%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU052+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:47:08 PM UTC 2026
% Result : Theorem 6.71s 1.97s
% Output : Refutation 8.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 21
% Syntax : Number of formulae : 178 ( 37 unt; 14 def)
% Number of atoms : 628 ( 114 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 773 ( 323 ~; 332 |; 86 &)
% ( 23 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 215 ( 0 sgn 191 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f31,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( one_to_one(X2)
=> relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( one_to_one(X2)
=> relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( relation(X2)
=> subset(relation_image(X2,set_intersection2(X0,X1)),set_intersection2(relation_image(X2,X0),relation_image(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_relat_1) ).
fof(f52,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f56,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f55]) ).
fof(f63,plain,
? [X0,X1,X2] :
( relation_image(X2,set_intersection2(X0,X1)) != set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
& one_to_one(X2)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f64,plain,
? [X0,X1,X2] :
( relation_image(X2,set_intersection2(X0,X1)) != set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
& one_to_one(X2)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( subset(relation_image(X2,set_intersection2(X0,X1)),set_intersection2(relation_image(X2,X0),relation_image(X2,X1)))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f75,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f76,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 ) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f78,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,relation_dom(X0))
& in(X5,X1)
& apply(X0,X5) = X3 )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X1)
& apply(X0,X8) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK0(X0,X1,X2) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),relation_dom(X0))
& in(sK1(X0,X1,X2),X1)
& sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ( in(sK2(X0,X1,X6),relation_dom(X0))
& in(sK2(X0,X1,X6),X1)
& apply(X0,sK2(X0,X1,X6)) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(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))],[f78]) ).
fof(f80,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,[],[f54]) ).
fof(f81,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,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( in(sK4(X0,X1,X2),X0)
& in(sK4(X0,X1,X2),X1) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f85]) ).
fof(f87,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f56]) ).
fof(f88,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X4) != apply(X0,X3) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK5(X0) != sK6(X0)
& in(sK5(X0),relation_dom(X0))
& in(sK6(X0),relation_dom(X0))
& apply(X0,sK5(X0)) = apply(X0,sK6(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X4) != apply(X0,X3) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f88]) ).
fof(f101,plain,
( relation_image(sK20,set_intersection2(sK18,sK19)) != set_intersection2(relation_image(sK20,sK18),relation_image(sK20,sK19))
& one_to_one(sK20)
& relation(sK20)
& function(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X0,sK18),skolemize(X1,sK19),skolemize(X2,sK20)],[f64]) ).
fof(f112,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f113,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK2(X0,X1,X6)) = X6
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f114,plain,
! [X2,X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f115,plain,
! [X2,X0,X1,X6] :
( in(sK2(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f116,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f122,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f123,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f124,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f86]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f86]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f86]) ).
fof(f130,plain,
! [X3,X0,X4] :
( apply(X0,X4) != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| X3 = X4
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f167,plain,
function(sK20),
inference(cnf_transformation,[],[f101]) ).
fof(f168,plain,
relation(sK20),
inference(cnf_transformation,[],[f101]) ).
fof(f169,plain,
one_to_one(sK20),
inference(cnf_transformation,[],[f101]) ).
fof(f170,plain,
relation_image(sK20,set_intersection2(sK18,sK19)) != set_intersection2(relation_image(sK20,sK18),relation_image(sK20,sK19)),
inference(cnf_transformation,[],[f101]) ).
fof(f171,plain,
! [X2,X0,X1] :
( subset(relation_image(X2,set_intersection2(X0,X1)),set_intersection2(relation_image(X2,X0),relation_image(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f184,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f116]) ).
fof(f185,plain,
! [X0,X1,X7] :
( in(apply(X0,X7),relation_image(X0,X1))
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f184]) ).
fof(f186,plain,
! [X0,X1,X6] :
( in(sK2(X0,X1,X6),relation_dom(X0))
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f115]) ).
fof(f187,plain,
! [X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f114]) ).
fof(f188,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_image(X0,X1))
| apply(X0,sK2(X0,X1,X6)) = X6
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f113]) ).
fof(f189,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f126]) ).
fof(f190,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f191,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f124]) ).
