%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET726+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 : n017.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 12:41:45 PM UTC 2026
% Result : Theorem 4.30s 2.22s
% Output : Refutation 8.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 19 unt; 0 def)
% Number of atoms : 257 ( 15 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 282 ( 85 ~; 82 |; 83 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-5 aty)
% Number of variables : 237 ( 211 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X2)
& member(X6,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X6) )
=> X5 = X6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f14,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X5,X2)
& member(X6,X4) )
=> ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ( member(X4,X2)
& member(X5,X3)
& member(X6,X3) )
=> ( ( apply(X0,X4,X5)
& apply(X1,X4,X6) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_maps) ).
fof(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( member(X3,X1)
& member(X4,X2) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) )
=> equal_maps(inverse_function(X0,X3,X4),X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII17) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) )
=> equal_maps(inverse_function(X0,X3,X4),X1,X4,X3) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6] :
( ( member(X4,X2)
& member(X5,X3)
& member(X6,X3) )
=> ( ( apply(X0,X4,X5)
& apply(X1,X4,X6) )
=> X5 = X6 ) )
=> equal_maps(X0,X1,X2,X3) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(inverse_function(X0,X3,X4),X1,X4,X3)
& maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(inverse_function(X0,X3,X4),X1,X4,X3)
& maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ? [X4,X5,X6] :
( X5 != X6
& apply(X0,X4,X5)
& apply(X1,X4,X6)
& member(X4,X2)
& member(X5,X3)
& member(X6,X3) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ? [X4,X5,X6] :
( X5 != X6
& apply(X0,X4,X5)
& apply(X1,X4,X6)
& member(X4,X2)
& member(X5,X3)
& member(X6,X3) ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(ennf_transformation,[],[f14]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ~ equal_maps(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)
& maps(sK0,sK3,sK4)
& maps(sK1,sK4,sK3)
& maps(sK2,sK4,sK3)
& identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3)
& identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4) ),
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)],[f36]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK5(X0,X2,X3),X2)
& apply(X0,X3,sK5(X0,X2,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X2,X3))],[f38]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
& apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& member(sK6(X0,X1,X2,X3),X2)
& member(sK7(X0,X1,X2,X3),X3)
& member(sK8(X0,X1,X2,X3),X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X4,sK6(X0,X1,X2,X3)),skolemize(X5,sK7(X0,X1,X2,X3)),skolemize(X6,sK8(X0,X1,X2,X3))],[f40]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(nnf_transformation,[],[f43]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ? [X8] :
( member(X8,X3)
& apply(X1,X5,X8)
& apply(X0,X8,X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ( member(sK9(X0,X1,X3,X5,X6),X3)
& apply(X1,X5,sK9(X0,X1,X3,X5,X6))
& apply(X0,sK9(X0,X1,X3,X5,X6),X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X8,sK9(X0,X1,X3,X5,X6))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ( ( apply(X0,X3,X4)
| ~ apply(inverse_function(X0,X1,X2),X4,X3) )
& ( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4) ) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(nnf_transformation,[],[f45]) ).
fof(f54,plain,
identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f56,plain,
maps(sK1,sK4,sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f57,plain,
maps(sK0,sK3,sK4),
inference(cnf_transformation,[],[f46]) ).
fof(f58,plain,
~ equal_maps(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( member(sK6(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f69,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK9(X0,X1,X3,X5,X6),X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,X5,sK9(X0,X1,X3,X5,X6))
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK9(X0,X1,X3,X5,X6),X3)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f51]) ).
fof(f74,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4)
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f75,plain,
member(sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK3),
inference(unit_resulting_resolution,[],[f62,f58]) ).
fof(f77,plain,
member(sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK3),
inference(unit_resulting_resolution,[],[f63,f58]) ).
fof(f78,plain,
apply(compose_function(sK1,sK0,sK3,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(unit_resulting_resolution,[],[f68,f54,f77]) ).
fof(f79,plain,
member(sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK4),
inference(unit_resulting_resolution,[],[f64,f58]) ).
