%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET718+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 : n009.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 6.89s 2.00s
% Output : Refutation 8.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 130 ( 16 unt; 3 def)
% Number of atoms : 533 ( 53 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 683 ( 280 ~; 315 |; 71 &)
% ( 11 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-5 aty)
% Number of variables : 320 ( 0 sgn 293 !; 27 ?)
% 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(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(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(f19,axiom,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
<=> ( injective(X0,X1,X2)
& surjective(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X2,X3)
& maps(X1,X3,X4)
& one_to_one(X0,X2,X3)
& one_to_one(X1,X3,X4) )
=> one_to_one(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII09) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X2,X3)
& maps(X1,X3,X4)
& one_to_one(X0,X2,X3)
& one_to_one(X1,X3,X4) )
=> one_to_one(compose_function(X1,X0,X2,X3,X4),X2,X4) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f37,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(f38,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,[],[f37]) ).
fof(f39,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(f40,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,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) )
| ~ member(X3,X2) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f44,plain,
? [X0,X1,X2,X3,X4] :
( ~ one_to_one(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X0,X2,X3)
& maps(X1,X3,X4)
& one_to_one(X0,X2,X3)
& one_to_one(X1,X3,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f45,plain,
? [X0,X1,X2,X3,X4] :
( ~ one_to_one(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X0,X2,X3)
& maps(X1,X3,X4)
& one_to_one(X0,X2,X3)
& one_to_one(X1,X3,X4) ),
inference(flattening,[],[f44]) ).
fof(f66,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,[],[f38]) ).
fof(f67,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,[],[f66]) ).
fof(f68,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(sK4(X0,X1,X3,X5,X6),X3)
& apply(X1,X5,sK4(X0,X1,X3,X5,X6))
& apply(X0,sK4(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,[sK4]),skolemize(X8,sK4(X0,X1,X3,X5,X6))],[f67]) ).
fof(f69,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,[],[f40]) ).
fof(f70,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,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
| ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
& apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
& apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
& member(sK5(X0,X1,X2),X1)
& member(sK6(X0,X1,X2),X1)
& member(sK7(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,[sK5,sK6,sK7]),skolemize(X3,sK5(X0,X1,X2)),skolemize(X4,sK6(X0,X1,X2)),skolemize(X5,sK7(X0,X1,X2))],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) )
& member(X3,X2) ) )
& ( ! [X3] :
( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) )
| ~ member(X3,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) )
& member(X3,X2) ) )
& ( ! [X5] :
( ? [X6] :
( member(X6,X1)
& apply(X0,X6,X5) )
| ~ member(X5,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,sK8(X0,X1,X2)) )
& member(sK8(X0,X1,X2),X2) ) )
& ( ! [X5] :
( ( member(sK9(X0,X1,X5),X1)
& apply(X0,sK9(X0,X1,X5),X5) )
| ~ member(X5,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X3,sK8(X0,X1,X2)),skolemize(X6,sK9(X0,X1,X5))],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) )
& ( ( injective(X0,X1,X2)
& surjective(X0,X1,X2) )
| ~ one_to_one(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) )
& ( ( injective(X0,X1,X2)
& surjective(X0,X1,X2) )
| ~ one_to_one(X0,X1,X2) ) ),
inference(flattening,[],[f75]) ).
fof(f92,plain,
( ~ one_to_one(compose_function(sK15,sK14,sK16,sK17,sK18),sK16,sK18)
& maps(sK14,sK16,sK17)
& maps(sK15,sK17,sK18)
& one_to_one(sK14,sK16,sK17)
& one_to_one(sK15,sK17,sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16),skolemize(X3,sK17),skolemize(X4,sK18)],[f45]) ).
fof(f122,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK4(X0,X1,X3,X5,X6),X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f68]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,X5,sK4(X0,X1,X3,X5,X6))
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f68]) ).
fof(f124,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK4(X0,X1,X3,X5,X6),X3)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f68]) ).
fof(f125,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ apply(X1,X5,X7)
| ~ member(X7,X3)
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ apply(X0,X7,X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f68]) ).
fof(f126,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,[],[f71]) ).
fof(f127,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f128,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f129,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f130,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f131,plain,
! [X2,X0,X1] :
( apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f132,plain,
! [X2,X0,X1] :
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f133,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| apply(X0,sK9(X0,X1,X5),X5) ),
inference(cnf_transformation,[],[f74]) ).
fof(f134,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| member(sK9(X0,X1,X5),X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f135,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f136,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK8(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f156,plain,
one_to_one(sK15,sK17,sK18),
inference(cnf_transformation,[],[f92]) ).
fof(f157,plain,
one_to_one(sK14,sK16,sK17),
inference(cnf_transformation,[],[f92]) ).