fof(f192,definition,
sF21 = set_intersection2(sK18,sK19),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f193,plain,
set_intersection2(sK18,sK19) = sF21,
inference(reorient_equations,[],[f192]) ).
fof(f194,definition,
sF22 = relation_image(sK20,sF21),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f195,plain,
relation_image(sK20,sF21) = sF22,
inference(reorient_equations,[],[f194]) ).
fof(f196,definition,
sF23 = relation_image(sK20,sK18),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f197,plain,
relation_image(sK20,sK18) = sF23,
inference(reorient_equations,[],[f196]) ).
fof(f198,definition,
sF24 = relation_image(sK20,sK19),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f199,plain,
relation_image(sK20,sK19) = sF24,
inference(reorient_equations,[],[f198]) ).
fof(f200,definition,
sF25 = set_intersection2(sF23,sF24),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f201,plain,
set_intersection2(sF23,sF24) = sF25,
inference(reorient_equations,[],[f200]) ).
fof(f202,plain,
sF22 != sF25,
inference(definition_folding,[],[f170,f201,f199,f197,f195,f193]) ).
fof(f204,plain,
! [X0] :
( ~ in(X0,sF24)
| apply(sK20,sK2(sK20,sK19,X0)) = X0
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f188,f199]) ).
fof(f205,plain,
! [X0] :
( ~ in(X0,sF23)
| apply(sK20,sK2(sK20,sK18,X0)) = X0
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f188,f197]) ).
fof(f206,plain,
! [X0] :
( ~ in(X0,sF23)
| apply(sK20,sK2(sK20,sK18,X0)) = X0
| ~ function(sK20) ),
inference(forward_subsumption_resolution,[],[f205,f168]) ).
fof(f207,plain,
! [X0] :
( ~ in(X0,sF24)
| apply(sK20,sK2(sK20,sK19,X0)) = X0
| ~ function(sK20) ),
inference(forward_subsumption_resolution,[],[f204,f168]) ).
fof(f209,plain,
! [X0] :
( ~ in(X0,sF23)
| apply(sK20,sK2(sK20,sK18,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f206,f167]) ).
fof(f210,plain,
! [X0] :
( ~ in(X0,sF24)
| apply(sK20,sK2(sK20,sK19,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f207,f167]) ).
fof(f212,plain,
! [X0] :
( ~ in(X0,sF25)
| in(X0,sF23) ),
inference(superposition,[],[f190,f201]) ).
fof(f214,plain,
! [X0] :
( ~ in(X0,sF25)
| in(X0,sF24) ),
inference(superposition,[],[f191,f201]) ).
fof(f223,plain,
! [X0] :
( subset(relation_image(sK20,set_intersection2(X0,sK19)),set_intersection2(relation_image(sK20,X0),sF24))
| ~ relation(sK20) ),
inference(superposition,[],[f171,f199]) ).
fof(f226,plain,
! [X0] : subset(relation_image(sK20,set_intersection2(X0,sK19)),set_intersection2(relation_image(sK20,X0),sF24)),
inference(forward_subsumption_resolution,[],[f223,f168]) ).
fof(f240,plain,
! [X0] :
( in(sK3(sF25,X0),sF24)
| subset(sF25,X0) ),
inference(resolution,[],[f122,f214]) ).
fof(f241,plain,
! [X0] :
( in(sK3(sF25,X0),sF23)
| subset(sF25,X0) ),
inference(resolution,[],[f122,f212]) ).
fof(f244,plain,
! [X0] :
( subset(sF25,X0)
| sK3(sF25,X0) = apply(sK20,sK2(sK20,sK19,sK3(sF25,X0))) ),
inference(resolution,[],[f240,f210]) ).
fof(f247,plain,
! [X0] :
( subset(sF25,X0)
| sK3(sF25,X0) = apply(sK20,sK2(sK20,sK18,sK3(sF25,X0))) ),
inference(resolution,[],[f241,f209]) ).
fof(f253,plain,
! [X0] :
( ~ in(X0,sK19)
| ~ in(X0,sK18)
| in(X0,sF21) ),
inference(superposition,[],[f189,f193]) ).
fof(f260,plain,
! [X0] :
( in(apply(sK20,X0),sF22)
| ~ in(X0,relation_dom(sK20))
| ~ in(X0,sF21)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f185,f195]) ).
