%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET721+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 : n019.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 12:41:44 PM UTC 2026
% Result : Theorem 1.72s 1.30s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 59 ( 5 unt; 0 def)
% Number of atoms : 380 ( 29 equ)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 542 ( 221 ~; 227 |; 71 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-5 aty)
% Number of variables : 267 ( 241 !; 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(f17,axiom,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X3,X1)
& member(X4,X1)
& member(X5,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X4,X5) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injective) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X2,X3)
& maps(X1,X3,X4)
& injective(compose_function(X1,X0,X2,X3,X4),X2,X4) )
=> injective(X0,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII12) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X2,X3)
& maps(X1,X3,X4)
& injective(compose_function(X1,X0,X2,X3,X4),X2,X4) )
=> injective(X0,X2,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,X2,X3,X4] :
( ~ injective(X0,X2,X3)
& maps(X0,X2,X3)
& maps(X1,X3,X4)
& injective(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( ~ injective(X0,X2,X3)
& maps(X0,X2,X3)
& maps(X1,X3,X4)
& injective(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
inference(flattening,[],[f33]) ).
fof(f35,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(f36,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,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( X3 = X4
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X2) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f38,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( X3 = X4
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X2) ) ),
inference(flattening,[],[f37]) ).
fof(f39,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(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(flattening,[],[f39]) ).
fof(f41,plain,
( ~ injective(sK0,sK2,sK3)
& maps(sK0,sK2,sK3)
& maps(sK1,sK3,sK4)
& injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,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)],[f34]) ).
fof(f42,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))],[f36]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
| ? [X3,X4,X5] :
( X3 != X4
& apply(X0,X3,X5)
& apply(X0,X4,X5)
& member(X3,X1)
& member(X4,X1)
& member(X5,X2) ) )
& ( ! [X3,X4,X5] :
( X3 = X4
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X2) )
| ~ injective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
| ? [X3,X4,X5] :
( X3 != X4
& apply(X0,X3,X5)
& apply(X0,X4,X5)
& member(X3,X1)
& member(X4,X1)
& member(X5,X2) ) )
& ( ! [X6,X7,X8] :
( X6 = X7
| ~ apply(X0,X6,X8)
| ~ apply(X0,X7,X8)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ member(X8,X2) )
| ~ injective(X0,X1,X2) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
| ( sK6(X0,X1,X2) != sK7(X0,X1,X2)
& apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
& apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
& member(sK6(X0,X1,X2),X1)
& member(sK7(X0,X1,X2),X1)
& member(sK8(X0,X1,X2),X2) ) )
& ( ! [X6,X7,X8] :
( X6 = X7
| ~ apply(X0,X6,X8)
| ~ apply(X0,X7,X8)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ member(X8,X2) )
| ~ injective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1,X2)),skolemize(X5,sK8(X0,X1,X2))],[f44]) ).
fof(f46,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,[],[f40]) ).
fof(f47,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,[],[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) ) )
& ( ( 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))],[f47]) ).
fof(f49,plain,
injective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(cnf_transformation,[],[f41]) ).
fof(f50,plain,
maps(sK1,sK3,sK4),
inference(cnf_transformation,[],[f41]) ).
fof(f52,plain,
~ injective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( member(sK5(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f56,plain,
! [X2,X0,X1,X8,X6,X7] :
( ~ injective(X0,X1,X2)
| ~ apply(X0,X6,X8)
| ~ apply(X0,X7,X8)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ member(X8,X2)
| X6 = X7 ),
inference(cnf_transformation,[],[f45]) ).
fof(f57,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f60,plain,
! [X2,X0,X1] :
( apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f61,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f62,plain,
! [X2,X0,X1] :
( sK6(X0,X1,X2) != sK7(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f66,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,[],[f48]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),X2,X1)
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),X0,X1)
| ~ member(X0,sK2)
| ~ member(X2,sK2)
| ~ member(X1,sK4)
| X0 = X2 ),
inference(resolution,[],[f56,f49]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,sK3)
| ~ apply(sK0,X1,X0)
| ~ apply(sK1,X0,X2)
| ~ member(X1,sK2)
| ~ member(X2,sK4)
| ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),X3,X2)
| ~ member(X3,sK2)
| ~ member(X1,sK2)
| ~ member(X2,sK4)
| X1 = X3 ),
inference(resolution,[],[f66,f75]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( ~ apply(compose_function(sK1,sK0,sK2,sK3,sK4),X3,X2)
| ~ apply(sK0,X1,X0)
| ~ apply(sK1,X0,X2)
| ~ member(X1,sK2)
| ~ member(X2,sK4)
| ~ member(X0,sK3)
| ~ member(X3,sK2)
| X1 = X3 ),
inference(duplicate_literal_removal,[],[f99]) ).
