%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET756+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:41:50 PM UTC 2026
% Result : Theorem 5.43s 1.81s
% Output : Refutation 7.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 154 ( 7 unt; 22 def)
% Number of atoms : 392 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 406 ( 168 ~; 175 |; 32 &)
% ( 27 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 28 ( 27 usr; 23 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 111 ( 0 sgn 96 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X1)
| member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f24,axiom,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& subset(X3,X2)
& subset(X4,X2) )
=> equal_set(inverse_image2(X0,union(X3,X4)),union(inverse_image2(X0,X3),inverse_image2(X0,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa06) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& subset(X3,X2)
& subset(X4,X2) )
=> equal_set(inverse_image2(X0,union(X3,X4)),union(inverse_image2(X0,X3),inverse_image2(X0,X4))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_set(inverse_image2(X0,union(X3,X4)),union(inverse_image2(X0,X3),inverse_image2(X0,X4)))
& maps(X0,X1,X2)
& subset(X3,X2)
& subset(X4,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_set(inverse_image2(X0,union(X3,X4)),union(inverse_image2(X0,X3),inverse_image2(X0,X4)))
& maps(X0,X1,X2)
& subset(X3,X2)
& subset(X4,X2) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f38,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f37]) ).
fof(f41,plain,
( ~ equal_set(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
& maps(sK0,sK1,sK2)
& subset(sK3,sK2)
& subset(sK4,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f35]) ).
fof(f42,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f43,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f45]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ? [X4] :
( member(X4,X1)
& apply(X0,X2,X4) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ( member(sK7(X0,X1,X2),X1)
& apply(X0,X2,sK7(X0,X1,X2)) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f49]) ).
fof(f54,plain,
~ equal_set(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),
inference(cnf_transformation,[],[f41]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f57,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f60,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f61,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f65,plain,
! [X2,X0,X1] :
( apply(X0,X2,sK7(X0,X1,X2))
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f66,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( member(X2,inverse_image2(X0,X1))
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f71,definition,
( spl9_1
<=> equal_set(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f73,plain,
( ~ equal_set(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| spl9_1 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
~ spl9_1,
inference(avatar_split_clause,[],[f54,f71]) ).
fof(f75,plain,
( ~ subset(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| ~ subset(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))
| spl9_1 ),
inference(resolution,[],[f73,f61]) ).
fof(f490,definition,
( spl9_32
<=> subset(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl9_32])],[avatar_definition]) ).
fof(f492,plain,
( ~ subset(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))
| spl9_32 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f494,definition,
( spl9_33
<=> subset(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))) ),
introduced(definition,[new_symbols(definition,[spl9_33])],[avatar_definition]) ).
fof(f496,plain,
( ~ subset(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| spl9_33 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f497,plain,
( ~ spl9_32
| ~ spl9_33
| spl9_1 ),
inference(avatar_split_clause,[],[f75,f71,f494,f490]) ).
fof(f498,plain,
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| spl9_32 ),
inference(resolution,[],[f492,f56]) ).
fof(f499,plain,
( ~ member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,union(sK3,sK4)))
| spl9_32 ),
inference(resolution,[],[f492,f57]) ).
fof(f501,definition,
( spl9_34
<=> member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,union(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl9_34])],[avatar_definition]) ).
fof(f503,plain,
( ~ member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,union(sK3,sK4)))
| spl9_34 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f504,plain,
( ~ spl9_34
| spl9_32 ),
inference(avatar_split_clause,[],[f499,f490,f501]) ).
fof(f544,definition,
( spl9_39
<=> member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))) ),
introduced(definition,[new_symbols(definition,[spl9_39])],[avatar_definition]) ).
fof(f546,plain,
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| ~ spl9_39 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f547,plain,
( spl9_39
| spl9_32 ),
inference(avatar_split_clause,[],[f498,f490,f544]) ).
fof(f551,plain,
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,union(sK3,sK4)))
| spl9_33 ),
inference(resolution,[],[f496,f56]) ).
fof(f554,definition,
( spl9_40
<=> member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,union(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl9_40])],[avatar_definition]) ).
fof(f556,plain,
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,union(sK3,sK4)))
| ~ spl9_40 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f557,plain,
( spl9_40
| spl9_33 ),
inference(avatar_split_clause,[],[f551,f494,f554]) ).
fof(f558,plain,
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK3))
| member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK4))
| ~ spl9_39 ),
inference(resolution,[],[f546,f58]) ).