fof(f266,plain,
! [X0] :
( in(apply(sK20,X0),sF22)
| ~ in(X0,relation_dom(sK20))
| ~ in(X0,sF21)
| ~ function(sK20) ),
inference(forward_subsumption_resolution,[],[f260,f168]) ).
fof(f269,plain,
! [X0] :
( in(apply(sK20,X0),sF22)
| ~ in(X0,relation_dom(sK20))
| ~ in(X0,sF21) ),
inference(forward_subsumption_resolution,[],[f266,f167]) ).
fof(f370,plain,
subset(relation_image(sK20,set_intersection2(sK18,sK19)),set_intersection2(sF23,sF24)),
inference(superposition,[],[f226,f197]) ).
fof(f373,plain,
subset(relation_image(sK20,set_intersection2(sK18,sK19)),sF25),
inference(forward_demodulation,[],[f370,f201]) ).
fof(f376,plain,
subset(relation_image(sK20,sF21),sF25),
inference(forward_demodulation,[],[f373,f193]) ).
fof(f379,plain,
subset(sF22,sF25),
inference(forward_demodulation,[],[f376,f195]) ).
fof(f383,plain,
( ~ subset(sF25,sF22)
| sF22 = sF25 ),
inference(resolution,[],[f379,f112]) ).
fof(f384,plain,
~ subset(sF25,sF22),
inference(forward_subsumption_resolution,[],[f383,f202]) ).
fof(f392,plain,
sK3(sF25,sF22) = apply(sK20,sK2(sK20,sK19,sK3(sF25,sF22))),
inference(resolution,[],[f384,f244]) ).
fof(f393,plain,
sK3(sF25,sF22) = apply(sK20,sK2(sK20,sK18,sK3(sF25,sF22))),
inference(resolution,[],[f384,f247]) ).
fof(f396,plain,
( in(sK3(sF25,sF22),sF22)
| ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),relation_dom(sK20))
| ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),sF21) ),
inference(superposition,[],[f269,f393]) ).
fof(f400,plain,
! [X0] :
( apply(sK20,X0) != sK3(sF25,sF22)
| ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),relation_dom(sK20))
| ~ in(X0,relation_dom(sK20))
| sK2(sK20,sK18,sK3(sF25,sF22)) = X0
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f130,f393]) ).
fof(f403,plain,
! [X0] :
( apply(sK20,X0) != sK3(sF25,sF22)
| ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),relation_dom(sK20))
| ~ in(X0,relation_dom(sK20))
| sK2(sK20,sK18,sK3(sF25,sF22)) = X0
| ~ relation(sK20)
| ~ function(sK20) ),
inference(forward_subsumption_resolution,[],[f400,f169]) ).
fof(f406,definition,
( spl26_7
<=> in(sK2(sK20,sK18,sK3(sF25,sF22)),sK18) ),
introduced(definition,[new_symbols(definition,[spl26_7])],[avatar_definition]) ).
fof(f408,plain,
( ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),sK18)
| spl26_7 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f410,definition,
( spl26_8
<=> in(sK2(sK20,sK18,sK3(sF25,sF22)),relation_dom(sK20)) ),
introduced(definition,[new_symbols(definition,[spl26_8])],[avatar_definition]) ).
fof(f412,plain,
( ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),relation_dom(sK20))
| spl26_8 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f414,definition,
( spl26_9
<=> in(sK3(sF25,sF22),sF23) ),
introduced(definition,[new_symbols(definition,[spl26_9])],[avatar_definition]) ).
fof(f415,plain,
( ~ in(sK3(sF25,sF22),sF23)
| spl26_9 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f416,plain,
( in(sK3(sF25,sF22),sF23)
| ~ spl26_9 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f419,definition,
( spl26_10
<=> in(sK2(sK20,sK18,sK3(sF25,sF22)),sK19) ),
introduced(definition,[new_symbols(definition,[spl26_10])],[avatar_definition]) ).
fof(f420,plain,
( in(sK2(sK20,sK18,sK3(sF25,sF22)),sK19)
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f421,plain,
( ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),sK19)
| spl26_10 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f423,definition,
( spl26_11
<=> in(sK3(sF25,sF22),sF24) ),
introduced(definition,[new_symbols(definition,[spl26_11])],[avatar_definition]) ).