fof(f109,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK0,X0,X1)
| ~ apply(sK1,X1,X2)
| ~ member(X0,sK2)
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| ~ member(X3,sK2)
| X0 = X3
| ~ member(X4,sK3)
| ~ apply(sK0,X3,X4)
| ~ apply(sK1,X4,X2)
| ~ member(X3,sK2)
| ~ member(X2,sK4) ),
inference(resolution,[],[f107,f66]) ).
fof(f115,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK1,X4,X2)
| ~ apply(sK1,X1,X2)
| ~ member(X0,sK2)
| ~ member(X2,sK4)
| ~ member(X1,sK3)
| ~ member(X3,sK2)
| X0 = X3
| ~ member(X4,sK3)
| ~ apply(sK0,X3,X4)
| ~ apply(sK0,X0,X1) ),
inference(duplicate_literal_removal,[],[f109]) ).
fof(f121,plain,
! [X2,X3,X0,X1] :
( ~ apply(sK1,X0,X1)
| ~ member(X2,sK2)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ member(X3,sK2)
| X2 = X3
| ~ member(X0,sK3)
| ~ apply(sK0,X3,X0)
| ~ apply(sK0,X2,X0) ),
inference(factoring,[],[f115]) ).
fof(f122,plain,
! [X2,X3,X0,X1] :
( ~ apply(sK1,X0,X1)
| ~ member(X2,sK2)
| ~ member(X1,sK4)
| ~ member(X0,sK3)
| ~ member(X3,sK2)
| X2 = X3
| ~ apply(sK0,X3,X0)
| ~ apply(sK0,X2,X0) ),
inference(duplicate_literal_removal,[],[f121]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK5(sK1,X1,X2),sK4)
| ~ member(X0,sK2)
| ~ member(X2,sK3)
| ~ member(X3,sK2)
| X0 = X3
| ~ apply(sK0,X3,X2)
| ~ apply(sK0,X0,X2)
| ~ member(X2,X4)
| ~ maps(sK1,X4,X1) ),
inference(resolution,[],[f122,f54]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK0,X2,X1)
| ~ member(X1,sK3)
| ~ member(X2,sK2)
| X0 = X2
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1)
| ~ member(X1,X3)
| ~ maps(sK1,X3,sK4)
| ~ member(X1,X4)
| ~ maps(sK1,X4,sK4) ),
inference(resolution,[],[f123,f55]) ).
fof(f138,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK0,X2,sK8(sK0,X0,X1))
| ~ member(sK6(sK0,X0,X1),sK2)
| sK6(sK0,X0,X1) = X2
| ~ member(X2,sK2)
| ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK8(sK0,X0,X1),X3)
| ~ maps(sK1,X3,sK4)
| ~ member(sK8(sK0,X0,X1),X4)
| ~ maps(sK1,X4,sK4)
| injective(sK0,X0,X1) ),
inference(resolution,[],[f130,f61]) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( ~ member(sK6(sK0,X0,X1),sK2)
| sK6(sK0,X0,X1) = sK7(sK0,X0,X1)
| ~ member(sK7(sK0,X0,X1),sK2)
| ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK8(sK0,X0,X1),X2)
| ~ maps(sK1,X2,sK4)
| ~ member(sK8(sK0,X0,X1),X3)
| ~ maps(sK1,X3,sK4)
| injective(sK0,X0,X1)
| injective(sK0,X0,X1) ),
inference(resolution,[],[f138,f60]) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( ~ member(sK6(sK0,X0,X1),sK2)
| sK6(sK0,X0,X1) = sK7(sK0,X0,X1)
| ~ member(sK7(sK0,X0,X1),sK2)
| ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK8(sK0,X0,X1),X2)
| ~ maps(sK1,X2,sK4)
| ~ member(sK8(sK0,X0,X1),X3)
| ~ maps(sK1,X3,sK4)
| injective(sK0,X0,X1) ),
inference(duplicate_literal_removal,[],[f207]) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK7(sK0,X0,X1),sK2)
| ~ member(sK6(sK0,X0,X1),sK2)
| ~ member(sK8(sK0,X0,X1),X2)
| ~ maps(sK1,X2,sK4)
| ~ member(sK8(sK0,X0,X1),X3)
| ~ maps(sK1,X3,sK4)
| injective(sK0,X0,X1) ),
inference(forward_subsumption_resolution,[],[f209,f62]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK7(sK0,X0,X1),sK2)
| ~ member(sK6(sK0,X0,X1),sK2)
| ~ member(sK8(sK0,X0,X1),X2)
| ~ maps(sK1,X2,sK4)
| ~ maps(sK1,sK3,sK4)
| injective(sK0,X0,X1) ),
inference(factoring,[],[f211]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK7(sK0,X0,X1),sK2)
| ~ member(sK6(sK0,X0,X1),sK2)
| ~ member(sK8(sK0,X0,X1),X2)
| ~ maps(sK1,X2,sK4)
| injective(sK0,X0,X1) ),
inference(forward_subsumption_resolution,[],[f214,f50]) ).
