%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU067+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 : n004.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 12:47:10 PM UTC 2026
% Result : Theorem 4.50s 1.55s
% Output : Refutation 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 19
% Syntax : Number of formulae : 161 ( 33 unt; 11 def)
% Number of atoms : 584 ( 85 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 707 ( 284 ~; 300 |; 93 &)
% ( 23 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 243 ( 0 sgn 222 !; 21 ?)
% 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] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f10,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(f31,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f32,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_image(X1,relation_dom(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_relat_1) ).
fof(f33,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> relation_image(X1,relation_inverse_image(X1,X0)) = set_intersection2(X0,relation_image(X1,relation_dom(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> relation_image(X1,relation_inverse_image(X1,X0)) = set_intersection2(X0,relation_image(X1,relation_dom(X1))) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f56,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(f57,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,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f67,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f68,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_image(X1,relation_dom(X1)))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f70,plain,
? [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) != set_intersection2(X0,relation_image(X1,relation_dom(X1)))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f71,plain,
? [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) != set_intersection2(X0,relation_image(X1,relation_dom(X1)))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f70]) ).
fof(f83,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f84,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f83]) ).
fof(f85,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,[],[f57]) ).
fof(f86,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,[],[f85]) ).
fof(f87,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))],[f86]) ).
fof(f88,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f59]) ).
fof(f89,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK3(X0,X1,X2)),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK3(X0,X1,X2)),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f90]) ).
fof(f92,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,[],[f60]) ).
fof(f93,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,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f93]) ).
fof(f95,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,[],[f10]) ).
fof(f96,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,[],[f95]) ).
fof(f97,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,[],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK5(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,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f97]) ).
fof(f110,plain,
( relation_image(sK18,relation_inverse_image(sK18,sK17)) != set_intersection2(sK17,relation_image(sK18,relation_dom(sK18)))
& relation(sK18)
& function(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f71]) ).
fof(f120,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f84]) ).
fof(f121,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,[],[f87]) ).
fof(f123,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,[],[f87]) ).
fof(f124,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,[],[f87]) ).
fof(f130,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f131,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f135,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f136,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f137,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f138,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f139,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f140,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f175,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f176,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_image(X1,relation_dom(X1)))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f177,plain,
function(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f178,plain,
relation(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f179,plain,
relation_image(sK18,relation_inverse_image(sK18,sK17)) != set_intersection2(sK17,relation_image(sK18,relation_dom(sK18))),
inference(cnf_transformation,[],[f110]) ).
fof(f193,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,[],[f124]) ).
fof(f194,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,[],[f193]) ).
fof(f195,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,[],[f123]) ).
fof(f197,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_image(X0,X1))
| apply(X0,sK2(X0,X1,X6)) = X6
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f121]) ).
fof(f198,plain,
! [X0,X1,X4] :
( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f131]) ).
fof(f199,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f130]) ).
fof(f201,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f140]) ).
fof(f202,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f139]) ).
fof(f203,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f138]) ).
fof(f204,definition,
sF19 = relation_inverse_image(sK18,sK17),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f205,plain,
relation_inverse_image(sK18,sK17) = sF19,
inference(reorient_equations,[],[f204]) ).
fof(f206,definition,
sF20 = relation_image(sK18,sF19),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f207,plain,
relation_image(sK18,sF19) = sF20,
inference(reorient_equations,[],[f206]) ).
fof(f208,definition,
sF21 = relation_dom(sK18),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f209,plain,
relation_dom(sK18) = sF21,
inference(reorient_equations,[],[f208]) ).
fof(f210,definition,
sF22 = relation_image(sK18,sF21),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f211,plain,
relation_image(sK18,sF21) = sF22,
inference(reorient_equations,[],[f210]) ).
fof(f212,definition,
sF23 = set_intersection2(sK17,sF22),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f213,plain,
set_intersection2(sK17,sF22) = sF23,
inference(reorient_equations,[],[f212]) ).
fof(f214,plain,
sF20 != sF23,
inference(definition_folding,[],[f179,f213,f211,f209,f207,f205]) ).
fof(f216,plain,
! [X0] :
( ~ in(X0,sF22)
| apply(sK18,sK2(sK18,sF21,X0)) = X0
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[],[f197,f211]) ).