fof(f99,plain,
sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3) != sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),
inference(unit_resulting_resolution,[],[f67,f58]) ).
fof(f103,plain,
apply(sK1,sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(unit_resulting_resolution,[],[f65,f58]) ).
fof(f107,plain,
apply(inverse_function(sK0,sK3,sK4),sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(unit_resulting_resolution,[],[f66,f58]) ).
fof(f135,plain,
apply(sK0,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(unit_resulting_resolution,[],[f74,f79,f77,f107]) ).
fof(f225,plain,
apply(sK0,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3))),
inference(unit_resulting_resolution,[],[f70,f77,f77,f78]) ).
fof(f226,plain,
apply(sK1,sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(unit_resulting_resolution,[],[f69,f77,f77,f78]) ).
fof(f227,plain,
member(sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),sK4),
inference(unit_resulting_resolution,[],[f71,f77,f77,f78]) ).
fof(f993,plain,
sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3) = sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(unit_resulting_resolution,[],[f59,f57,f77,f79,f135,f227,f225]) ).
fof(f1036,plain,
~ apply(sK1,sK9(sK1,sK0,sK4,sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK7(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(unit_resulting_resolution,[],[f59,f56,f75,f77,f99,f227,f226]) ).
fof(f1054,plain,
~ apply(sK1,sK6(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3),sK8(inverse_function(sK0,sK3,sK4),sK1,sK4,sK3)),
inference(forward_demodulation,[],[f1036,f993]) ).
fof(f1059,plain,
$false,
inference(forward_subsumption_resolution,[],[f1054,f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET726+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 28 02:34:51 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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
% 4.30/2.22 % (3159359)Detected formulas, will run a generic FOF schedule.
% 4.30/2.22 % (3159372)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=492396446:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.30/2.22 % (3159378)dis-21_1_sil=8000:lcm=predicate:random_seed=2810180824: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)
% 4.30/2.22 % (3159373)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=4056596743:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.30/2.22 % (3159376)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3535387446:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.30/2.22 % (3159375)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2375364636:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.30/2.22 % (3159374)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=2994579706:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.30/2.22 % (3159377)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3103027285:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.30/2.22 % (3159375)Refutation not found, incomplete strategy
% 4.30/2.22 % (3159375)------------------------------
% 4.30/2.22 % (3159375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/2.22 % (3159375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/2.22 % (3159375)CaDiCaL version: 2.1.3
% 4.30/2.22 % (3159375)Termination reason: Refutation not found, incomplete strategy
% 4.30/2.22 % (3159375)Time elapsed: 0.030 s
% 4.30/2.22 % (3159375)Peak memory usage: 89 MB
% 4.30/2.22 % (3159375)Instructions burned: 27 (million)
% 4.30/2.22 % (3159378)Instruction limit reached!
% 4.30/2.22 % (3159378)------------------------------
% 4.30/2.22 % (3159378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/2.22 % (3159378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/2.22 % (3159378)CaDiCaL version: 2.1.3
% 4.30/2.22 % (3159378)Termination reason: Instruction limit
% 4.30/2.22 % (3159378)Termination phase: Saturation
% 4.30/2.22 % (3159378)Time elapsed: 0.118 s
% 4.30/2.22 % (3159378)Peak memory usage: 89 MB
% 4.30/2.22 % (3159378)Instructions burned: 130 (million)
% 4.30/2.22 % (3159376)Instruction limit reached!
% 4.30/2.22 % (3159376)------------------------------
% 4.30/2.22 % (3159376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/2.22 % (3159376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/2.22 % (3159376)CaDiCaL version: 2.1.3
% 4.30/2.22 % (3159376)Termination reason: Instruction limit
% 4.30/2.22 % (3159376)Termination phase: Saturation
% 4.30/2.22 % (3159376)Time elapsed: 0.106 s
% 4.30/2.22 % (3159376)Peak memory usage: 89 MB
% 4.30/2.22 % (3159376)Instructions burned: 119 (million)
% 4.30/2.22 % (3159377)Instruction limit reached!
