%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET724+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 : n015.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 2.15s 1.14s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 5 unt; 0 def)
% Number of atoms : 345 ( 21 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 490 ( 203 ~; 208 |; 64 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-5 aty)
% Number of variables : 259 ( 233 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
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(f18,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X5)
& maps(X2,X4,X5)
& surjective(X0,X3,X4)
& equal_maps(compose_function(X1,X0,X3,X4,X5),compose_function(X2,X0,X3,X4,X5),X3,X5) )
=> equal_maps(X1,X2,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII15) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X5)
& maps(X2,X4,X5)
& surjective(X0,X3,X4)
& equal_maps(compose_function(X1,X0,X3,X4,X5),compose_function(X2,X0,X3,X4,X5),X3,X5) )
=> equal_maps(X1,X2,X4,X5) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) ) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ equal_maps(X1,X2,X4,X5)
& maps(X0,X3,X4)
& maps(X1,X4,X5)
& maps(X2,X4,X5)
& surjective(X0,X3,X4)
& equal_maps(compose_function(X1,X0,X3,X4,X5),compose_function(X2,X0,X3,X4,X5),X3,X5) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ equal_maps(X1,X2,X4,X5)
& maps(X0,X3,X4)
& maps(X1,X4,X5)
& maps(X2,X4,X5)
& surjective(X0,X3,X4)
& equal_maps(compose_function(X1,X0,X3,X4,X5),compose_function(X2,X0,X3,X4,X5),X3,X5) ),
inference(flattening,[],[f34]) ).
fof(f38,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,[],[f15]) ).
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(flattening,[],[f38]) ).
fof(f40,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(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ! [X3] :
( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) )
| ~ member(X3,X2) )
| ~ surjective(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f43,plain,
( ~ equal_maps(sK1,sK2,sK4,sK5)
& maps(sK0,sK3,sK4)
& maps(sK1,sK4,sK5)
& maps(sK2,sK4,sK5)
& surjective(sK0,sK3,sK4)
& equal_maps(compose_function(sK1,sK0,sK3,sK4,sK5),compose_function(sK2,sK0,sK3,sK4,sK5),sK3,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f35]) ).
fof(f45,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) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ apply(X0,X4,X5)
| ~ apply(X1,X4,X6)
| ~ member(X4,X2)
| ~ member(X5,X3)
| ~ member(X6,X3) )
| ~ equal_maps(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f46,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) ) )
& ( ! [X7,X8,X9] :
( X8 = X9
| ~ apply(X0,X7,X8)
| ~ apply(X1,X7,X9)
| ~ member(X7,X2)
| ~ member(X8,X3)
| ~ member(X9,X3) )
| ~ equal_maps(X0,X1,X2,X3) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ( equal_maps(X0,X1,X2,X3)
| ( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3)
& apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& apply(X1,sK7(X0,X1,X2,X3),sK9(X0,X1,X2,X3))
& member(sK7(X0,X1,X2,X3),X2)
& member(sK8(X0,X1,X2,X3),X3)
& member(sK9(X0,X1,X2,X3),X3) ) )
& ( ! [X7,X8,X9] :
( X8 = X9
| ~ apply(X0,X7,X8)
| ~ apply(X1,X7,X9)
| ~ member(X7,X2)
| ~ member(X8,X3)
| ~ member(X9,X3) )
| ~ equal_maps(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X4,sK7(X0,X1,X2,X3)),skolemize(X5,sK8(X0,X1,X2,X3)),skolemize(X6,sK9(X0,X1,X2,X3))],[f46]) ).
fof(f48,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,[],[f41]) ).
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) ) )
& ( ? [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,[],[f48]) ).
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) ) )
& ( ( member(sK10(X0,X1,X3,X5,X6),X3)
& apply(X1,X5,sK10(X0,X1,X3,X5,X6))
& apply(X0,sK10(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,[sK10]),skolemize(X8,sK10(X0,X1,X3,X5,X6))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( member(sK11(X0,X1,X3),X1)
& apply(X0,sK11(X0,X1,X3),X3) )
| ~ member(X3,X2) )
| ~ surjective(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X4,sK11(X0,X1,X3))],[f42]) ).
fof(f52,plain,
equal_maps(compose_function(sK1,sK0,sK3,sK4,sK5),compose_function(sK2,sK0,sK3,sK4,sK5),sK3,sK5),
inference(cnf_transformation,[],[f43]) ).