fof(f569,definition,
( spl9_41
<=> member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK4)) ),
introduced(definition,[new_symbols(definition,[spl9_41])],[avatar_definition]) ).
fof(f571,plain,
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK4))
| ~ spl9_41 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f573,definition,
( spl9_42
<=> member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK3)) ),
introduced(definition,[new_symbols(definition,[spl9_42])],[avatar_definition]) ).
fof(f575,plain,
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK3))
| ~ spl9_42 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f576,plain,
( spl9_41
| spl9_42
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f558,f544,f573,f569]) ).
fof(f578,plain,
( member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),union(sK3,sK4))
| ~ spl9_40 ),
inference(resolution,[],[f556,f66]) ).
fof(f589,definition,
( spl9_43
<=> member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),union(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl9_43])],[avatar_definition]) ).
fof(f591,plain,
( member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),union(sK3,sK4))
| ~ spl9_43 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f592,plain,
( spl9_43
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f578,f554,f589]) ).
fof(f593,plain,
( apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))))
| ~ spl9_41 ),
inference(resolution,[],[f571,f65]) ).
fof(f651,definition,
( spl9_47
<=> apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))))) ),
introduced(definition,[new_symbols(definition,[spl9_47])],[avatar_definition]) ).
fof(f653,plain,
( apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))))
| ~ spl9_47 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f654,plain,
( spl9_47
| ~ spl9_41 ),
inference(avatar_split_clause,[],[f593,f569,f651]) ).
fof(f661,plain,
( apply(sK0,sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))))
| ~ spl9_40 ),
inference(resolution,[],[f556,f65]) ).
fof(f674,plain,
( member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK3)
| member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK4)
| ~ spl9_43 ),
inference(resolution,[],[f591,f58]) ).
fof(f687,definition,
( spl9_48
<=> apply(sK0,sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))))) ),
introduced(definition,[new_symbols(definition,[spl9_48])],[avatar_definition]) ).
fof(f689,plain,
( apply(sK0,sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))))
| ~ spl9_48 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f690,plain,
( spl9_48
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f661,f554,f687]) ).
fof(f691,plain,
( apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))))
| ~ spl9_42 ),
inference(resolution,[],[f575,f65]) ).
fof(f721,definition,
( spl9_49
<=> member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK4) ),
introduced(definition,[new_symbols(definition,[spl9_49])],[avatar_definition]) ).
fof(f723,plain,
( member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK4)
| ~ spl9_49 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f725,definition,
( spl9_50
<=> member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK3) ),
introduced(definition,[new_symbols(definition,[spl9_50])],[avatar_definition]) ).
fof(f727,plain,
( member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK3)
| ~ spl9_50 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f728,plain,
( spl9_49
| spl9_50
| ~ spl9_43 ),
inference(avatar_split_clause,[],[f674,f589,f725,f721]) ).
fof(f741,definition,
( spl9_51
<=> apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))))) ),
introduced(definition,[new_symbols(definition,[spl9_51])],[avatar_definition]) ).
fof(f743,plain,
( apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))))
| ~ spl9_51 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f744,plain,
( spl9_51
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f691,f573,f741]) ).
fof(f752,plain,
( member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK4)
| ~ spl9_41 ),
inference(resolution,[],[f571,f66]) ).
fof(f762,plain,
( ! [X0] :
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,X0))
| ~ member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),X0) )
| ~ spl9_47 ),
inference(resolution,[],[f653,f67]) ).
fof(f841,plain,
( ! [X0] :
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,X0))
| ~ member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),X0) )
| ~ spl9_48 ),
inference(resolution,[],[f689,f67]) ).
fof(f855,definition,
( spl9_54
<=> ! [X0] :
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,X0))
| ~ member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_54])],[avatar_definition]) ).
fof(f856,plain,
( ! [X0] :
( ~ member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),X0)
| member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,X0)) )
| ~ spl9_54 ),
inference(avatar_component_clause,[],[f855]) ).
fof(f857,plain,
( spl9_54
| ~ spl9_48 ),
inference(avatar_split_clause,[],[f841,f687,f855]) ).
fof(f938,plain,
( ! [X0] :
( ~ member(X0,union(sK3,sK4))
| ~ apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),X0) )
| spl9_34 ),
inference(resolution,[],[f503,f67]) ).