fof(f217,plain,
! [X0] :
( ~ in(X0,sF22)
| apply(sK18,sK2(sK18,sF21,X0)) = X0
| ~ function(sK18) ),
inference(forward_subsumption_resolution,[],[f216,f178]) ).
fof(f219,plain,
! [X0] :
( ~ in(X0,sF22)
| apply(sK18,sK2(sK18,sF21,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f217,f177]) ).
fof(f221,plain,
! [X0] :
( ~ in(X0,sF23)
| in(X0,sK17) ),
inference(superposition,[],[f202,f213]) ).
fof(f222,plain,
! [X0] :
( ~ in(X0,sF23)
| in(X0,sF22) ),
inference(superposition,[],[f203,f213]) ).
fof(f225,plain,
! [X0] :
( ~ in(X0,sF22)
| ~ in(X0,sK17)
| in(X0,sF23) ),
inference(superposition,[],[f201,f213]) ).
fof(f228,plain,
! [X0] :
( in(apply(sK18,X0),sF20)
| ~ in(X0,relation_dom(sK18))
| ~ in(X0,sF19)
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[],[f194,f207]) ).
fof(f232,plain,
! [X0] :
( in(apply(sK18,X0),sF20)
| ~ in(X0,relation_dom(sK18))
| ~ in(X0,sF19)
| ~ function(sK18) ),
inference(forward_subsumption_resolution,[],[f228,f178]) ).
fof(f234,plain,
! [X0] :
( in(apply(sK18,X0),sF20)
| ~ in(X0,relation_dom(sK18))
| ~ in(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f232,f177]) ).
fof(f237,plain,
! [X0] :
( in(apply(sK18,X0),sF20)
| ~ in(X0,sF21)
| ~ in(X0,sF19) ),
inference(forward_demodulation,[],[f234,f209]) ).
fof(f239,plain,
! [X0] :
( ~ in(X0,sF19)
| in(X0,relation_dom(sK18))
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[],[f199,f205]) ).
fof(f240,plain,
! [X0] :
( ~ in(X0,sF19)
| in(X0,relation_dom(sK18))
| ~ function(sK18) ),
inference(forward_subsumption_resolution,[],[f239,f178]) ).
fof(f241,plain,
! [X0] :
( ~ in(X0,sF19)
| in(X0,relation_dom(sK18)) ),
inference(forward_subsumption_resolution,[],[f240,f177]) ).
fof(f242,plain,
! [X0] :
( ~ in(X0,sF19)
| in(X0,sF21) ),
inference(forward_demodulation,[],[f241,f209]) ).
fof(f252,plain,
! [X0] :
( in(sK4(sF23,X0),sF22)
| subset(sF23,X0) ),
inference(resolution,[],[f136,f222]) ).
fof(f253,plain,
! [X0] :
( in(sK4(sF23,X0),sK17)
| subset(sF23,X0) ),
inference(resolution,[],[f136,f221]) ).
fof(f258,plain,
! [X0] :
( subset(sF23,X0)
| sK4(sF23,X0) = apply(sK18,sK2(sK18,sF21,sK4(sF23,X0))) ),
inference(resolution,[],[f252,f219]) ).
fof(f295,plain,
! [X0,X1] :
( in(sK2(sK18,X0,X1),sF21)
| ~ in(X1,relation_image(sK18,X0))
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[],[f195,f209]) ).
fof(f296,plain,
! [X0,X1] :
( in(sK2(sK18,X0,X1),sF21)
| ~ in(X1,relation_image(sK18,X0))
| ~ function(sK18) ),
inference(forward_subsumption_resolution,[],[f295,f178]) ).
fof(f297,plain,
! [X0,X1] :
( in(sK2(sK18,X0,X1),sF21)
| ~ in(X1,relation_image(sK18,X0)) ),
inference(forward_subsumption_resolution,[],[f296,f177]) ).
fof(f310,plain,
( subset(relation_image(sK18,sF19),sK17)
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[],[f175,f205]) ).
fof(f311,plain,
( subset(relation_image(sK18,sF19),sK17)
| ~ function(sK18) ),
inference(forward_subsumption_resolution,[],[f310,f178]) ).
fof(f312,plain,
subset(relation_image(sK18,sF19),sK17),
inference(forward_subsumption_resolution,[],[f311,f177]) ).
fof(f313,plain,
subset(sF20,sK17),
inference(forward_demodulation,[],[f312,f207]) ).