fof(f160,plain,
~ one_to_one(compose_function(sK15,sK14,sK16,sK17,sK18),sK16,sK18),
inference(cnf_transformation,[],[f92]) ).
fof(f164,definition,
sF19 = compose_function(sK15,sK14,sK16,sK17,sK18),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f165,plain,
compose_function(sK15,sK14,sK16,sK17,sK18) = sF19,
inference(reorient_equations,[],[f164]) ).
fof(f166,plain,
~ one_to_one(sF19,sK16,sK18),
inference(definition_folding,[],[f160,f165]) ).
fof(f167,plain,
injective(sK14,sK16,sK17),
inference(resolution,[],[f157,f138]) ).
fof(f168,plain,
surjective(sK14,sK16,sK17),
inference(resolution,[],[f157,f137]) ).
fof(f169,plain,
injective(sK15,sK17,sK18),
inference(resolution,[],[f156,f138]) ).
fof(f170,plain,
surjective(sK15,sK17,sK18),
inference(resolution,[],[f156,f137]) ).
fof(f173,plain,
! [X0,X1] :
( member(sK4(sK15,sK14,sK17,X0,X1),sK17)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK18) ),
inference(superposition,[],[f124,f165]) ).
fof(f174,plain,
! [X0,X1] :
( apply(sK14,X0,sK4(sK15,sK14,sK17,X0,X1))
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK18) ),
inference(superposition,[],[f123,f165]) ).
fof(f175,plain,
! [X0,X1] :
( apply(sK15,sK4(sK15,sK14,sK17,X0,X1),X1)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK18) ),
inference(superposition,[],[f122,f165]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ apply(sK14,X2,X1)
| ~ apply(sK14,X0,X1)
| ~ member(X0,sK16)
| ~ member(X2,sK16)
| ~ member(X1,sK17)
| X0 = X2 ),
inference(resolution,[],[f126,f167]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ apply(sK15,X2,X1)
| ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(X2,sK17)
| ~ member(X1,sK18)
| X0 = X2 ),
inference(resolution,[],[f126,f169]) ).
fof(f191,plain,
! [X2,X0,X1] :
( ~ apply(sK14,X0,sK4(sK15,sK14,sK17,X1,X2))
| ~ member(X0,sK16)
| ~ member(X1,sK16)
| ~ member(sK4(sK15,sK14,sK17,X1,X2),sK17)
| X0 = X1
| ~ apply(sF19,X1,X2)
| ~ member(X1,sK16)
| ~ member(X2,sK18) ),
inference(resolution,[],[f189,f174]) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ apply(sK14,X0,sK4(sK15,sK14,sK17,X1,X2))
| ~ member(X0,sK16)
| ~ member(X1,sK16)
| ~ member(sK4(sK15,sK14,sK17,X1,X2),sK17)
| X0 = X1
| ~ apply(sF19,X1,X2)
| ~ member(X2,sK18) ),
inference(duplicate_literal_removal,[],[f191]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ apply(sK14,X0,sK4(sK15,sK14,sK17,X1,X2))
| ~ member(X0,sK16)
| ~ member(X1,sK16)
| X0 = X1
| ~ apply(sF19,X1,X2)
| ~ member(X2,sK18) ),
inference(forward_subsumption_resolution,[],[f194,f173]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(sK4(sK15,sK14,sK17,X2,X1),sK17)
| ~ member(X1,sK18)
| sK4(sK15,sK14,sK17,X2,X1) = X0
| ~ apply(sF19,X2,X1)
| ~ member(X2,sK16)
| ~ member(X1,sK18) ),
inference(resolution,[],[f190,f175]) ).
fof(f199,plain,
! [X2,X0,X1] :
( ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(sK4(sK15,sK14,sK17,X2,X1),sK17)
| ~ member(X1,sK18)
| sK4(sK15,sK14,sK17,X2,X1) = X0
| ~ apply(sF19,X2,X1)
| ~ member(X2,sK16) ),
inference(duplicate_literal_removal,[],[f196]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ apply(sF19,X2,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK18)
| sK4(sK15,sK14,sK17,X2,X1) = X0
| ~ apply(sK15,X0,X1)
| ~ member(X2,sK16) ),
inference(forward_subsumption_resolution,[],[f199,f173]) ).
fof(f203,plain,
! [X0] :
( apply(sK14,sK9(sK14,sK16,X0),X0)
| ~ member(X0,sK17) ),
inference(resolution,[],[f133,f168]) ).
fof(f204,plain,
! [X0] :
( apply(sK15,sK9(sK15,sK17,X0),X0)
| ~ member(X0,sK18) ),
inference(resolution,[],[f133,f170]) ).