fof(f953,plain,
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK4))
| ~ spl9_49
| ~ spl9_54 ),
inference(resolution,[],[f856,f723]) ).
fof(f972,plain,
( ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| spl9_33 ),
inference(resolution,[],[f496,f57]) ).
fof(f974,definition,
( spl9_59
<=> member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))) ),
introduced(definition,[new_symbols(definition,[spl9_59])],[avatar_definition]) ).
fof(f976,plain,
( ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| spl9_59 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f977,plain,
( ~ spl9_59
| spl9_33 ),
inference(avatar_split_clause,[],[f972,f494,f974]) ).
fof(f978,plain,
( ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK4))
| spl9_59 ),
inference(resolution,[],[f976,f59]) ).
fof(f979,plain,
( ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK3))
| spl9_59 ),
inference(resolution,[],[f976,f60]) ).
fof(f983,plain,
( $false
| ~ spl9_49
| ~ spl9_54
| spl9_59 ),
inference(forward_subsumption_resolution,[],[f978,f953]) ).
fof(f984,plain,
( ~ spl9_49
| ~ spl9_54
| spl9_59 ),
inference(avatar_contradiction_clause,[],[f983]) ).
fof(f997,definition,
( spl9_61
<=> member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK3)) ),
introduced(definition,[new_symbols(definition,[spl9_61])],[avatar_definition]) ).
fof(f999,plain,
( ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK3))
| spl9_61 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f1000,plain,
( ~ spl9_61
| spl9_59 ),
inference(avatar_split_clause,[],[f979,f974,f997]) ).
fof(f1022,plain,
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK3))
| ~ spl9_50
| ~ spl9_54 ),
inference(resolution,[],[f727,f856]) ).
fof(f1032,plain,
( $false
| ~ spl9_50
| ~ spl9_54
| spl9_61 ),
inference(forward_subsumption_resolution,[],[f1022,f999]) ).
fof(f1033,plain,
( ~ spl9_50
| ~ spl9_54
| spl9_61 ),
inference(avatar_contradiction_clause,[],[f1032]) ).
fof(f1097,definition,
( spl9_64
<=> ! [X0] :
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,X0))
| ~ member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_64])],[avatar_definition]) ).
fof(f1098,plain,
( ! [X0] :
( ~ member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),X0)
| member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,X0)) )
| ~ spl9_64 ),
inference(avatar_component_clause,[],[f1097]) ).
fof(f1099,plain,
( spl9_64
| ~ spl9_47 ),
inference(avatar_split_clause,[],[f762,f651,f1097]) ).
fof(f1176,definition,
( spl9_67
<=> member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK4) ),
introduced(definition,[new_symbols(definition,[spl9_67])],[avatar_definition]) ).
fof(f1178,plain,
( member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK4)
| ~ spl9_67 ),
inference(avatar_component_clause,[],[f1176]) ).
fof(f1179,plain,
( spl9_67
| ~ spl9_41 ),
inference(avatar_split_clause,[],[f752,f569,f1176]) ).
fof(f1183,plain,
( ! [X0] : member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(X0,sK4))
| ~ spl9_67 ),
inference(resolution,[],[f1178,f59]) ).
fof(f1295,definition,
( spl9_75
<=> ! [X0] : member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(X0,sK4)) ),
introduced(definition,[new_symbols(definition,[spl9_75])],[avatar_definition]) ).
fof(f1296,plain,
( ! [X0] : member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(X0,sK4))
| ~ spl9_75 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f1297,plain,
( spl9_75
| ~ spl9_67 ),
inference(avatar_split_clause,[],[f1183,f1176,f1295]) ).
fof(f1302,plain,
( ! [X0] : member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,union(X0,sK4)))
| ~ spl9_64
| ~ spl9_75 ),
inference(resolution,[],[f1296,f1098]) ).
fof(f1312,plain,
( $false
| spl9_34
| ~ spl9_64
| ~ spl9_75 ),
inference(backward_subsumption_resolution,[],[f503,f1302]) ).
fof(f1313,plain,
( spl9_34
| ~ spl9_64
| ~ spl9_75 ),
inference(avatar_contradiction_clause,[],[f1312]) ).
fof(f1321,plain,
( member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK3)
| ~ spl9_42 ),
inference(resolution,[],[f575,f66]) ).
fof(f1359,definition,
( spl9_76
<=> member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK3) ),
introduced(definition,[new_symbols(definition,[spl9_76])],[avatar_definition]) ).