fof(f326,plain,
! [X0] :
( ~ in(X0,sF20)
| in(X0,sK17) ),
inference(resolution,[],[f135,f313]) ).
fof(f331,plain,
! [X0] :
( in(sK4(sF20,X0),sK17)
| subset(sF20,X0) ),
inference(resolution,[],[f326,f136]) ).
fof(f377,plain,
( subset(sF20,relation_image(sK18,relation_dom(sK18)))
| ~ relation(sK18) ),
inference(superposition,[],[f176,f207]) ).
fof(f382,plain,
subset(sF20,relation_image(sK18,relation_dom(sK18))),
inference(forward_subsumption_resolution,[],[f377,f178]) ).
fof(f385,plain,
subset(sF20,relation_image(sK18,sF21)),
inference(forward_demodulation,[],[f382,f209]) ).
fof(f387,plain,
subset(sF20,sF22),
inference(forward_demodulation,[],[f385,f211]) ).
fof(f388,plain,
! [X0] :
( ~ in(X0,sF20)
| in(X0,sF22) ),
inference(resolution,[],[f387,f135]) ).
fof(f402,plain,
! [X0] :
( in(sK4(sF20,X0),sF22)
| subset(sF20,X0) ),
inference(resolution,[],[f388,f136]) ).
fof(f405,plain,
! [X0] :
( subset(sF20,X0)
| ~ in(sK4(sF20,X0),sK17)
| in(sK4(sF20,X0),sF23) ),
inference(resolution,[],[f402,f225]) ).
fof(f407,plain,
! [X0] :
( in(sK4(sF20,X0),sF23)
| subset(sF20,X0) ),
inference(forward_subsumption_resolution,[],[f405,f331]) ).
fof(f408,plain,
( subset(sF20,sF23)
| subset(sF20,sF23) ),
inference(resolution,[],[f407,f137]) ).
fof(f411,plain,
subset(sF20,sF23),
inference(duplicate_literal_removal,[],[f408]) ).
fof(f413,plain,
( ~ subset(sF23,sF20)
| sF20 = sF23 ),
inference(resolution,[],[f411,f120]) ).
fof(f414,plain,
~ subset(sF23,sF20),
inference(forward_subsumption_resolution,[],[f413,f214]) ).
fof(f415,plain,
sK4(sF23,sF20) = apply(sK18,sK2(sK18,sF21,sK4(sF23,sF20))),
inference(resolution,[],[f414,f258]) ).
fof(f417,plain,
( in(sK4(sF23,sF20),sF20)
| ~ in(sK2(sK18,sF21,sK4(sF23,sF20)),sF21)
| ~ in(sK2(sK18,sF21,sK4(sF23,sF20)),sF19) ),
inference(superposition,[],[f237,f415]) ).
fof(f423,plain,
! [X0] :
( ~ in(sK4(sF23,sF20),X0)
| ~ in(sK2(sK18,sF21,sK4(sF23,sF20)),relation_dom(sK18))
| in(sK2(sK18,sF21,sK4(sF23,sF20)),relation_inverse_image(sK18,X0))
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[],[f198,f415]) ).
fof(f426,plain,
! [X0] :
( ~ in(sK4(sF23,sF20),X0)
| ~ in(sK2(sK18,sF21,sK4(sF23,sF20)),relation_dom(sK18))
| in(sK2(sK18,sF21,sK4(sF23,sF20)),relation_inverse_image(sK18,X0))
| ~ function(sK18) ),
inference(forward_subsumption_resolution,[],[f423,f178]) ).
fof(f428,definition,
( spl24_8
<=> in(sK2(sK18,sF21,sK4(sF23,sF20)),sF19) ),
introduced(definition,[new_symbols(definition,[spl24_8])],[avatar_definition]) ).
fof(f430,plain,
( ~ in(sK2(sK18,sF21,sK4(sF23,sF20)),sF19)
| spl24_8 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f432,definition,
( spl24_9
<=> in(sK4(sF23,sF20),sF20) ),
introduced(definition,[new_symbols(definition,[spl24_9])],[avatar_definition]) ).
fof(f434,plain,
( in(sK4(sF23,sF20),sF20)
| ~ spl24_9 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f437,definition,
( spl24_10
<=> in(sK4(sF23,sF20),sF22) ),
introduced(definition,[new_symbols(definition,[spl24_10])],[avatar_definition]) ).