fof(f424,plain,
( ~ in(sK3(sF25,sF22),sF24)
| spl26_11 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f425,plain,
( in(sK3(sF25,sF22),sF24)
| ~ spl26_11 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f428,definition,
( spl26_12
<=> in(sK2(sK20,sK18,sK3(sF25,sF22)),sF21) ),
introduced(definition,[new_symbols(definition,[spl26_12])],[avatar_definition]) ).
fof(f430,plain,
( ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),sF21)
| spl26_12 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f432,definition,
( spl26_13
<=> in(sK3(sF25,sF22),sF22) ),
introduced(definition,[new_symbols(definition,[spl26_13])],[avatar_definition]) ).
fof(f434,plain,
( in(sK3(sF25,sF22),sF22)
| ~ spl26_13 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f435,plain,
( ~ spl26_12
| ~ spl26_8
| spl26_13 ),
inference(avatar_split_clause,[],[f396,f432,f410,f428]) ).
fof(f443,plain,
! [X0] :
( apply(sK20,X0) != sK3(sF25,sF22)
| ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),relation_dom(sK20))
| ~ in(X0,relation_dom(sK20))
| sK2(sK20,sK18,sK3(sF25,sF22)) = X0
| ~ function(sK20) ),
inference(forward_subsumption_resolution,[],[f403,f168]) ).
fof(f446,plain,
! [X0] :
( apply(sK20,X0) != sK3(sF25,sF22)
| ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),relation_dom(sK20))
| ~ in(X0,relation_dom(sK20))
| sK2(sK20,sK18,sK3(sF25,sF22)) = X0 ),
inference(forward_subsumption_resolution,[],[f443,f167]) ).
fof(f452,definition,
( spl26_16
<=> ! [X0] :
( apply(sK20,X0) != sK3(sF25,sF22)
| sK2(sK20,sK18,sK3(sF25,sF22)) = X0
| ~ in(X0,relation_dom(sK20)) ) ),
introduced(definition,[new_symbols(definition,[spl26_16])],[avatar_definition]) ).
fof(f453,plain,
( ! [X0] :
( apply(sK20,X0) != sK3(sF25,sF22)
| sK2(sK20,sK18,sK3(sF25,sF22)) = X0
| ~ in(X0,relation_dom(sK20)) )
| ~ spl26_16 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f455,plain,
( ~ spl26_8
| spl26_16 ),
inference(avatar_split_clause,[],[f446,f452,f410]) ).
fof(f472,definition,
( spl26_18
<=> in(sK2(sK20,sK19,sK3(sF25,sF22)),relation_dom(sK20)) ),
introduced(definition,[new_symbols(definition,[spl26_18])],[avatar_definition]) ).
fof(f473,plain,
( in(sK2(sK20,sK19,sK3(sF25,sF22)),relation_dom(sK20))
| ~ spl26_18 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f474,plain,
( ~ in(sK2(sK20,sK19,sK3(sF25,sF22)),relation_dom(sK20))
| spl26_18 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f509,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK18))
| ~ relation(sK20)
| ~ function(sK20)
| spl26_8 ),
inference(resolution,[],[f412,f186]) ).
fof(f510,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK18))
| ~ function(sK20)
| spl26_8 ),
inference(forward_subsumption_resolution,[],[f509,f168]) ).
fof(f511,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK18))
| spl26_8 ),
inference(forward_subsumption_resolution,[],[f510,f167]) ).
fof(f512,plain,
( ~ in(sK3(sF25,sF22),sF23)
| spl26_8 ),
inference(forward_demodulation,[],[f511,f197]) ).
fof(f513,plain,
( ~ spl26_9
| spl26_8 ),
inference(avatar_split_clause,[],[f512,f410,f414]) ).
fof(f514,plain,
( subset(sF25,sF22)
| spl26_9 ),
inference(resolution,[],[f415,f241]) ).
fof(f515,plain,
( $false
| spl26_9 ),
inference(forward_subsumption_resolution,[],[f514,f384]) ).
fof(f516,plain,
spl26_9,
inference(avatar_contradiction_clause,[],[f515]) ).