fof(f53,plain,
surjective(sK0,sK3,sK4),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
~ equal_maps(sK1,sK2,sK4,sK5),
inference(cnf_transformation,[],[f43]) ).
fof(f61,plain,
! [X2,X3,X0,X1,X8,X9,X7] :
( ~ equal_maps(X0,X1,X2,X3)
| ~ apply(X0,X7,X8)
| ~ apply(X1,X7,X9)
| ~ member(X7,X2)
| ~ member(X8,X3)
| ~ member(X9,X3)
| X8 = X9 ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( member(sK9(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK7(X0,X1,X2,X3),sK9(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK7(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( sK8(X0,X1,X2,X3) != sK9(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f50]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK11(X0,X1,X3),X3)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( member(sK11(X0,X1,X3),X1)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ apply(compose_function(sK2,sK0,sK3,sK4,sK5),X0,X2)
| ~ apply(compose_function(sK1,sK0,sK3,sK4,sK5),X0,X1)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(X2,sK5)
| X1 = X2 ),
inference(resolution,[],[f61,f52]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ apply(compose_function(sK1,sK0,sK3,sK4,sK5),X0,X1)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(X2,sK5)
| X1 = X2
| ~ member(X3,sK4)
| ~ apply(sK0,X0,X3)
| ~ apply(sK2,X3,X2)
| ~ member(X0,sK3)
| ~ member(X2,sK5) ),
inference(resolution,[],[f88,f71]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( ~ apply(compose_function(sK1,sK0,sK3,sK4,sK5),X0,X1)
| ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(X2,sK5)
| X1 = X2
| ~ member(X3,sK4)
| ~ apply(sK0,X0,X3)
| ~ apply(sK2,X3,X2) ),
inference(duplicate_literal_removal,[],[f92]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,sK3)
| ~ member(X1,sK5)
| ~ member(X2,sK5)
| X1 = X2
| ~ member(X3,sK4)
| ~ apply(sK0,X0,X3)
| ~ apply(sK2,X3,X2)
| ~ member(X4,sK4)
| ~ apply(sK0,X0,X4)
| ~ apply(sK1,X4,X1)
| ~ member(X0,sK3)
| ~ member(X1,sK5) ),
inference(resolution,[],[f99,f71]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK2,X3,X2)
| ~ member(X1,sK5)
| ~ member(X2,sK5)
| X1 = X2
| ~ member(X3,sK4)
| ~ apply(sK0,X0,X3)
| ~ member(X0,sK3)
| ~ member(X4,sK4)
| ~ apply(sK0,X0,X4)
| ~ apply(sK1,X4,X1) ),
inference(duplicate_literal_removal,[],[f100]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ apply(sK0,X4,sK7(X1,sK2,X2,X3))
| ~ member(sK9(X1,sK2,X2,X3),sK5)
| sK9(X1,sK2,X2,X3) = X0
| ~ member(sK7(X1,sK2,X2,X3),sK4)
| ~ member(X0,sK5)
| ~ member(X4,sK3)
| ~ member(X5,sK4)
| ~ apply(sK0,X4,X5)
| ~ apply(sK1,X5,X0)
| equal_maps(X1,sK2,X2,X3) ),
inference(resolution,[],[f107,f65]) ).
fof(f197,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK0,X0,sK7(X1,sK2,X2,X3))
| ~ member(sK9(X1,sK2,X2,X3),sK5)
| sK9(X1,sK2,X2,X3) = X4
| ~ member(sK7(X1,sK2,X2,X3),sK4)
| ~ member(X4,sK5)
| ~ member(X0,sK3)
| ~ member(sK7(X1,sK2,X2,X3),sK4)
| ~ apply(sK1,sK7(X1,sK2,X2,X3),X4)
| equal_maps(X1,sK2,X2,X3) ),
inference(factoring,[],[f110]) ).
fof(f198,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK1,sK7(X1,sK2,X2,X3),X4)
| ~ member(sK9(X1,sK2,X2,X3),sK5)
| sK9(X1,sK2,X2,X3) = X4
| ~ member(sK7(X1,sK2,X2,X3),sK4)
| ~ member(X4,sK5)
| ~ member(X0,sK3)
| ~ apply(sK0,X0,sK7(X1,sK2,X2,X3))
| equal_maps(X1,sK2,X2,X3) ),
inference(duplicate_literal_removal,[],[f197]) ).