fof(f220,plain,
! [X0,X1] :
( ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK7(sK0,X0,X1),sK2)
| ~ member(sK6(sK0,X0,X1),sK2)
| ~ maps(sK1,sK3,sK4)
| injective(sK0,X0,X1) ),
inference(factoring,[],[f216]) ).
fof(f222,plain,
! [X0,X1] :
( ~ member(sK8(sK0,X0,X1),sK3)
| ~ member(sK7(sK0,X0,X1),sK2)
| ~ member(sK6(sK0,X0,X1),sK2)
| injective(sK0,X0,X1) ),
inference(forward_subsumption_resolution,[],[f220,f50]) ).
fof(f231,plain,
! [X0] :
( ~ member(sK7(sK0,X0,sK3),sK2)
| ~ member(sK6(sK0,X0,sK3),sK2)
| injective(sK0,X0,sK3)
| injective(sK0,X0,sK3) ),
inference(resolution,[],[f222,f57]) ).
fof(f232,plain,
! [X0] :
( ~ member(sK7(sK0,X0,sK3),sK2)
| ~ member(sK6(sK0,X0,sK3),sK2)
| injective(sK0,X0,sK3) ),
inference(duplicate_literal_removal,[],[f231]) ).
fof(f233,plain,
( ~ member(sK6(sK0,sK2,sK3),sK2)
| injective(sK0,sK2,sK3)
| injective(sK0,sK2,sK3) ),
inference(resolution,[],[f232,f58]) ).
fof(f234,plain,
( ~ member(sK6(sK0,sK2,sK3),sK2)
| injective(sK0,sK2,sK3) ),
inference(duplicate_literal_removal,[],[f233]) ).
fof(f235,plain,
injective(sK0,sK2,sK3),
inference(forward_subsumption_resolution,[],[f234,f59]) ).
fof(f236,plain,
$false,
inference(forward_subsumption_resolution,[],[f235,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET721+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:38:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 1.72/1.30 % (3610830)Detected formulas, will run a generic FOF schedule.
% 1.72/1.30 % (3610837)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=2402983229:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.72/1.30 % (3610838)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4120366228:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.72/1.30 % (3610839)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=256417482:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.72/1.30 % (3610836)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=3630366864:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.72/1.30 % (3610840)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3787325653:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.72/1.30 % (3610835)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=3492335390:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.72/1.30 % (3610841)dis-21_1_sil=8000:lcm=predicate:random_seed=2342237820: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)
% 1.72/1.30 % (3610839)First to succeed.
% 1.72/1.30 % (3610838)Also succeeded, but the first one will report.
% 1.72/1.30 % (3610841)Also succeeded, but the first one will report.
% 1.72/1.30 % (3610839)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3610830"
% 1.72/1.30 % (3610840)Instruction limit reached!
% 1.72/1.30 % (3610840)------------------------------
% 1.72/1.30 % (3610840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.72/1.30 % (3610840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/1.30 % (3610840)CaDiCaL version: 2.1.3
% 1.72/1.30 % (3610840)Termination reason: Instruction limit
% 1.72/1.30 % (3610840)Termination phase: Saturation
% 1.72/1.30 % (3610840)Time elapsed: 0.097 s
% 1.72/1.30 % (3610840)Peak memory usage: 89 MB
% 1.72/1.30 % (3610840)Instructions burned: 139 (million)
% 1.72/1.30 % (3610839)Refutation found. Thanks to Tanya!
% 1.72/1.30 % SZS status Theorem for theBenchmark
% 1.72/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.49 % (3610839)------------------------------
% 3.71/1.49 % (3610839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.49 % (3610839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.49 % (3610839)CaDiCaL version: 2.1.3
% 3.71/1.49 % (3610839)Termination reason: Refutation
% 3.71/1.49 % (3610839)Time elapsed: 0.012 s
% 3.71/1.49 % (3610839)Peak memory usage: 88 MB
% 3.71/1.49 % (3610839)Instructions burned: 17 (million)
% 3.71/1.49 % (3610839)------------------------------
% 3.71/1.49 % (3610839)------------------------------
% 3.71/1.49 % (3610830)Success in time 0.447 s
% 3.71/1.49 % Vampire exiting
%------------------------------------------------------------------------------