fof(f211,plain,
! [X0,X1] :
( ~ member(sK4(sK15,sK14,sK17,X0,X1),sK17)
| ~ member(sK9(sK14,sK16,sK4(sK15,sK14,sK17,X0,X1)),sK16)
| ~ member(X0,sK16)
| sK9(sK14,sK16,sK4(sK15,sK14,sK17,X0,X1)) = X0
| ~ apply(sF19,X0,X1)
| ~ member(X1,sK18) ),
inference(resolution,[],[f203,f195]) ).
fof(f213,plain,
! [X2,X3,X0,X1,X4,X5] :
( apply(compose_function(X2,sK14,X3,X1,X4),sK9(sK14,sK16,X0),X5)
| ~ member(X0,X1)
| ~ member(X0,sK17)
| ~ apply(X2,X0,X5)
| ~ member(sK9(sK14,sK16,X0),X3)
| ~ member(X5,X4) ),
inference(resolution,[],[f203,f125]) ).
fof(f216,plain,
! [X0,X1] :
( ~ member(sK9(sK14,sK16,sK4(sK15,sK14,sK17,X0,X1)),sK16)
| ~ member(X0,sK16)
| sK9(sK14,sK16,sK4(sK15,sK14,sK17,X0,X1)) = X0
| ~ apply(sF19,X0,X1)
| ~ member(X1,sK18) ),
inference(forward_subsumption_resolution,[],[f211,f173]) ).
fof(f244,plain,
! [X2,X0,X1] :
( ~ apply(sK15,X2,sK7(sF19,X0,X1))
| ~ member(X2,sK17)
| ~ member(sK7(sF19,X0,X1),sK18)
| sK4(sK15,sK14,sK17,sK6(sF19,X0,X1),sK7(sF19,X0,X1)) = X2
| injective(sF19,X0,X1)
| ~ member(sK6(sF19,X0,X1),sK16) ),
inference(resolution,[],[f130,f200]) ).
fof(f260,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK15,sK14,sK17,X0,sK7(sF19,X1,X2)),sK17)
| ~ member(sK7(sF19,X1,X2),sK18)
| sK4(sK15,sK14,sK17,X0,sK7(sF19,X1,X2)) = sK4(sK15,sK14,sK17,sK6(sF19,X1,X2),sK7(sF19,X1,X2))
| injective(sF19,X1,X2)
| ~ member(sK6(sF19,X1,X2),sK16)
| ~ apply(sF19,X0,sK7(sF19,X1,X2))
| ~ member(X0,sK16)
| ~ member(sK7(sF19,X1,X2),sK18) ),
inference(resolution,[],[f244,f175]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK15,sK14,sK17,X0,sK7(sF19,X1,X2)),sK17)
| ~ member(sK7(sF19,X1,X2),sK18)
| sK4(sK15,sK14,sK17,X0,sK7(sF19,X1,X2)) = sK4(sK15,sK14,sK17,sK6(sF19,X1,X2),sK7(sF19,X1,X2))
| injective(sF19,X1,X2)
| ~ member(sK6(sF19,X1,X2),sK16)
| ~ apply(sF19,X0,sK7(sF19,X1,X2))
| ~ member(X0,sK16) ),
inference(duplicate_literal_removal,[],[f260]) ).
fof(f264,plain,
! [X2,X0,X1] :
( ~ apply(sF19,X0,sK7(sF19,X1,X2))
| sK4(sK15,sK14,sK17,X0,sK7(sF19,X1,X2)) = sK4(sK15,sK14,sK17,sK6(sF19,X1,X2),sK7(sF19,X1,X2))
| injective(sF19,X1,X2)
| ~ member(sK6(sF19,X1,X2),sK16)
| ~ member(sK7(sF19,X1,X2),sK18)
| ~ member(X0,sK16) ),
inference(forward_subsumption_resolution,[],[f263,f173]) ).
fof(f266,plain,
! [X0,X1] :
( sK4(sK15,sK14,sK17,sK6(sF19,X0,X1),sK7(sF19,X0,X1)) = sK4(sK15,sK14,sK17,sK5(sF19,X0,X1),sK7(sF19,X0,X1))
| injective(sF19,X0,X1)
| ~ member(sK6(sF19,X0,X1),sK16)
| ~ member(sK7(sF19,X0,X1),sK18)
| ~ member(sK5(sF19,X0,X1),sK16)
| injective(sF19,X0,X1) ),
inference(resolution,[],[f264,f131]) ).
fof(f267,plain,
! [X0,X1] :
( ~ member(sK7(sF19,X0,X1),sK18)
| injective(sF19,X0,X1)
| ~ member(sK6(sF19,X0,X1),sK16)
| sK4(sK15,sK14,sK17,sK6(sF19,X0,X1),sK7(sF19,X0,X1)) = sK4(sK15,sK14,sK17,sK5(sF19,X0,X1),sK7(sF19,X0,X1))
| ~ member(sK5(sF19,X0,X1),sK16) ),
inference(duplicate_literal_removal,[],[f266]) ).
