))
| ~ in(sK9(sK30,X0),X2)
| ~ relation(sF32) ),
inference(resolution,[],[f841,f240]) ).
fof(f878,plain,
( relation(sF32)
| ~ relation(sK29)
| ~ relation(sK30) ),
inference(superposition,[],[f159,f253]) ).
fof(f879,plain,
( ~ relation(sK29)
| ~ relation(sK30)
| spl37_4 ),
inference(forward_subsumption_resolution,[],[f878,f313]) ).
fof(f880,plain,
( ~ relation(sK30)
| spl37_4 ),
inference(forward_subsumption_resolution,[],[f879,f201]) ).
fof(f881,plain,
( $false
| spl37_4 ),
inference(forward_subsumption_resolution,[],[f880,f202]) ).
fof(f882,plain,
spl37_4,
inference(avatar_contradiction_clause,[],[f881]) ).
fof(f900,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK29)
| ~ in(X0,sF36)
| in(X1,relation_inverse_image(sF32,X2))
| ~ in(sK9(sK30,X0),X2) )
| ~ spl37_4 ),
inference(forward_subsumption_resolution,[],[f848,f312]) ).
fof(f959,plain,
! [X0] :
( in(sK9(sK30,X0),sF33)
| ~ relation(sK30)
| ~ in(X0,relation_dom(sK30))
| ~ in(X0,sK28) ),
inference(superposition,[],[f390,f255]) ).
fof(f962,plain,
! [X0] :
( in(sK9(sK30,X0),sF33)
| ~ in(X0,relation_dom(sK30))
| ~ in(X0,sK28) ),
inference(forward_subsumption_resolution,[],[f959,f202]) ).
fof(f963,plain,
! [X0] :
( in(sK9(sK30,X0),sF33)
| ~ in(X0,sF36)
| ~ in(X0,sK28) ),
inference(forward_demodulation,[],[f962,f262]) ).
fof(f1226,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(sK29,X0,X1),sF36)
| in(X1,relation_inverse_image(sF32,X2))
| ~ in(sK9(sK30,sK5(sK29,X0,X1)),X2)
| ~ in(X1,relation_inverse_image(sK29,X0))
| ~ relation(sK29) )
| ~ spl37_4 ),
inference(resolution,[],[f900,f241]) ).
fof(f1237,plain,
( ! [X2,X0,X1] :
( in(X1,relation_inverse_image(sF32,X2))
| ~ in(sK9(sK30,sK5(sK29,X0,X1)),X2)
| ~ in(X1,relation_inverse_image(sK29,X0))
| ~ relation(sK29) )
| ~ spl37_4 ),
inference(forward_subsumption_resolution,[],[f1226,f620]) ).
fof(f1240,plain,
( ! [X2,X0,X1] :
( ~ in(sK9(sK30,sK5(sK29,X0,X1)),X2)
| in(X1,relation_inverse_image(sF32,X2))
| ~ in(X1,relation_inverse_image(sK29,X0)) )
| ~ spl37_4 ),
inference(forward_subsumption_resolution,[],[f1237,f201]) ).
fof(f1244,plain,
( ! [X0,X1] :
( in(X0,relation_inverse_image(sF32,sF33))
| ~ in(X0,relation_inverse_image(sK29,X1))
| ~ in(sK5(sK29,X1,X0),sF36)
| ~ in(sK5(sK29,X1,X0),sK28) )
| ~ spl37_4 ),
inference(resolution,[],[f1240,f963]) ).
fof(f1247,plain,
( ! [X0,X1] :
( in(X0,relation_inverse_image(sF32,sF33))
| ~ in(X0,relation_inverse_image(sK29,X1))
| ~ in(sK5(sK29,X1,X0),sK28) )
| ~ spl37_4 ),
inference(forward_subsumption_resolution,[],[f1244,f620]) ).