fof(f518,plain,
( sK3(sF25,sF22) != sK3(sF25,sF22)
| sK2(sK20,sK19,sK3(sF25,sF22)) = sK2(sK20,sK18,sK3(sF25,sF22))
| ~ in(sK2(sK20,sK19,sK3(sF25,sF22)),relation_dom(sK20))
| ~ spl26_16 ),
inference(superposition,[],[f453,f392]) ).
fof(f519,plain,
( sK2(sK20,sK19,sK3(sF25,sF22)) = sK2(sK20,sK18,sK3(sF25,sF22))
| ~ in(sK2(sK20,sK19,sK3(sF25,sF22)),relation_dom(sK20))
| ~ spl26_16 ),
inference(trivial_inequality_removal,[],[f518]) ).
fof(f528,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK19))
| ~ relation(sK20)
| ~ function(sK20)
| spl26_18 ),
inference(resolution,[],[f474,f186]) ).
fof(f529,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK19))
| ~ function(sK20)
| spl26_18 ),
inference(forward_subsumption_resolution,[],[f528,f168]) ).
fof(f530,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK19))
| spl26_18 ),
inference(forward_subsumption_resolution,[],[f529,f167]) ).
fof(f531,plain,
( ~ in(sK3(sF25,sF22),sF24)
| spl26_18 ),
inference(forward_demodulation,[],[f530,f199]) ).
fof(f532,plain,
( ~ spl26_11
| spl26_18 ),
inference(avatar_split_clause,[],[f531,f472,f423]) ).
fof(f533,plain,
( subset(sF25,sF22)
| spl26_11 ),
inference(resolution,[],[f424,f240]) ).
fof(f534,plain,
( $false
| spl26_11 ),
inference(forward_subsumption_resolution,[],[f533,f384]) ).
fof(f535,plain,
spl26_11,
inference(avatar_contradiction_clause,[],[f534]) ).
fof(f536,plain,
( sK2(sK20,sK19,sK3(sF25,sF22)) = sK2(sK20,sK18,sK3(sF25,sF22))
| ~ spl26_16
| ~ spl26_18 ),
inference(forward_subsumption_resolution,[],[f519,f473]) ).
fof(f538,plain,
( in(sK2(sK20,sK18,sK3(sF25,sF22)),sK19)
| ~ in(sK3(sF25,sF22),relation_image(sK20,sK19))
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl26_16
| ~ spl26_18 ),
inference(superposition,[],[f187,f536]) ).
fof(f540,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK19))
| ~ relation(sK20)
| ~ function(sK20)
| spl26_10
| ~ spl26_16
| ~ spl26_18 ),
inference(forward_subsumption_resolution,[],[f538,f421]) ).
fof(f541,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK19))
| ~ function(sK20)
| spl26_10
| ~ spl26_16
| ~ spl26_18 ),
inference(forward_subsumption_resolution,[],[f540,f168]) ).
fof(f542,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK19))
| spl26_10
| ~ spl26_16
| ~ spl26_18 ),
inference(forward_subsumption_resolution,[],[f541,f167]) ).
fof(f543,plain,
( ~ in(sK3(sF25,sF22),sF24)
| spl26_10
| ~ spl26_16
| ~ spl26_18 ),
inference(forward_demodulation,[],[f542,f199]) ).
fof(f544,plain,
( $false
| spl26_10
| ~ spl26_11
| ~ spl26_16
| ~ spl26_18 ),
inference(forward_subsumption_resolution,[],[f543,f425]) ).
fof(f545,plain,
( spl26_10
| ~ spl26_11
| ~ spl26_16
| ~ spl26_18 ),
inference(avatar_contradiction_clause,[],[f544]) ).
fof(f559,plain,
( ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),sK18)
| in(sK2(sK20,sK18,sK3(sF25,sF22)),sF21)
| ~ spl26_10 ),
inference(resolution,[],[f420,f253]) ).
fof(f560,plain,
( ~ in(sK2(sK20,sK18,sK3(sF25,sF22)),sK18)
| ~ spl26_10
| spl26_12 ),
inference(forward_subsumption_resolution,[],[f559,f430]) ).