fof(f1361,plain,
( member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK3)
| ~ spl9_76 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f1362,plain,
( spl9_76
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f1321,f573,f1359]) ).
fof(f1367,plain,
( ! [X0] : member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(sK3,X0))
| ~ spl9_76 ),
inference(resolution,[],[f1361,f60]) ).
fof(f1438,definition,
( spl9_82
<=> ! [X0] :
( ~ member(X0,union(sK3,sK4))
| ~ apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_82])],[avatar_definition]) ).
fof(f1439,plain,
( ! [X0] :
( ~ apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),X0)
| ~ member(X0,union(sK3,sK4)) )
| ~ spl9_82 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f1440,plain,
( spl9_82
| spl9_34 ),
inference(avatar_split_clause,[],[f938,f501,f1438]) ).
fof(f1441,plain,
( ~ member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(sK3,sK4))
| ~ spl9_51
| ~ spl9_82 ),
inference(resolution,[],[f1439,f743]) ).
fof(f1446,plain,
( $false
| ~ spl9_51
| ~ spl9_76
| ~ spl9_82 ),
inference(forward_subsumption_resolution,[],[f1441,f1367]) ).
fof(f1447,plain,
( ~ spl9_51
| ~ spl9_76
| ~ spl9_82 ),
inference(avatar_contradiction_clause,[],[f1446]) ).
cnf(s1,plain,
~ spl9_1,
inference(sat_conversion,[],[f74]) ).
cnf(s32,plain,
( spl9_1
| ~ spl9_32
| ~ spl9_33 ),
inference(sat_conversion,[],[f497]) ).
cnf(s33,plain,
( spl9_32
| ~ spl9_34 ),
inference(sat_conversion,[],[f504]) ).
cnf(s37,plain,
( spl9_32
| spl9_39 ),
inference(sat_conversion,[],[f547]) ).
cnf(s38,plain,
( spl9_33
| spl9_40 ),
inference(sat_conversion,[],[f557]) ).
cnf(s39,plain,
( ~ spl9_39
| spl9_41
| spl9_42 ),
inference(sat_conversion,[],[f576]) ).
cnf(s40,plain,
( ~ spl9_40
| spl9_43 ),
inference(sat_conversion,[],[f592]) ).
cnf(s43,plain,
( ~ spl9_41
| spl9_47 ),
inference(sat_conversion,[],[f654]) ).
cnf(s44,plain,
( ~ spl9_40
| spl9_48 ),
inference(sat_conversion,[],[f690]) ).
cnf(s45,plain,
( ~ spl9_43
| spl9_49
| spl9_50 ),
inference(sat_conversion,[],[f728]) ).
cnf(s46,plain,
( ~ spl9_42
| spl9_51 ),
inference(sat_conversion,[],[f744]) ).
cnf(s51,plain,
( ~ spl9_48
| spl9_54 ),
inference(sat_conversion,[],[f857]) ).
cnf(s58,plain,
( spl9_33
| ~ spl9_59 ),
inference(sat_conversion,[],[f977]) ).
cnf(s59,plain,
( ~ spl9_49
| ~ spl9_54
| spl9_59 ),
inference(sat_conversion,[],[f984]) ).
cnf(s61,plain,
( spl9_59
| ~ spl9_61 ),
inference(sat_conversion,[],[f1000]) ).
cnf(s62,plain,
( ~ spl9_50
| ~ spl9_54
| spl9_61 ),
inference(sat_conversion,[],[f1033]) ).
cnf(s66,plain,
( ~ spl9_47
| spl9_64 ),
inference(sat_conversion,[],[f1099]) ).
cnf(s69,plain,
( ~ spl9_41
| spl9_67 ),
inference(sat_conversion,[],[f1179]) ).
cnf(s77,plain,
( ~ spl9_67
| spl9_75 ),
inference(sat_conversion,[],[f1297]) ).
cnf(s78,plain,
( spl9_34
| ~ spl9_64
| ~ spl9_75 ),
inference(sat_conversion,[],[f1313]) ).
cnf(s79,plain,
( ~ spl9_42
| spl9_76 ),
inference(sat_conversion,[],[f1362]) ).
cnf(s85,plain,
( spl9_34
| spl9_82 ),
inference(sat_conversion,[],[f1440]) ).