fof(f1249,plain,
( ! [X0,X1] :
( ~ in(sK5(sK29,X1,X0),sK28)
| ~ in(X0,relation_inverse_image(sK29,X1))
| in(X0,sF34) )
| ~ spl37_4 ),
inference(forward_demodulation,[],[f1247,f257]) ).
fof(f1252,plain,
( ! [X0] :
( ~ in(X0,relation_inverse_image(sK29,sK28))
| in(X0,sF34)
| ~ in(X0,relation_inverse_image(sK29,sK28))
| ~ relation(sK29) )
| ~ spl37_4 ),
inference(resolution,[],[f1249,f242]) ).
fof(f1253,plain,
( ! [X0] :
( ~ in(X0,relation_inverse_image(sK29,sK28))
| in(X0,sF34)
| ~ relation(sK29) )
| ~ spl37_4 ),
inference(duplicate_literal_removal,[],[f1252]) ).
fof(f1254,plain,
( ! [X0] :
( ~ in(X0,relation_inverse_image(sK29,sK28))
| in(X0,sF34) )
| ~ spl37_4 ),
inference(forward_subsumption_resolution,[],[f1253,f201]) ).
fof(f1255,plain,
( ! [X0] :
( ~ in(X0,sF31)
| in(X0,sF34) )
| ~ spl37_4 ),
inference(forward_demodulation,[],[f1254,f251]) ).
fof(f1273,plain,
( ! [X0] :
( in(sK6(sF31,X0),sF34)
| subset(sF31,X0) )
| ~ spl37_4 ),
inference(resolution,[],[f1255,f142]) ).
fof(f1334,plain,
( subset(sF31,sF34)
| subset(sF31,sF34)
| ~ spl37_4 ),
inference(resolution,[],[f1273,f143]) ).
fof(f1335,plain,
( subset(sF31,sF34)
| ~ spl37_4 ),
inference(duplicate_literal_removal,[],[f1334]) ).
fof(f1336,plain,
( $false
| ~ spl37_4 ),
inference(forward_subsumption_resolution,[],[f1335,f258]) ).
fof(f1337,plain,
~ spl37_4,
inference(avatar_contradiction_clause,[],[f1336]) ).
cnf(s14,plain,
spl37_4,
inference(sat_conversion,[],[f882]) ).
cnf(s29,plain,
~ spl37_4,
inference(sat_conversion,[],[f1337]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s14,s29]) ).
fof(f1338,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU079+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:32:24 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.10/1.88 % (1843090)Detected formulas, will run a generic FOF schedule.
% 7.10/1.88 % (1843100)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2354855307:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.10/1.88 % (1843097)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=3448930430:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.10/1.88 % (1843099)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1848249601:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.10/1.88 % (1843101)dis-21_1_sil=8000:lcm=predicate:random_seed=2138226135: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)
% 7.10/1.88 % (1843098)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=957610382:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.10/1.88 % (1843095)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=4181167128:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.10/1.88 % (1843096)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=418283043:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.10/1.88 % (1843098)Refutation not found, incomplete strategy
% 7.10/1.88 % (1843098)------------------------------
% 7.10/1.88 % (1843098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843098)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843098)Termination reason: Refutation not found, incomplete strategy
% 7.10/1.88 % (1843098)Time elapsed: 0.005 s
% 7.10/1.88 % (1843098)Peak memory usage: 88 MB
% 7.10/1.88 % (1843098)Instructions burned: 6 (million)
% 7.10/1.88 % (1843100)Instruction limit reached!
% 7.10/1.88 % (1843100)------------------------------
% 7.10/1.88 % (1843100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843100)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843100)Termination reason: Instruction limit
% 7.10/1.88 % (1843100)Termination phase: Saturation
% 7.10/1.88 % (1843100)Time elapsed: 0.052 s
% 7.10/1.88 % (1843100)Peak memory usage: 90 MB
% 7.10/1.88 % (1843100)Instructions burned: 140 (million)
% 7.10/1.88 % (1843099)Instruction limit reached!