fof(f207,plain,
! [X2,X0,X1] :
( ~ member(sK9(sK1,sK2,X0,X1),sK5)
| sK9(sK1,sK2,X0,X1) = sK8(sK1,sK2,X0,X1)
| ~ member(sK7(sK1,sK2,X0,X1),sK4)
| ~ member(sK8(sK1,sK2,X0,X1),sK5)
| ~ member(X2,sK3)
| ~ apply(sK0,X2,sK7(sK1,sK2,X0,X1))
| equal_maps(sK1,sK2,X0,X1)
| equal_maps(sK1,sK2,X0,X1) ),
inference(resolution,[],[f198,f66]) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ member(sK9(sK1,sK2,X0,X1),sK5)
| sK9(sK1,sK2,X0,X1) = sK8(sK1,sK2,X0,X1)
| ~ member(sK7(sK1,sK2,X0,X1),sK4)
| ~ member(sK8(sK1,sK2,X0,X1),sK5)
| ~ member(X2,sK3)
| ~ apply(sK0,X2,sK7(sK1,sK2,X0,X1))
| equal_maps(sK1,sK2,X0,X1) ),
inference(duplicate_literal_removal,[],[f207]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ apply(sK0,X2,sK7(sK1,sK2,X0,X1))
| ~ member(sK7(sK1,sK2,X0,X1),sK4)
| ~ member(sK8(sK1,sK2,X0,X1),sK5)
| ~ member(X2,sK3)
| ~ member(sK9(sK1,sK2,X0,X1),sK5)
| equal_maps(sK1,sK2,X0,X1) ),
inference(forward_subsumption_resolution,[],[f210,f67]) ).
fof(f213,plain,
! [X2,X3,X0,X1] :
( ~ member(sK11(sK0,X2,sK7(sK1,sK2,X0,X1)),sK3)
| ~ member(sK8(sK1,sK2,X0,X1),sK5)
| ~ member(sK7(sK1,sK2,X0,X1),sK4)
| ~ member(sK9(sK1,sK2,X0,X1),sK5)
| equal_maps(sK1,sK2,X0,X1)
| ~ member(sK7(sK1,sK2,X0,X1),X3)
| ~ surjective(sK0,X2,X3) ),
inference(resolution,[],[f211,f72]) ).
fof(f214,plain,
! [X2,X3,X0,X1] :
( ~ member(sK9(sK1,sK2,X0,X1),sK5)
| ~ member(sK7(sK1,sK2,X0,X1),sK4)
| ~ member(sK8(sK1,sK2,X0,X1),sK5)
| equal_maps(sK1,sK2,X0,X1)
| ~ member(sK7(sK1,sK2,X0,X1),X2)
| ~ surjective(sK0,sK3,X2)
| ~ member(sK7(sK1,sK2,X0,X1),X3)
| ~ surjective(sK0,sK3,X3) ),
inference(resolution,[],[f213,f73]) ).
fof(f215,plain,
! [X2,X0,X1] :
( ~ member(sK7(sK1,sK2,X0,sK5),sK4)
| ~ member(sK8(sK1,sK2,X0,sK5),sK5)
| equal_maps(sK1,sK2,X0,sK5)
| ~ member(sK7(sK1,sK2,X0,sK5),X1)
| ~ surjective(sK0,sK3,X1)
| ~ member(sK7(sK1,sK2,X0,sK5),X2)
| ~ surjective(sK0,sK3,X2)
| equal_maps(sK1,sK2,X0,sK5) ),
inference(resolution,[],[f214,f62]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ member(sK7(sK1,sK2,X0,sK5),sK4)
| ~ member(sK8(sK1,sK2,X0,sK5),sK5)
| equal_maps(sK1,sK2,X0,sK5)
| ~ member(sK7(sK1,sK2,X0,sK5),X1)
| ~ surjective(sK0,sK3,X1)
| ~ member(sK7(sK1,sK2,X0,sK5),X2)
| ~ surjective(sK0,sK3,X2) ),
inference(duplicate_literal_removal,[],[f215]) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ member(sK7(sK1,sK2,X0,sK5),sK4)
| equal_maps(sK1,sK2,X0,sK5)
| ~ member(sK7(sK1,sK2,X0,sK5),X1)
| ~ surjective(sK0,sK3,X1)
| ~ member(sK7(sK1,sK2,X0,sK5),X2)
| ~ surjective(sK0,sK3,X2) ),
inference(forward_subsumption_resolution,[],[f216,f63]) ).