cnf(s86,plain,
( ~ spl9_51
| ~ spl9_76
| ~ spl9_82 ),
inference(sat_conversion,[],[f1447]) ).
cnf(s114,plain,
spl9_33,
inference(rat,[],[s45,s59,s62,s51,s40,s44,s61,s38,s58]) ).
cnf(s115,plain,
( ~ spl9_42
| ~ spl9_82 ),
inference(rat,[],[s86,s46,s79]) ).
cnf(s116,plain,
spl9_32,
inference(rat,[],[s78,s66,s77,s43,s69,s39,s115,s85,s33,s37]) ).
cnf(s117,plain,
$false,
inference(rat,[],[s32,s1,s114,s116]) ).
fof(f1448,plain,
$false,
inference(avatar_sat_refutation,[],[s117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET756+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 % Computer : n002.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Mon Sep 28 02:46:37 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 5.43/1.81 % (4104917)Detected formulas, will run a generic FOF schedule.
% 5.43/1.81 % (4104924)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=2375009646:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.43/1.81 % (4104925)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3694369280:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.43/1.81 % (4104922)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=3060513517:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.43/1.81 % (4104923)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=860390489:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.43/1.81 % (4104928)dis-21_1_sil=8000:lcm=predicate:random_seed=3197275295: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)
% 5.43/1.81 % (4104926)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=30965411:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.43/1.81 % (4104927)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3548653522:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.43/1.81 % (4104925)Refutation not found, incomplete strategy
% 5.43/1.81 % (4104925)------------------------------
% 5.43/1.81 % (4104925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104925)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104925)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.81 % (4104925)Time elapsed: 0.003 s
% 5.43/1.81 % (4104925)Peak memory usage: 88 MB
% 5.43/1.81 % (4104925)Instructions burned: 3 (million)
% 5.43/1.81 % (4104926)Instruction limit reached!
% 5.43/1.81 % (4104926)------------------------------
% 5.43/1.81 % (4104926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104926)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104926)Termination reason: Instruction limit
% 5.43/1.81 % (4104926)Termination phase: Saturation
% 5.43/1.81 % (4104926)Time elapsed: 0.067 s
% 5.43/1.81 % (4104926)Peak memory usage: 88 MB
% 5.43/1.81 % (4104926)Instructions burned: 119 (million)
% 5.43/1.81 % (4104928)Instruction limit reached!
% 5.43/1.81 % (4104928)------------------------------
% 5.43/1.81 % (4104928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104928)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104928)Termination reason: Instruction limit
% 5.43/1.81 % (4104928)Termination phase: Saturation
% 5.43/1.81 % (4104928)Time elapsed: 0.079 s
% 5.43/1.81 % (4104928)Peak memory usage: 90 MB
% 5.43/1.81 % (4104928)Instructions burned: 129 (million)
% 5.43/1.81 % (4104927)Instruction limit reached!
% 5.43/1.81 % (4104927)------------------------------
% 5.43/1.81 % (4104927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104927)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104927)Termination reason: Instruction limit
% 5.43/1.81 % (4104927)Termination phase: Saturation
% 5.43/1.81 % (4104927)Time elapsed: 0.092 s
% 5.43/1.81 % (4104927)Peak memory usage: 89 MB
% 5.43/1.81 % (4104927)Instructions burned: 140 (million)
% 5.43/1.81 % (4104936)lrs+10_1_sil=8000:sp=occurrence:random_seed=255532461:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.43/1.81 % (4104937)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2302565359:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.43/1.81 % (4104938)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3620264165:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.43/1.81 % (4104925)------------------------------
% 5.43/1.81 % (4104925)------------------------------
% 5.43/1.81 % (4104937)Instruction limit reached!
% 5.43/1.81 % (4104937)------------------------------
% 5.43/1.81 % (4104937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104937)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104937)Termination reason: Instruction limit
% 5.43/1.81 % (4104937)Termination phase: Saturation
% 5.43/1.81 % (4104937)Time elapsed: 0.078 s
% 5.43/1.81 % (4104937)Peak memory usage: 88 MB
% 5.43/1.81 % (4104937)Instructions burned: 157 (million)
% 5.43/1.81 % (4104936)Instruction limit reached!