% 7.10/1.88 % (1843099)------------------------------
% 7.10/1.88 % (1843099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843099)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843099)Termination reason: Instruction limit
% 7.10/1.88 % (1843099)Termination phase: Saturation
% 7.10/1.88 % (1843099)Time elapsed: 0.070 s
% 7.10/1.88 % (1843099)Peak memory usage: 89 MB
% 7.10/1.88 % (1843099)Instructions burned: 120 (million)
% 7.10/1.88 % (1843101)Instruction limit reached!
% 7.10/1.88 % (1843101)------------------------------
% 7.10/1.88 % (1843101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843101)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843101)Termination reason: Instruction limit
% 7.10/1.88 % (1843101)Termination phase: Saturation
% 7.10/1.88 % (1843101)Time elapsed: 0.081 s
% 7.10/1.88 % (1843101)Peak memory usage: 90 MB
% 7.10/1.88 % (1843101)Instructions burned: 130 (million)
% 7.10/1.88 % (1843109)lrs+10_1_sil=8000:sp=occurrence:random_seed=2882705055:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.10/1.88 % (1843110)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4109195684:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.10/1.88 % (1843111)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1183573027:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.10/1.88 % (1843098)------------------------------
% 7.10/1.88 % (1843098)------------------------------
% 7.10/1.88 % (1843110)Instruction limit reached!
% 7.10/1.88 % (1843110)------------------------------
% 7.10/1.88 % (1843110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843110)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843110)Termination reason: Instruction limit
% 7.10/1.88 % (1843110)Termination phase: Saturation
% 7.10/1.88 % (1843110)Time elapsed: 0.080 s
% 7.10/1.88 % (1843110)Peak memory usage: 91 MB
% 7.10/1.88 % (1843110)Instructions burned: 159 (million)
% 7.10/1.88 % (1843109)Instruction limit reached!
% 7.10/1.88 % (1843109)------------------------------
% 7.10/1.88 % (1843109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843109)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843109)Termination reason: Instruction limit
% 7.10/1.88 % (1843109)Termination phase: Saturation
% 7.10/1.88 % (1843109)Time elapsed: 0.109 s
% 7.10/1.88 % (1843109)Peak memory usage: 91 MB
% 7.10/1.88 % (1843109)Instructions burned: 287 (million)
% 7.10/1.88 % (1843115)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=4136340433:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 7.10/1.88 % (1843117)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3481215604:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 7.10/1.88 % (1843116)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=29736679:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 7.10/1.88 % (1843116)Refutation not found, incomplete strategy
% 7.10/1.88 % (1843116)------------------------------
% 7.10/1.88 % (1843116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843116)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843116)Termination reason: Refutation not found, incomplete strategy
% 7.10/1.88 % (1843116)Time elapsed: 0.005 s
% 7.10/1.88 % (1843116)Peak memory usage: 89 MB
% 7.10/1.88 % (1843116)Instructions burned: 6 (million)
% 7.10/1.88 % (1843111)Instruction limit reached!
% 7.10/1.88 % (1843111)------------------------------
% 7.10/1.88 % (1843111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843111)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843111)Termination reason: Instruction limit
% 7.10/1.88 % (1843111)Termination phase: Saturation
% 7.10/1.88 % (1843111)Time elapsed: 0.220 s
% 7.10/1.88 % (1843111)Peak memory usage: 93 MB
% 7.10/1.88 % (1843111)Instructions burned: 326 (million)
% 7.10/1.88 % (1843115)Instruction limit reached!