fof(f438,plain,
( ~ in(sK4(sF23,sF20),sF22)
| spl24_10 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f447,definition,
( spl24_12
<=> in(sK2(sK18,sF21,sK4(sF23,sF20)),sF21) ),
introduced(definition,[new_symbols(definition,[spl24_12])],[avatar_definition]) ).
fof(f449,plain,
( ~ in(sK2(sK18,sF21,sK4(sF23,sF20)),sF21)
| spl24_12 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f451,definition,
( spl24_13
<=> in(sK4(sF23,sF20),sK17) ),
introduced(definition,[new_symbols(definition,[spl24_13])],[avatar_definition]) ).
fof(f452,plain,
( in(sK4(sF23,sF20),sK17)
| ~ spl24_13 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f453,plain,
( ~ in(sK4(sF23,sF20),sK17)
| spl24_13 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f456,plain,
( in(sK4(sF23,sF20),sF20)
| ~ in(sK2(sK18,sF21,sK4(sF23,sF20)),sF19) ),
inference(forward_subsumption_resolution,[],[f417,f242]) ).
fof(f459,plain,
! [X0] :
( ~ in(sK4(sF23,sF20),X0)
| ~ in(sK2(sK18,sF21,sK4(sF23,sF20)),relation_dom(sK18))
| in(sK2(sK18,sF21,sK4(sF23,sF20)),relation_inverse_image(sK18,X0)) ),
inference(forward_subsumption_resolution,[],[f426,f177]) ).
fof(f460,plain,
( ~ spl24_8
| spl24_9 ),
inference(avatar_split_clause,[],[f456,f432,f428]) ).
fof(f462,plain,
! [X0] :
( ~ in(sK2(sK18,sF21,sK4(sF23,sF20)),sF21)
| ~ in(sK4(sF23,sF20),X0)
| in(sK2(sK18,sF21,sK4(sF23,sF20)),relation_inverse_image(sK18,X0)) ),
inference(forward_demodulation,[],[f459,f209]) ).
fof(f468,definition,
( spl24_15
<=> ! [X0] :
( ~ in(sK4(sF23,sF20),X0)
| in(sK2(sK18,sF21,sK4(sF23,sF20)),relation_inverse_image(sK18,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl24_15])],[avatar_definition]) ).
fof(f469,plain,
( ! [X0] :
( in(sK2(sK18,sF21,sK4(sF23,sF20)),relation_inverse_image(sK18,X0))
| ~ in(sK4(sF23,sF20),X0) )
| ~ spl24_15 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f470,plain,
( spl24_15
| ~ spl24_12 ),
inference(avatar_split_clause,[],[f462,f447,f468]) ).
fof(f487,plain,
( ~ in(sK4(sF23,sF20),relation_image(sK18,sF21))
| spl24_12 ),
inference(resolution,[],[f449,f297]) ).
fof(f490,plain,
( ~ in(sK4(sF23,sF20),sF22)
| spl24_12 ),
inference(forward_demodulation,[],[f487,f211]) ).
fof(f492,plain,
( ~ spl24_10
| spl24_12 ),
inference(avatar_split_clause,[],[f490,f447,f437]) ).
fof(f494,plain,
( subset(sF23,sF20)
| spl24_10 ),
inference(resolution,[],[f438,f252]) ).
fof(f495,plain,
( $false
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f494,f414]) ).
fof(f496,plain,
spl24_10,
inference(avatar_contradiction_clause,[],[f495]) ).
fof(f497,plain,
( subset(sF23,sF20)
| spl24_13 ),
inference(resolution,[],[f453,f253]) ).
fof(f498,plain,
( $false
| spl24_13 ),
inference(forward_subsumption_resolution,[],[f497,f414]) ).
fof(f499,plain,
spl24_13,
inference(avatar_contradiction_clause,[],[f498]) ).
fof(f514,plain,
( in(sK2(sK18,sF21,sK4(sF23,sF20)),sF19)
| ~ in(sK4(sF23,sF20),sK17)
| ~ spl24_15 ),
inference(superposition,[],[f469,f205]) ).
fof(f515,plain,
( ~ in(sK4(sF23,sF20),sK17)
| spl24_8
| ~ spl24_15 ),
inference(forward_subsumption_resolution,[],[f514,f430]) ).