% 5.43/1.81 % (4104936)------------------------------
% 5.43/1.81 % (4104936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104936)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104936)Termination reason: Instruction limit
% 5.43/1.81 % (4104936)Termination phase: Saturation
% 5.43/1.81 % (4104936)Time elapsed: 0.176 s
% 5.43/1.81 % (4104936)Peak memory usage: 92 MB
% 5.43/1.81 % (4104936)Instructions burned: 286 (million)
% 5.43/1.81 % (4104943)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=2204742158:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.43/1.81 % (4104944)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=131320955:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.43/1.81 % (4104944)Refutation not found, incomplete strategy
% 5.43/1.81 % (4104944)------------------------------
% 5.43/1.81 % (4104944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104944)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104944)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.81 % (4104944)Time elapsed: 0.002 s
% 5.43/1.81 % (4104944)Peak memory usage: 88 MB
% 5.43/1.81 % (4104944)Instructions burned: 1 (million)
% 5.43/1.81 % (4104938)Instruction limit reached!
% 5.43/1.81 % (4104938)------------------------------
% 5.43/1.81 % (4104938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104938)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104938)Termination reason: Instruction limit
% 5.43/1.81 % (4104938)Termination phase: Saturation
% 5.43/1.81 % (4104938)Time elapsed: 0.205 s
% 5.43/1.81 % (4104938)Peak memory usage: 91 MB
% 5.43/1.81 % (4104938)Instructions burned: 326 (million)
% 5.43/1.81 % (4104943)Instruction limit reached!
% 5.43/1.81 % (4104943)------------------------------
% 5.43/1.81 % (4104943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104943)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104943)Termination reason: Instruction limit
% 5.43/1.81 % (4104943)Termination phase: Saturation
% 5.43/1.81 % (4104943)Time elapsed: 0.124 s
% 5.43/1.81 % (4104943)Peak memory usage: 89 MB
% 5.43/1.81 % (4104943)Instructions burned: 248 (million)
% 5.43/1.81 % (4104945)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3077883680:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.43/1.81 % (4104924)First to succeed.
% 5.43/1.81 % (4104924)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4104917"
% 5.43/1.81 % (4104948)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3717145638:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.43/1.81 % (4104950)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2823271882:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.43/1.81 % (4104922)Also succeeded, but the first one will report.
% 5.43/1.81 % (4104948)Instruction limit reached!
% 5.43/1.81 % (4104948)------------------------------
% 5.43/1.81 % (4104948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104948)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104948)Termination reason: Instruction limit
% 5.43/1.81 % (4104948)Termination phase: Saturation
% 5.43/1.81 % (4104948)Time elapsed: 0.075 s
% 5.43/1.81 % (4104948)Peak memory usage: 89 MB
% 5.43/1.81 % (4104948)Instructions burned: 113 (million)
% 5.43/1.81 % (4104944)------------------------------
% 5.43/1.81 % (4104944)------------------------------
% 5.43/1.81 % (4104950)Instruction limit reached!
% 5.43/1.81 % (4104950)------------------------------
% 5.43/1.81 % (4104950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.81 % (4104950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.81 % (4104950)CaDiCaL version: 2.1.3
% 5.43/1.81 % (4104950)Termination reason: Instruction limit
% 5.43/1.81 % (4104950)Termination phase: Saturation
% 5.43/1.81 % (4104950)Time elapsed: 0.069 s
% 5.43/1.81 % (4104950)Peak memory usage: 89 MB
% 5.43/1.81 % (4104950)Instructions burned: 127 (million)
% 5.43/1.81 % (4104953)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3855771710:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 5.43/1.81 % (4104954)lrs+10_1_sil=8000:sp=occurrence:random_seed=1573714228:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 5.43/1.81 % (4104924)Refutation found. Thanks to Tanya!
% 5.43/1.81 % SZS status Theorem for theBenchmark
% 5.43/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 7.34/2.01 % (4104924)------------------------------
% 7.34/2.01 % (4104924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/2.01 % (4104924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/2.01 % (4104924)CaDiCaL version: 2.1.3
% 7.34/2.01 % (4104924)Termination reason: Refutation
% 7.34/2.01 % (4104924)Time elapsed: 0.599 s
% 7.34/2.01 % (4104924)Peak memory usage: 132 MB
% 7.34/2.01 % (4104924)Instructions burned: 1225 (million)
% 7.34/2.01 % (4104924)------------------------------
% 7.34/2.01 % (4104924)------------------------------
% 7.34/2.01 % (4104917)Success in time 0.965 s
% 7.34/2.02 % Vampire exiting
%------------------------------------------------------------------------------