fof(f562,plain,
( ~ spl26_7
| ~ spl26_10
| spl26_12 ),
inference(avatar_split_clause,[],[f560,f428,f419,f406]) ).
fof(f563,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK18))
| ~ relation(sK20)
| ~ function(sK20)
| spl26_7 ),
inference(resolution,[],[f408,f187]) ).
fof(f564,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK18))
| ~ function(sK20)
| spl26_7 ),
inference(forward_subsumption_resolution,[],[f563,f168]) ).
fof(f565,plain,
( ~ in(sK3(sF25,sF22),relation_image(sK20,sK18))
| spl26_7 ),
inference(forward_subsumption_resolution,[],[f564,f167]) ).
fof(f566,plain,
( ~ in(sK3(sF25,sF22),sF23)
| spl26_7 ),
inference(forward_demodulation,[],[f565,f197]) ).
fof(f567,plain,
( $false
| spl26_7
| ~ spl26_9 ),
inference(forward_subsumption_resolution,[],[f566,f416]) ).
fof(f568,plain,
( spl26_7
| ~ spl26_9 ),
inference(avatar_contradiction_clause,[],[f567]) ).
fof(f569,plain,
( subset(sF25,sF22)
| ~ spl26_13 ),
inference(resolution,[],[f434,f123]) ).
fof(f572,plain,
( $false
| ~ spl26_13 ),
inference(forward_subsumption_resolution,[],[f569,f384]) ).
fof(f573,plain,
~ spl26_13,
inference(avatar_contradiction_clause,[],[f572]) ).
cnf(s5,plain,
( ~ spl26_8
| ~ spl26_12
| spl26_13 ),
inference(sat_conversion,[],[f435]) ).
cnf(s10,plain,
( ~ spl26_8
| spl26_16 ),
inference(sat_conversion,[],[f455]) ).
cnf(s19,plain,
( spl26_8
| ~ spl26_9 ),
inference(sat_conversion,[],[f513]) ).
cnf(s20,plain,
spl26_9,
inference(sat_conversion,[],[f516]) ).
cnf(s21,plain,
( ~ spl26_11
| spl26_18 ),
inference(sat_conversion,[],[f532]) ).
cnf(s22,plain,
spl26_11,
inference(sat_conversion,[],[f535]) ).
cnf(s23,plain,
( spl26_10
| ~ spl26_11
| ~ spl26_16
| ~ spl26_18 ),
inference(sat_conversion,[],[f545]) ).
cnf(s24,plain,
( ~ spl26_7
| ~ spl26_10
| spl26_12 ),
inference(sat_conversion,[],[f562]) ).
cnf(s25,plain,
( spl26_7
| ~ spl26_9 ),
inference(sat_conversion,[],[f568]) ).
cnf(s26,plain,
~ spl26_13,
inference(sat_conversion,[],[f573]) ).
cnf(s27,plain,
spl26_18,
inference(rat,[],[s21,s22]) ).
cnf(s28,plain,
spl26_7,
inference(rat,[],[s25,s20]) ).
cnf(s29,plain,
spl26_8,
inference(rat,[],[s19,s20]) ).
cnf(s35,plain,
spl26_16,
inference(rat,[],[s10,s29]) ).
cnf(s36,plain,
spl26_10,
inference(rat,[],[s23,s27,s22,s35]) ).
cnf(s37,plain,
spl26_12,
inference(rat,[],[s24,s28,s36]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s5,s26,s37,s29]) ).
fof(f574,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU052+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 03:27:45 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 6.71/1.97 % (2987036)Detected formulas, will run a generic FOF schedule.
% 6.71/1.97 % (2987047)dis-21_1_sil=8000:lcm=predicate:random_seed=2796416171: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)
% 6.71/1.97 % (2987047)Instruction limit reached!