fof(f269,plain,
! [X0] :
( injective(sF19,X0,sK18)
| ~ member(sK6(sF19,X0,sK18),sK16)
| sK4(sK15,sK14,sK17,sK6(sF19,X0,sK18),sK7(sF19,X0,sK18)) = sK4(sK15,sK14,sK17,sK5(sF19,X0,sK18),sK7(sF19,X0,sK18))
| ~ member(sK5(sF19,X0,sK18),sK16)
| injective(sF19,X0,sK18) ),
inference(resolution,[],[f267,f127]) ).
fof(f270,plain,
! [X0] :
( ~ member(sK6(sF19,X0,sK18),sK16)
| injective(sF19,X0,sK18)
| sK4(sK15,sK14,sK17,sK6(sF19,X0,sK18),sK7(sF19,X0,sK18)) = sK4(sK15,sK14,sK17,sK5(sF19,X0,sK18),sK7(sF19,X0,sK18))
| ~ member(sK5(sF19,X0,sK18),sK16) ),
inference(duplicate_literal_removal,[],[f269]) ).
fof(f271,plain,
( injective(sF19,sK16,sK18)
| sK4(sK15,sK14,sK17,sK6(sF19,sK16,sK18),sK7(sF19,sK16,sK18)) = sK4(sK15,sK14,sK17,sK5(sF19,sK16,sK18),sK7(sF19,sK16,sK18))
| ~ member(sK5(sF19,sK16,sK18),sK16)
| injective(sF19,sK16,sK18) ),
inference(resolution,[],[f270,f128]) ).
fof(f272,plain,
( injective(sF19,sK16,sK18)
| sK4(sK15,sK14,sK17,sK6(sF19,sK16,sK18),sK7(sF19,sK16,sK18)) = sK4(sK15,sK14,sK17,sK5(sF19,sK16,sK18),sK7(sF19,sK16,sK18))
| ~ member(sK5(sF19,sK16,sK18),sK16) ),
inference(duplicate_literal_removal,[],[f271]) ).
fof(f273,plain,
( injective(sF19,sK16,sK18)
| sK4(sK15,sK14,sK17,sK6(sF19,sK16,sK18),sK7(sF19,sK16,sK18)) = sK4(sK15,sK14,sK17,sK5(sF19,sK16,sK18),sK7(sF19,sK16,sK18)) ),
inference(forward_subsumption_resolution,[],[f272,f129]) ).
fof(f275,definition,
( spl20_1
<=> sK4(sK15,sK14,sK17,sK6(sF19,sK16,sK18),sK7(sF19,sK16,sK18)) = sK4(sK15,sK14,sK17,sK5(sF19,sK16,sK18),sK7(sF19,sK16,sK18)) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f277,plain,
( sK4(sK15,sK14,sK17,sK6(sF19,sK16,sK18),sK7(sF19,sK16,sK18)) = sK4(sK15,sK14,sK17,sK5(sF19,sK16,sK18),sK7(sF19,sK16,sK18))
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f279,definition,
( spl20_2
<=> injective(sF19,sK16,sK18) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f280,plain,
( ~ injective(sF19,sK16,sK18)
| spl20_2 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f281,plain,
( injective(sF19,sK16,sK18)
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f282,plain,
( spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f273,f279,f275]) ).
fof(f383,plain,
! [X0,X1] :
( apply(sF19,sK9(sK14,sK16,X0),X1)
| ~ member(X0,sK17)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1)
| ~ member(sK9(sK14,sK16,X0),sK16)
| ~ member(X1,sK18) ),
inference(superposition,[],[f213,f165]) ).
fof(f384,plain,
! [X0,X1] :
( apply(sF19,sK9(sK14,sK16,X0),X1)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1)
| ~ member(sK9(sK14,sK16,X0),sK16)
| ~ member(X1,sK18) ),
inference(duplicate_literal_removal,[],[f383]) ).
fof(f397,plain,
! [X2,X0,X1] :
( ~ apply(sK15,X0,sK8(sF19,X1,X2))
| ~ member(X0,sK17)
| ~ member(sK9(sK14,sK16,X0),sK16)
| ~ member(sK8(sF19,X1,X2),sK18)
| ~ member(sK9(sK14,sK16,X0),X1)
| surjective(sF19,X1,X2) ),
inference(resolution,[],[f384,f136]) ).