% 7.10/1.88 % (1843115)------------------------------
% 7.10/1.88 % (1843115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843115)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843115)Termination reason: Instruction limit
% 7.10/1.88 % (1843115)Termination phase: Saturation
% 7.10/1.88 % (1843115)Time elapsed: 0.131 s
% 7.10/1.88 % (1843115)Peak memory usage: 93 MB
% 7.10/1.88 % (1843115)Instructions burned: 250 (million)
% 7.10/1.88 % (1843121)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2558930250:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 7.10/1.88 % (1843116)------------------------------
% 7.10/1.88 % (1843116)------------------------------
% 7.10/1.88 % (1843122)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3061396673:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 7.10/1.88 % (1843121)Instruction limit reached!
% 7.10/1.88 % (1843121)------------------------------
% 7.10/1.88 % (1843121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843121)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843121)Termination reason: Instruction limit
% 7.10/1.88 % (1843121)Termination phase: Saturation
% 7.10/1.88 % (1843121)Time elapsed: 0.075 s
% 7.10/1.88 % (1843121)Peak memory usage: 90 MB
% 7.10/1.88 % (1843121)Instructions burned: 113 (million)
% 7.10/1.88 % (1843122)Instruction limit reached!
% 7.10/1.88 % (1843122)------------------------------
% 7.10/1.88 % (1843122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843122)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843122)Termination reason: Instruction limit
% 7.10/1.88 % (1843122)Termination phase: Saturation
% 7.10/1.88 % (1843122)Time elapsed: 0.067 s
% 7.10/1.88 % (1843122)Peak memory usage: 89 MB
% 7.10/1.88 % (1843122)Instructions burned: 128 (million)
% 7.10/1.88 % (1843095)First to succeed.
% 7.10/1.88 % (1843095)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1843090"
% 7.10/1.88 % (1843125)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2259125892:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 7.10/1.88 % (1843126)lrs+10_1_sil=8000:sp=occurrence:random_seed=3059521397:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 7.10/1.88 % (1843125)Instruction limit reached!
% 7.10/1.88 % (1843125)------------------------------
% 7.10/1.88 % (1843125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843125)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843125)Termination reason: Instruction limit
% 7.10/1.88 % (1843125)Termination phase: Saturation
% 7.10/1.88 % (1843125)Time elapsed: 0.066 s
% 7.10/1.88 % (1843125)Peak memory usage: 89 MB
% 7.10/1.88 % (1843125)Instructions burned: 115 (million)
% 7.10/1.88 % (1843117)Also succeeded, but the first one will report.
% 7.10/1.88 % (1843127)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1565900683:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 7.10/1.88 % (1843127)Refutation not found, incomplete strategy
% 7.10/1.88 % (1843127)------------------------------
% 7.10/1.88 % (1843127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.10/1.88 % (1843127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.10/1.88 % (1843127)CaDiCaL version: 2.1.3
% 7.10/1.88 % (1843127)Termination reason: Refutation not found, incomplete strategy
% 7.10/1.88 % (1843127)Time elapsed: 0.004 s
% 7.10/1.88 % (1843127)Peak memory usage: 88 MB
% 7.10/1.88 % (1843127)Instructions burned: 4 (million)
% 7.10/1.88 % (1843130)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=334136465:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 7.10/1.88 % (1843095)Refutation found. Thanks to Tanya!
% 7.10/1.88 % SZS status Theorem for theBenchmark
% 7.10/1.88 % SZS output start Proof for theBenchmark
% See solution above
% 9.08/1.98 % (1843095)------------------------------
% 9.08/1.98 % (1843095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.08/1.98 % (1843095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.08/1.98 % (1843095)CaDiCaL version: 2.1.3
% 9.08/1.98 % (1843095)Termination reason: Refutation
% 9.08/1.98 % (1843095)Time elapsed: 0.831 s
% 9.08/1.98 % (1843095)Peak memory usage: 131 MB
% 9.08/1.98 % (1843095)Instructions burned: 1199 (million)
% 9.08/1.98 % (1843095)------------------------------
% 9.08/1.98 % (1843095)------------------------------
% 9.08/1.98 % (1843090)Success in time 1.248 s
% 9.08/1.98 % Vampire exiting
%------------------------------------------------------------------------------