fof(f518,plain,
( $false
| spl24_8
| ~ spl24_13
| ~ spl24_15 ),
inference(forward_subsumption_resolution,[],[f515,f452]) ).
fof(f519,plain,
( spl24_8
| ~ spl24_13
| ~ spl24_15 ),
inference(avatar_contradiction_clause,[],[f518]) ).
fof(f525,plain,
( subset(sF23,sF20)
| ~ spl24_9 ),
inference(resolution,[],[f434,f137]) ).
fof(f530,plain,
( $false
| ~ spl24_9 ),
inference(forward_subsumption_resolution,[],[f525,f414]) ).
fof(f531,plain,
~ spl24_9,
inference(avatar_contradiction_clause,[],[f530]) ).
cnf(s10,plain,
( ~ spl24_8
| spl24_9 ),
inference(sat_conversion,[],[f460]) ).
cnf(s12,plain,
( ~ spl24_12
| spl24_15 ),
inference(sat_conversion,[],[f470]) ).
cnf(s13,plain,
( ~ spl24_10
| spl24_12 ),
inference(sat_conversion,[],[f492]) ).
cnf(s15,plain,
spl24_10,
inference(sat_conversion,[],[f496]) ).
cnf(s16,plain,
spl24_13,
inference(sat_conversion,[],[f499]) ).
cnf(s17,plain,
( spl24_8
| ~ spl24_13
| ~ spl24_15 ),
inference(sat_conversion,[],[f519]) ).
cnf(s18,plain,
~ spl24_9,
inference(sat_conversion,[],[f531]) ).
cnf(s19,plain,
spl24_12,
inference(rat,[],[s13,s15]) ).
cnf(s20,plain,
spl24_15,
inference(rat,[],[s12,s19]) ).
cnf(s21,plain,
spl24_8,
inference(rat,[],[s17,s16,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s10,s18,s21]) ).
fof(f532,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU067+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:29:24 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 4.50/1.55 % (4122286)Detected formulas, will run a generic FOF schedule.
% 4.50/1.55 % (4122291)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=967293288:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.50/1.55 % (4122295)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3066995390:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.50/1.55 % (4122294)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3038330427:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.50/1.55 % (4122293)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=1326480373:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.50/1.55 % (4122297)dis-21_1_sil=8000:lcm=predicate:random_seed=3764731745: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)
% 4.50/1.55 % (4122292)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=2494426776:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.50/1.55 % (4122296)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3561312313:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.50/1.55 % (4122294)Refutation not found, incomplete strategy
% 4.50/1.55 % (4122294)------------------------------
% 4.50/1.55 % (4122294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.55 % (4122294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.55 % (4122294)CaDiCaL version: 2.1.3
% 4.50/1.55 % (4122294)Termination reason: Refutation not found, incomplete strategy
% 4.50/1.55 % (4122294)Time elapsed: 0.002 s
% 4.50/1.55 % (4122294)Peak memory usage: 88 MB
% 4.50/1.55 % (4122294)Instructions burned: 1 (million)
% 4.50/1.55 % (4122295)Instruction limit reached!
% 4.50/1.55 % (4122295)------------------------------
% 4.50/1.55 % (4122295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.55 % (4122295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.55 % (4122295)CaDiCaL version: 2.1.3
% 4.50/1.55 % (4122295)Termination reason: Instruction limit
% 4.50/1.55 % (4122295)Termination phase: Saturation
% 4.50/1.55 % (4122295)Time elapsed: 0.069 s
% 4.50/1.55 % (4122295)Peak memory usage: 88 MB
% 4.50/1.55 % (4122295)Instructions burned: 120 (million)
% 4.50/1.55 % (4122297)Instruction limit reached!
% 4.50/1.55 % (4122297)------------------------------
% 4.50/1.55 % (4122297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.55 % (4122297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.55 % (4122297)CaDiCaL version: 2.1.3
% 4.50/1.55 % (4122297)Termination reason: Instruction limit
% 4.50/1.55 % (4122297)Termination phase: Saturation
% 4.50/1.55 % (4122297)Time elapsed: 0.071 s
% 4.50/1.55 % (4122297)Peak memory usage: 90 MB
% 4.50/1.55 % (4122297)Instructions burned: 129 (million)
% 4.50/1.55 % (4122296)Instruction limit reached!