fof(f406,plain,
! [X0,X1] :
( ~ member(sK9(sK15,sK17,sK8(sF19,X0,X1)),sK17)
| ~ member(sK9(sK14,sK16,sK9(sK15,sK17,sK8(sF19,X0,X1))),sK16)
| ~ member(sK8(sF19,X0,X1),sK18)
| ~ member(sK9(sK14,sK16,sK9(sK15,sK17,sK8(sF19,X0,X1))),X0)
| surjective(sF19,X0,X1)
| ~ member(sK8(sF19,X0,X1),sK18) ),
inference(resolution,[],[f397,f204]) ).
fof(f407,plain,
! [X0,X1] :
( ~ member(sK9(sK14,sK16,sK9(sK15,sK17,sK8(sF19,X0,X1))),sK16)
| ~ member(sK9(sK15,sK17,sK8(sF19,X0,X1)),sK17)
| ~ member(sK8(sF19,X0,X1),sK18)
| ~ member(sK9(sK14,sK16,sK9(sK15,sK17,sK8(sF19,X0,X1))),X0)
| surjective(sF19,X0,X1) ),
inference(duplicate_literal_removal,[],[f406]) ).
fof(f416,plain,
! [X0] :
( member(sK9(sK14,sK16,X0),sK16)
| ~ member(X0,sK17) ),
inference(resolution,[],[f134,f168]) ).
fof(f417,plain,
! [X0] :
( member(sK9(sK15,sK17,X0),sK17)
| ~ member(X0,sK18) ),
inference(resolution,[],[f134,f170]) ).
fof(f421,plain,
! [X0,X1] :
( ~ member(sK4(sK15,sK14,sK17,X0,X1),sK17)
| ~ member(X0,sK16)
| sK9(sK14,sK16,sK4(sK15,sK14,sK17,X0,X1)) = X0
| ~ apply(sF19,X0,X1)
| ~ member(X1,sK18) ),
inference(resolution,[],[f416,f216]) ).
fof(f426,plain,
! [X0,X1] :
( ~ apply(sF19,X0,X1)
| sK9(sK14,sK16,sK4(sK15,sK14,sK17,X0,X1)) = X0
| ~ member(X0,sK16)
| ~ member(X1,sK18) ),
inference(forward_subsumption_resolution,[],[f421,f173]) ).
fof(f450,plain,
! [X0,X1] :
( ~ member(sK7(sF19,X0,X1),sK18)
| ~ member(sK6(sF19,X0,X1),sK16)
| sK6(sF19,X0,X1) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK6(sF19,X0,X1),sK7(sF19,X0,X1)))
| injective(sF19,X0,X1) ),
inference(resolution,[],[f426,f130]) ).
fof(f451,plain,
! [X0,X1] :
( ~ member(sK7(sF19,X0,X1),sK18)
| ~ member(sK5(sF19,X0,X1),sK16)
| sK5(sF19,X0,X1) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK5(sF19,X0,X1),sK7(sF19,X0,X1)))
| injective(sF19,X0,X1) ),
inference(resolution,[],[f426,f131]) ).
fof(f491,plain,
! [X0] :
( ~ member(sK6(sF19,X0,sK18),sK16)
| sK6(sF19,X0,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK6(sF19,X0,sK18),sK7(sF19,X0,sK18)))
| injective(sF19,X0,sK18)
| injective(sF19,X0,sK18) ),
inference(resolution,[],[f450,f127]) ).
fof(f492,plain,
! [X0] :
( ~ member(sK6(sF19,X0,sK18),sK16)
| sK6(sF19,X0,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK6(sF19,X0,sK18),sK7(sF19,X0,sK18)))
| injective(sF19,X0,sK18) ),
inference(duplicate_literal_removal,[],[f491]) ).
fof(f493,plain,
( sK6(sF19,sK16,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK6(sF19,sK16,sK18),sK7(sF19,sK16,sK18)))
| injective(sF19,sK16,sK18)
| injective(sF19,sK16,sK18) ),
inference(resolution,[],[f492,f128]) ).
fof(f494,plain,
( sK6(sF19,sK16,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK6(sF19,sK16,sK18),sK7(sF19,sK16,sK18)))
| injective(sF19,sK16,sK18) ),
inference(duplicate_literal_removal,[],[f493]) ).
fof(f495,plain,
! [X0] :
( ~ member(sK5(sF19,X0,sK18),sK16)
| sK5(sF19,X0,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK5(sF19,X0,sK18),sK7(sF19,X0,sK18)))
| injective(sF19,X0,sK18)
| injective(sF19,X0,sK18) ),
inference(resolution,[],[f451,f127]) ).
fof(f496,plain,
! [X0] :
( ~ member(sK5(sF19,X0,sK18),sK16)
| sK5(sF19,X0,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK5(sF19,X0,sK18),sK7(sF19,X0,sK18)))
| injective(sF19,X0,sK18) ),
inference(duplicate_literal_removal,[],[f495]) ).