% 6.71/1.97 % (2987047)------------------------------
% 6.71/1.97 % (2987047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987047)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987047)Termination reason: Instruction limit
% 6.71/1.97 % (2987047)Termination phase: Saturation
% 6.71/1.97 % (2987047)Time elapsed: 0.040 s
% 6.71/1.97 % (2987047)Peak memory usage: 90 MB
% 6.71/1.97 % (2987047)Instructions burned: 131 (million)
% 6.71/1.97 % (2987042)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=3733896791:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.71/1.97 % (2987045)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3395000103:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.71/1.97 % (2987043)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=1427833244:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.71/1.97 % (2987044)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=536203093:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.71/1.97 % (2987041)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=3285679617:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.71/1.97 % (2987044)Refutation not found, incomplete strategy
% 6.71/1.97 % (2987044)------------------------------
% 6.71/1.97 % (2987044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987044)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987044)Termination reason: Refutation not found, incomplete strategy
% 6.71/1.97 % (2987044)Time elapsed: 0.002 s
% 6.71/1.97 % (2987044)Peak memory usage: 88 MB
% 6.71/1.97 % (2987044)Instructions burned: 1 (million)
% 6.71/1.97 % (2987046)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=855754818:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.71/1.97 % (2987045)Instruction limit reached!
% 6.71/1.97 % (2987045)------------------------------
% 6.71/1.97 % (2987045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987045)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987045)Termination reason: Instruction limit
% 6.71/1.97 % (2987045)Termination phase: Saturation
% 6.71/1.97 % (2987045)Time elapsed: 0.073 s
% 6.71/1.97 % (2987045)Peak memory usage: 88 MB
% 6.71/1.97 % (2987045)Instructions burned: 120 (million)
% 6.71/1.97 % (2987046)Instruction limit reached!
% 6.71/1.97 % (2987046)------------------------------
% 6.71/1.97 % (2987046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987046)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987046)Termination reason: Instruction limit
% 6.71/1.97 % (2987046)Termination phase: Saturation
% 6.71/1.97 % (2987046)Time elapsed: 0.092 s
% 6.71/1.97 % (2987046)Peak memory usage: 90 MB
% 6.71/1.97 % (2987046)Instructions burned: 139 (million)
% 6.71/1.97 % (2987054)lrs+10_1_sil=8000:sp=occurrence:random_seed=2482999998:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.71/1.97 % (2987054)Instruction limit reached!
% 6.71/1.97 % (2987054)------------------------------
% 6.71/1.97 % (2987054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987054)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987054)Termination reason: Instruction limit
% 6.71/1.97 % (2987054)Termination phase: Saturation
% 6.71/1.97 % (2987054)Time elapsed: 0.090 s
% 6.71/1.97 % (2987054)Peak memory usage: 91 MB
% 6.71/1.97 % (2987054)Instructions burned: 288 (million)
% 6.71/1.97 % (2987056)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3673656269:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.71/1.97 % (2987044)------------------------------
% 6.71/1.97 % (2987044)------------------------------
% 6.71/1.97 % (2987057)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3713581171:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.71/1.97 % (2987056)Instruction limit reached!
% 6.71/1.97 % (2987056)------------------------------
% 6.71/1.97 % (2987056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987056)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987056)Termination reason: Instruction limit
% 6.71/1.97 % (2987056)Termination phase: Saturation
% 6.71/1.97 % (2987056)Time elapsed: 0.079 s
% 6.71/1.97 % (2987056)Peak memory usage: 90 MB
% 6.71/1.97 % (2987056)Instructions burned: 157 (million)
% 6.71/1.97 % (2987059)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=3996098610:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.71/1.97 % (2987059)Instruction limit reached!
% 6.71/1.97 % (2987059)------------------------------
% 6.71/1.97 % (2987059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987059)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987059)Termination reason: Instruction limit
% 6.71/1.97 % (2987059)Termination phase: Saturation
% 6.71/1.97 % (2987059)Time elapsed: 0.073 s
% 6.71/1.97 % (2987059)Peak memory usage: 95 MB
% 6.71/1.97 % (2987059)Instructions burned: 251 (million)
% 6.71/1.97 % (2987062)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3795385175:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.71/1.97 % (2987062)Refutation not found, incomplete strategy
% 6.71/1.97 % (2987062)------------------------------
% 6.71/1.97 % (2987062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987062)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987062)Termination reason: Refutation not found, incomplete strategy
% 6.71/1.97 % (2987062)Time elapsed: 0.003 s
% 6.71/1.97 % (2987062)Peak memory usage: 88 MB
% 6.71/1.97 % (2987062)Instructions burned: 3 (million)
% 6.71/1.97 % (2987057)Instruction limit reached!