% 4.50/1.55 % (4122296)------------------------------
% 4.50/1.55 % (4122296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.55 % (4122296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.55 % (4122296)CaDiCaL version: 2.1.3
% 4.50/1.55 % (4122296)Termination reason: Instruction limit
% 4.50/1.55 % (4122296)Termination phase: Saturation
% 4.50/1.55 % (4122296)Time elapsed: 0.094 s
% 4.50/1.55 % (4122296)Peak memory usage: 89 MB
% 4.50/1.55 % (4122296)Instructions burned: 140 (million)
% 4.50/1.55 % (4122305)lrs+10_1_sil=8000:sp=occurrence:random_seed=1455275490:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.50/1.55 % (4122306)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2112486282:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.50/1.55 % (4122307)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2342705104:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.50/1.55 % (4122294)------------------------------
% 4.50/1.55 % (4122294)------------------------------
% 4.50/1.55 % (4122306)Instruction limit reached!
% 4.50/1.55 % (4122306)------------------------------
% 4.50/1.55 % (4122306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.55 % (4122306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.55 % (4122306)CaDiCaL version: 2.1.3
% 4.50/1.55 % (4122306)Termination reason: Instruction limit
% 4.50/1.55 % (4122306)Termination phase: Saturation
% 4.50/1.55 % (4122306)Time elapsed: 0.079 s
% 4.50/1.55 % (4122306)Peak memory usage: 90 MB
% 4.50/1.55 % (4122306)Instructions burned: 157 (million)
% 4.50/1.55 % (4122291)First to succeed.
% 4.50/1.55 % (4122291)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4122286"
% 4.50/1.55 % (4122305)Instruction limit reached!
% 4.50/1.55 % (4122305)------------------------------
% 4.50/1.55 % (4122305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.55 % (4122305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.55 % (4122305)CaDiCaL version: 2.1.3
% 4.50/1.55 % (4122305)Termination reason: Instruction limit
% 4.50/1.55 % (4122305)Termination phase: Saturation
% 4.50/1.55 % (4122305)Time elapsed: 0.167 s
% 4.50/1.55 % (4122305)Peak memory usage: 91 MB
% 4.50/1.55 % (4122305)Instructions burned: 286 (million)
% 4.50/1.55 % (4122311)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=2976447101:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.50/1.55 % (4122307)Instruction limit reached!
% 4.50/1.55 % (4122307)------------------------------
% 4.50/1.55 % (4122307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.55 % (4122307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.55 % (4122307)CaDiCaL version: 2.1.3
% 4.50/1.55 % (4122307)Termination reason: Instruction limit
% 4.50/1.55 % (4122307)Termination phase: Saturation
% 4.50/1.55 % (4122307)Time elapsed: 0.209 s
% 4.50/1.55 % (4122307)Peak memory usage: 91 MB
% 4.50/1.55 % (4122307)Instructions burned: 325 (million)
% 4.50/1.55 % (4122312)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1809805374:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.50/1.55 % (4122312)Refutation not found, incomplete strategy
% 4.50/1.55 % (4122312)------------------------------
% 4.50/1.55 % (4122312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.55 % (4122312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.55 % (4122312)CaDiCaL version: 2.1.3
% 4.50/1.55 % (4122312)Termination reason: Refutation not found, incomplete strategy
% 4.50/1.55 % (4122312)Time elapsed: 0.003 s
% 4.50/1.55 % (4122312)Peak memory usage: 88 MB
% 4.50/1.55 % (4122312)Instructions burned: 3 (million)
% 4.50/1.55 % (4122291)Refutation found. Thanks to Tanya!
% 4.50/1.55 % SZS status Theorem for theBenchmark
% 4.50/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.48/1.74 % (4122291)------------------------------
% 5.48/1.74 % (4122291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/1.74 % (4122291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.74 % (4122291)CaDiCaL version: 2.1.3
% 5.48/1.74 % (4122291)Termination reason: Refutation
% 5.48/1.74 % (4122291)Time elapsed: 0.388 s
% 5.48/1.74 % (4122291)Peak memory usage: 130 MB
% 5.48/1.74 % (4122291)Instructions burned: 1000 (million)
% 5.48/1.74 % (4122291)------------------------------
% 5.48/1.74 % (4122291)------------------------------
% 5.48/1.74 % (4122286)Success in time 0.688 s
% 5.48/1.74 % Vampire exiting
%------------------------------------------------------------------------------