fof(f497,plain,
( sK5(sF19,sK16,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK5(sF19,sK16,sK18),sK7(sF19,sK16,sK18)))
| injective(sF19,sK16,sK18)
| injective(sF19,sK16,sK18) ),
inference(resolution,[],[f496,f129]) ).
fof(f498,plain,
( sK5(sF19,sK16,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK5(sF19,sK16,sK18),sK7(sF19,sK16,sK18)))
| injective(sF19,sK16,sK18) ),
inference(duplicate_literal_removal,[],[f497]) ).
fof(f534,plain,
! [X0,X1] :
( ~ member(sK9(sK15,sK17,sK8(sF19,X0,X1)),sK17)
| ~ member(sK8(sF19,X0,X1),sK18)
| ~ member(sK9(sK14,sK16,sK9(sK15,sK17,sK8(sF19,X0,X1))),X0)
| surjective(sF19,X0,X1)
| ~ member(sK9(sK15,sK17,sK8(sF19,X0,X1)),sK17) ),
inference(resolution,[],[f407,f416]) ).
fof(f535,plain,
! [X0,X1] :
( ~ member(sK9(sK15,sK17,sK8(sF19,X0,X1)),sK17)
| ~ member(sK8(sF19,X0,X1),sK18)
| ~ member(sK9(sK14,sK16,sK9(sK15,sK17,sK8(sF19,X0,X1))),X0)
| surjective(sF19,X0,X1) ),
inference(duplicate_literal_removal,[],[f534]) ).
fof(f536,plain,
! [X0,X1] :
( ~ member(sK9(sK14,sK16,sK9(sK15,sK17,sK8(sF19,X0,X1))),X0)
| ~ member(sK8(sF19,X0,X1),sK18)
| surjective(sF19,X0,X1) ),
inference(forward_subsumption_resolution,[],[f535,f417]) ).
fof(f537,plain,
! [X0] :
( ~ member(sK8(sF19,sK16,X0),sK18)
| surjective(sF19,sK16,X0)
| ~ member(sK9(sK15,sK17,sK8(sF19,sK16,X0)),sK17) ),
inference(resolution,[],[f536,f416]) ).
fof(f538,plain,
! [X0] :
( ~ member(sK8(sF19,sK16,X0),sK18)
| surjective(sF19,sK16,X0) ),
inference(forward_subsumption_resolution,[],[f537,f417]) ).
fof(f539,plain,
( surjective(sF19,sK16,sK18)
| surjective(sF19,sK16,sK18) ),
inference(resolution,[],[f538,f135]) ).
fof(f540,plain,
surjective(sF19,sK16,sK18),
inference(duplicate_literal_removal,[],[f539]) ).
fof(f543,plain,
( ~ injective(sF19,sK16,sK18)
| one_to_one(sF19,sK16,sK18) ),
inference(resolution,[],[f540,f139]) ).
fof(f544,plain,
( one_to_one(sF19,sK16,sK18)
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f543,f281]) ).
fof(f545,plain,
( $false
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f544,f166]) ).
fof(f546,plain,
~ spl20_2,
inference(avatar_contradiction_clause,[],[f545]) ).
fof(f551,plain,
( sK6(sF19,sK16,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK6(sF19,sK16,sK18),sK7(sF19,sK16,sK18)))
| spl20_2 ),
inference(forward_subsumption_resolution,[],[f494,f280]) ).
fof(f552,plain,
( sK5(sF19,sK16,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK5(sF19,sK16,sK18),sK7(sF19,sK16,sK18)))
| spl20_2 ),
inference(forward_subsumption_resolution,[],[f498,f280]) ).
fof(f564,plain,
( sK6(sF19,sK16,sK18) = sK9(sK14,sK16,sK4(sK15,sK14,sK17,sK5(sF19,sK16,sK18),sK7(sF19,sK16,sK18)))
| ~ spl20_1
| spl20_2 ),
inference(forward_demodulation,[],[f551,f277]) ).
fof(f574,plain,
( sK6(sF19,sK16,sK18) = sK5(sF19,sK16,sK18)
| ~ spl20_1
| spl20_2 ),
inference(forward_demodulation,[],[f564,f552]) ).
fof(f581,plain,
( sK5(sF19,sK16,sK18) != sK5(sF19,sK16,sK18)
| injective(sF19,sK16,sK18)
| ~ spl20_1
| spl20_2 ),
inference(superposition,[],[f132,f574]) ).
fof(f583,plain,
( injective(sF19,sK16,sK18)
| ~ spl20_1
| spl20_2 ),
inference(trivial_inequality_removal,[],[f581]) ).
fof(f584,plain,
( $false
| ~ spl20_1
| spl20_2 ),
inference(forward_subsumption_resolution,[],[f583,f280]) ).
fof(f585,plain,
( ~ spl20_1
| spl20_2 ),
inference(avatar_contradiction_clause,[],[f584]) ).
cnf(s1,plain,
( spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f282]) ).
cnf(s2,plain,
~ spl20_2,
inference(sat_conversion,[],[f546]) ).
cnf(s5,plain,
( ~ spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f585]) ).
cnf(s6,plain,
~ spl20_1,
inference(rat,[],[s5,s2]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s2,s6]) ).
fof(f586,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET718+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 02:37:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 6.89/2.00 % (2614314)Detected formulas, will run a generic FOF schedule.