% 6.71/1.97 % (2987057)------------------------------
% 6.71/1.97 % (2987057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987057)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987057)Termination reason: Instruction limit
% 6.71/1.97 % (2987057)Termination phase: Saturation
% 6.71/1.97 % (2987057)Time elapsed: 0.194 s
% 6.71/1.97 % (2987057)Peak memory usage: 91 MB
% 6.71/1.97 % (2987057)Instructions burned: 326 (million)
% 6.71/1.97 % (2987063)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2781362828:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.71/1.97 % (2987065)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1306974174:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.71/1.97 % (2987065)Instruction limit reached!
% 6.71/1.97 % (2987065)------------------------------
% 6.71/1.97 % (2987065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987065)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987065)Termination reason: Instruction limit
% 6.71/1.97 % (2987065)Termination phase: Saturation
% 6.71/1.97 % (2987065)Time elapsed: 0.041 s
% 6.71/1.97 % (2987065)Peak memory usage: 90 MB
% 6.71/1.97 % (2987065)Instructions burned: 114 (million)
% 6.71/1.97 % (2987067)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3796402473:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.71/1.97 % (2987062)------------------------------
% 6.71/1.97 % (2987062)------------------------------
% 6.71/1.97 % (2987041)First to succeed.
% 6.71/1.97 % (2987041)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2987036"
% 6.71/1.97 % (2987070)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=876406729:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.71/1.97 % (2987067)Instruction limit reached!
% 6.71/1.97 % (2987067)------------------------------
% 6.71/1.97 % (2987067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987067)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987067)Termination reason: Instruction limit
% 6.71/1.97 % (2987067)Termination phase: Saturation
% 6.71/1.97 % (2987067)Time elapsed: 0.067 s
% 6.71/1.97 % (2987067)Peak memory usage: 89 MB
% 6.71/1.97 % (2987067)Instructions burned: 127 (million)
% 6.71/1.97 % (2987070)Instruction limit reached!
% 6.71/1.97 % (2987070)------------------------------
% 6.71/1.97 % (2987070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987070)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987070)Termination reason: Instruction limit
% 6.71/1.97 % (2987070)Termination phase: Saturation
% 6.71/1.97 % (2987070)Time elapsed: 0.036 s
% 6.71/1.97 % (2987070)Peak memory usage: 89 MB
% 6.71/1.97 % (2987070)Instructions burned: 117 (million)
% 6.71/1.97 % (2987074)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1653704653:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.71/1.97 % (2987072)lrs+10_1_sil=8000:sp=occurrence:random_seed=3257133641:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.71/1.97 % (2987074)Refutation not found, incomplete strategy
% 6.71/1.97 % (2987074)------------------------------
% 6.71/1.97 % (2987074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.97 % (2987074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.97 % (2987074)CaDiCaL version: 2.1.3
% 6.71/1.97 % (2987074)Termination reason: Refutation not found, incomplete strategy
% 6.71/1.97 % (2987074)Time elapsed: 0.003 s
% 6.71/1.97 % (2987074)Peak memory usage: 88 MB
% 6.71/1.97 % (2987074)Instructions burned: 3 (million)
% 6.71/1.97 % (2987075)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=509967188:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.71/1.97 % (2987041)Refutation found. Thanks to Tanya!
% 6.71/1.97 % SZS status Theorem for theBenchmark
% 6.71/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 8.38/2.07 % (2987041)------------------------------
% 8.38/2.07 % (2987041)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.38/2.07 % (2987041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.38/2.07 % (2987041)CaDiCaL version: 2.1.3
% 8.38/2.07 % (2987041)Termination reason: Refutation
% 8.38/2.07 % (2987041)Time elapsed: 0.679 s
% 8.38/2.07 % (2987041)Peak memory usage: 128 MB
% 8.38/2.07 % (2987041)Instructions burned: 1006 (million)
% 8.38/2.07 % (2987041)------------------------------
% 8.38/2.07 % (2987041)------------------------------
% 8.38/2.07 % (2987036)Success in time 1.116 s
% 8.38/2.07 % Vampire exiting
%------------------------------------------------------------------------------