fof(f218,plain,
! [X0,X1] :
( equal_maps(sK1,sK2,sK4,sK5)
| ~ member(sK7(sK1,sK2,sK4,sK5),X0)
| ~ surjective(sK0,sK3,X0)
| ~ member(sK7(sK1,sK2,sK4,sK5),X1)
| ~ surjective(sK0,sK3,X1)
| equal_maps(sK1,sK2,sK4,sK5) ),
inference(resolution,[],[f217,f64]) ).
fof(f221,plain,
! [X0,X1] :
( equal_maps(sK1,sK2,sK4,sK5)
| ~ member(sK7(sK1,sK2,sK4,sK5),X0)
| ~ surjective(sK0,sK3,X0)
| ~ member(sK7(sK1,sK2,sK4,sK5),X1)
| ~ surjective(sK0,sK3,X1) ),
inference(duplicate_literal_removal,[],[f218]) ).
fof(f224,plain,
! [X0,X1] :
( ~ member(sK7(sK1,sK2,sK4,sK5),X1)
| ~ surjective(sK0,sK3,X0)
| ~ member(sK7(sK1,sK2,sK4,sK5),X0)
| ~ surjective(sK0,sK3,X1) ),
inference(forward_subsumption_resolution,[],[f221,f57]) ).
fof(f226,plain,
! [X0] :
( ~ member(sK7(sK1,sK2,sK4,sK5),X0)
| ~ surjective(sK0,sK3,X0)
| ~ surjective(sK0,sK3,X0) ),
inference(factoring,[],[f224]) ).
fof(f227,plain,
! [X0] :
( ~ member(sK7(sK1,sK2,sK4,sK5),X0)
| ~ surjective(sK0,sK3,X0) ),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f230,plain,
( ~ surjective(sK0,sK3,sK4)
| equal_maps(sK1,sK2,sK4,sK5) ),
inference(resolution,[],[f227,f64]) ).
fof(f231,plain,
equal_maps(sK1,sK2,sK4,sK5),
inference(forward_subsumption_resolution,[],[f230,f53]) ).
fof(f232,plain,
$false,
inference(forward_subsumption_resolution,[],[f231,f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET724+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:42:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.15/1.14 % (2211199)Detected formulas, will run a generic FOF schedule.
% 2.15/1.14 % (2211208)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2087429915:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.15/1.14 % (2211208)First to succeed.
% 2.15/1.14 % (2211208)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2211199"
% 2.15/1.14 % (2211206)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=4056499661:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.15/1.14 % (2211207)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2070316614:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.15/1.14 % (2211205)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=1563978428:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.15/1.14 % (2211204)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=3215295534:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.15/1.14 % (2211210)dis-21_1_sil=8000:lcm=predicate:random_seed=853110396: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)
% 2.15/1.14 % (2211209)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3003164960:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.15/1.14 % (2211210)Also succeeded, but the first one will report.
% 2.15/1.14 % (2211207)Also succeeded, but the first one will report.
% 2.15/1.14 % (2211209)Instruction limit reached!
% 2.15/1.14 % (2211209)------------------------------
% 2.15/1.14 % (2211209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/1.14 % (2211209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/1.14 % (2211209)CaDiCaL version: 2.1.3
% 2.15/1.14 % (2211209)Termination reason: Instruction limit
% 2.15/1.14 % (2211209)Termination phase: Saturation
% 2.15/1.14 % (2211209)Time elapsed: 0.098 s
% 2.15/1.14 % (2211209)Peak memory usage: 89 MB
% 2.15/1.14 % (2211209)Instructions burned: 139 (million)
% 2.15/1.14 % (2211208)Refutation found. Thanks to Tanya!
% 2.15/1.14 % SZS status Theorem for theBenchmark
% 2.15/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.34 % (2211208)------------------------------
% 2.71/1.34 % (2211208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.34 % (2211208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.34 % (2211208)CaDiCaL version: 2.1.3
% 2.71/1.34 % (2211208)Termination reason: Refutation
% 2.71/1.34 % (2211208)Time elapsed: 0.007 s
% 2.71/1.34 % (2211208)Peak memory usage: 88 MB
% 2.71/1.34 % (2211208)Instructions burned: 19 (million)
% 2.71/1.34 % (2211208)------------------------------
% 2.71/1.34 % (2211208)------------------------------
% 2.71/1.34 % (2211199)Success in time 0.299 s
% 2.71/1.34 % Vampire exiting
%------------------------------------------------------------------------------