% 6.89/2.00 % (2614323)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2220980834:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.89/2.00 % (2614323)Instruction limit reached!
% 6.89/2.00 % (2614323)------------------------------
% 6.89/2.00 % (2614323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614323)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614323)Termination reason: Instruction limit
% 6.89/2.00 % (2614323)Termination phase: Saturation
% 6.89/2.00 % (2614323)Time elapsed: 0.035 s
% 6.89/2.00 % (2614323)Peak memory usage: 88 MB
% 6.89/2.00 % (2614323)Instructions burned: 130 (million)
% 6.89/2.00 % (2614324)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1033283102:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.89/2.00 % (2614322)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=891710706:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.89/2.00 % (2614321)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=3851309950:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.89/2.00 % (2614320)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=370842687:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.89/2.00 % (2614319)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=2433957454:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.89/2.00 % (2614322)Refutation not found, incomplete strategy
% 6.89/2.00 % (2614322)------------------------------
% 6.89/2.00 % (2614322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614322)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614322)Termination reason: Refutation not found, incomplete strategy
% 6.89/2.00 % (2614322)Time elapsed: 0.003 s
% 6.89/2.00 % (2614322)Peak memory usage: 88 MB
% 6.89/2.00 % (2614322)Instructions burned: 3 (million)
% 6.89/2.00 % (2614325)dis-21_1_sil=8000:lcm=predicate:random_seed=2992430776: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)
% 6.89/2.00 % (2614324)Instruction limit reached!
% 6.89/2.00 % (2614324)------------------------------
% 6.89/2.00 % (2614324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614324)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614324)Termination reason: Instruction limit
% 6.89/2.00 % (2614324)Termination phase: Saturation
% 6.89/2.00 % (2614324)Time elapsed: 0.049 s
% 6.89/2.00 % (2614324)Peak memory usage: 89 MB
% 6.89/2.00 % (2614324)Instructions burned: 141 (million)
% 6.89/2.00 % (2614325)Instruction limit reached!
% 6.89/2.00 % (2614325)------------------------------
% 6.89/2.00 % (2614325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614325)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614325)Termination reason: Instruction limit
% 6.89/2.00 % (2614325)Termination phase: Saturation
% 6.89/2.00 % (2614325)Time elapsed: 0.058 s
% 6.89/2.00 % (2614325)Peak memory usage: 89 MB
% 6.89/2.00 % (2614325)Instructions burned: 131 (million)
% 6.89/2.00 % (2614327)lrs+10_1_sil=8000:sp=occurrence:random_seed=1388940143:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.89/2.00 % (2614334)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3920469867:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.89/2.00 % (2614334)Refutation not found, incomplete strategy
% 6.89/2.00 % (2614334)------------------------------
% 6.89/2.00 % (2614334)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614334)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614334)Termination reason: Refutation not found, incomplete strategy
% 6.89/2.00 % (2614334)Time elapsed: 0.001 s
% 6.89/2.00 % (2614334)Peak memory usage: 88 MB
% 6.89/2.00 % (2614334)Instructions burned: 2 (million)
% 6.89/2.00 % (2614335)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4283372492:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.89/2.00 % (2614322)------------------------------
% 6.89/2.00 % (2614322)------------------------------
% 6.89/2.00 % (2614327)Instruction limit reached!
% 6.89/2.00 % (2614327)------------------------------
% 6.89/2.00 % (2614327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614327)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614327)Termination reason: Instruction limit
% 6.89/2.00 % (2614327)Termination phase: Saturation
% 6.89/2.00 % (2614327)Time elapsed: 0.158 s
% 6.89/2.00 % (2614327)Peak memory usage: 92 MB
% 6.89/2.00 % (2614327)Instructions burned: 286 (million)
% 6.89/2.00 % (2614334)------------------------------
% 6.89/2.00 % (2614334)------------------------------
% 6.89/2.00 % (2614339)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=2749937120:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.89/2.00 % (2614335)Instruction limit reached!
% 6.89/2.00 % (2614335)------------------------------
% 6.89/2.00 % (2614335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614335)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614335)Termination reason: Instruction limit
% 6.89/2.00 % (2614335)Termination phase: Saturation
% 6.89/2.00 % (2614335)Time elapsed: 0.167 s
% 6.89/2.00 % (2614335)Peak memory usage: 91 MB
% 6.89/2.00 % (2614335)Instructions burned: 326 (million)
% 6.89/2.00 % (2614340)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3953656194:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.89/2.00 % (2614341)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=277923975:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.89/2.00 % (2614339)Instruction limit reached!