% 4.30/2.22 % (3159377)------------------------------
% 4.30/2.22 % (3159377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/2.22 % (3159377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/2.22 % (3159377)CaDiCaL version: 2.1.3
% 4.30/2.22 % (3159377)Termination reason: Instruction limit
% 4.30/2.22 % (3159377)Termination phase: Saturation
% 4.30/2.22 % (3159377)Time elapsed: 0.145 s
% 4.30/2.22 % (3159377)Peak memory usage: 89 MB
% 4.30/2.22 % (3159377)Instructions burned: 139 (million)
% 4.30/2.22 % (3159388)lrs+10_1_sil=8000:sp=occurrence:random_seed=2954462943:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 4.30/2.22 % (3159389)lrs+10_1_sil=32000:urr=on:br=off:random_seed=327088449:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.30/2.22 % (3159390)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1819338060:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 4.30/2.22 % (3159375)------------------------------
% 4.30/2.22 % (3159375)------------------------------
% 4.30/2.22 % (3159389)First to succeed.
% 4.30/2.22 % (3159389)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3159359"
% 4.30/2.22 % (3159388)Instruction limit reached!
% 4.30/2.22 % (3159388)------------------------------
% 4.30/2.22 % (3159388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/2.22 % (3159388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/2.22 % (3159388)CaDiCaL version: 2.1.3
% 4.30/2.22 % (3159388)Termination reason: Instruction limit
% 4.30/2.22 % (3159388)Termination phase: Saturation
% 4.30/2.22 % (3159388)Time elapsed: 0.259 s
% 4.30/2.22 % (3159388)Peak memory usage: 93 MB
% 4.30/2.22 % (3159388)Instructions burned: 285 (million)
% 4.30/2.22 % (3159372)Also succeeded, but the first one will report.
% 4.30/2.22 % (3159394)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=1184579849:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 4.30/2.22 % (3159390)Instruction limit reached!
% 4.30/2.22 % (3159390)------------------------------
% 4.30/2.22 % (3159390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/2.22 % (3159390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/2.22 % (3159390)CaDiCaL version: 2.1.3
% 4.30/2.22 % (3159390)Termination reason: Instruction limit
% 4.30/2.22 % (3159390)Termination phase: Saturation
% 4.30/2.22 % (3159390)Time elapsed: 0.344 s
% 4.30/2.22 % (3159390)Peak memory usage: 93 MB
% 4.30/2.22 % (3159390)Instructions burned: 326 (million)
% 4.30/2.22 % (3159395)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=260499124:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 4.30/2.22 % (3159395)Refutation not found, incomplete strategy
% 4.30/2.22 % (3159395)------------------------------
% 4.30/2.22 % (3159395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/2.22 % (3159395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/2.22 % (3159395)CaDiCaL version: 2.1.3
% 4.30/2.22 % (3159395)Termination reason: Refutation not found, incomplete strategy
% 4.30/2.22 % (3159395)Time elapsed: 0.001 s
% 4.30/2.22 % (3159395)Peak memory usage: 88 MB
% 4.30/2.22 % (3159395)Instructions burned: 1 (million)
% 4.30/2.22 % (3159389)Refutation found. Thanks to Tanya!
% 4.30/2.22 % SZS status Theorem for theBenchmark
% 4.30/2.22 % SZS output start Proof for theBenchmark
% See solution above
% 8.43/2.52 % (3159389)------------------------------
% 8.43/2.52 % (3159389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.43/2.52 % (3159389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/2.52 % (3159389)CaDiCaL version: 2.1.3
% 8.43/2.52 % (3159389)Termination reason: Refutation
% 8.43/2.52 % (3159389)Time elapsed: 0.106 s
% 8.43/2.52 % (3159389)Peak memory usage: 90 MB
% 8.43/2.52 % (3159389)Instructions burned: 118 (million)
% 8.43/2.52 % (3159389)------------------------------
% 8.43/2.52 % (3159389)------------------------------
% 8.43/2.52 % (3159359)Success in time 1.056 s
% 8.43/2.52 % Vampire exiting
%------------------------------------------------------------------------------