% 6.89/2.00 % (2614339)------------------------------
% 6.89/2.00 % (2614339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614339)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614339)Termination reason: Instruction limit
% 6.89/2.00 % (2614339)Termination phase: Saturation
% 6.89/2.00 % (2614339)Time elapsed: 0.131 s
% 6.89/2.00 % (2614339)Peak memory usage: 92 MB
% 6.89/2.00 % (2614339)Instructions burned: 249 (million)
% 6.89/2.00 % (2614343)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=840031560:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.89/2.00 % (2614340)Instruction limit reached!
% 6.89/2.00 % (2614340)------------------------------
% 6.89/2.00 % (2614340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614340)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614340)Termination reason: Instruction limit
% 6.89/2.00 % (2614340)Termination phase: Saturation
% 6.89/2.00 % (2614340)Time elapsed: 0.162 s
% 6.89/2.00 % (2614340)Peak memory usage: 88 MB
% 6.89/2.00 % (2614340)Instructions burned: 294 (million)
% 6.89/2.00 % (2614343)Instruction limit reached!
% 6.89/2.00 % (2614343)------------------------------
% 6.89/2.00 % (2614343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614343)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614343)Termination reason: Instruction limit
% 6.89/2.00 % (2614343)Termination phase: Saturation
% 6.89/2.00 % (2614343)Time elapsed: 0.077 s
% 6.89/2.00 % (2614343)Peak memory usage: 90 MB
% 6.89/2.00 % (2614343)Instructions burned: 113 (million)
% 6.89/2.00 % (2614346)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2618117988:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.89/2.00 % (2614319)First to succeed.
% 6.89/2.00 % (2614319)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2614314"
% 6.89/2.00 % (2614348)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=629443439:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.89/2.00 % (2614346)Instruction limit reached!
% 6.89/2.00 % (2614346)------------------------------
% 6.89/2.00 % (2614346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614346)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614346)Termination reason: Instruction limit
% 6.89/2.00 % (2614346)Termination phase: Saturation
% 6.89/2.00 % (2614346)Time elapsed: 0.070 s
% 6.89/2.00 % (2614346)Peak memory usage: 89 MB
% 6.89/2.00 % (2614346)Instructions burned: 128 (million)
% 6.89/2.00 % (2614349)lrs+10_1_sil=8000:sp=occurrence:random_seed=4140219880:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.89/2.00 % (2614348)Instruction limit reached!
% 6.89/2.00 % (2614348)------------------------------
% 6.89/2.00 % (2614348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614348)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614348)Termination reason: Instruction limit
% 6.89/2.00 % (2614348)Termination phase: Saturation
% 6.89/2.00 % (2614348)Time elapsed: 0.070 s
% 6.89/2.00 % (2614348)Peak memory usage: 89 MB
% 6.89/2.00 % (2614348)Instructions burned: 114 (million)
% 6.89/2.00 % (2614352)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3871598882:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 6.89/2.00 % (2614352)Refutation not found, incomplete strategy
% 6.89/2.00 % (2614352)------------------------------
% 6.89/2.00 % (2614352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/2.00 % (2614352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/2.00 % (2614352)CaDiCaL version: 2.1.3
% 6.89/2.00 % (2614352)Termination reason: Refutation not found, incomplete strategy
% 6.89/2.00 % (2614352)Time elapsed: 0.002 s
% 6.89/2.00 % (2614352)Peak memory usage: 88 MB
% 6.89/2.00 % (2614352)Instructions burned: 1 (million)
% 6.89/2.00 % (2614341)Also succeeded, but the first one will report.
% 6.89/2.00 % (2614319)Refutation found. Thanks to Tanya!
% 6.89/2.00 % SZS status Theorem for theBenchmark
% 6.89/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 8.76/2.20 % (2614319)------------------------------
% 8.76/2.20 % (2614319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.76/2.20 % (2614319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.76/2.20 % (2614319)CaDiCaL version: 2.1.3
% 8.76/2.20 % (2614319)Termination reason: Refutation
% 8.76/2.20 % (2614319)Time elapsed: 0.732 s
% 8.76/2.20 % (2614319)Peak memory usage: 130 MB
% 8.76/2.20 % (2614319)Instructions burned: 1087 (million)
% 8.76/2.20 % (2614319)------------------------------
% 8.76/2.20 % (2614319)------------------------------
% 8.76/2.20 % (2614314)Success in time 1.162 s
% 8.76/2.20 % Vampire exiting
%------------------------------------------------------------------------------