%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET719+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 6.56s 1.97s
% Output : Refutation 8.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 148 ( 31 unt; 12 def)
% Number of atoms : 538 ( 48 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 662 ( 272 ~; 293 |; 66 &)
% ( 16 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 8 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 298 ( 0 sgn 277 !; 21 ?)
% 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(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(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(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,X2,X3)
& maps(X1,X3,X4)
& one_to_one(X0,X2,X3)
& one_to_one(X1,X3,X4) )
=> equal_maps(inverse_function(compose_function(X1,X0,X2,X3,X4),X2,X4),compose_function(inverse_function(X0,X2,X3),inverse_function(X1,X3,X4),X4,X3,X2),X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII10) ).
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) )
=> equal_maps(inverse_function(compose_function(X1,X0,X2,X3,X4),X2,X4),compose_function(inverse_function(X0,X2,X3),inverse_function(X1,X3,X4),X4,X3,X2),X4,X2) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
=> ( injective(X0,X1,X2)
& surjective(X0,X1,X2) ) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f34,plain,
! [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 ) ) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f36,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(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(ennf_transformation,[],[f14]) ).
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(flattening,[],[f41]) ).
fof(f43,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,[],[f36]) ).
fof(f44,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,[],[f43]) ).
fof(f45,plain,
! [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) )
| ~ injective(X0,X1,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f46,plain,
! [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) )
| ~ injective(X0,X1,X2) ),
inference(flattening,[],[f45]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
& surjective(X0,X1,X2) )
| ~ one_to_one(X0,X1,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f51,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(inverse_function(compose_function(X1,X0,X2,X3,X4),X2,X4),compose_function(inverse_function(X0,X2,X3),inverse_function(X1,X3,X4),X4,X3,X2),X4,X2)
& 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(f52,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(inverse_function(compose_function(X1,X0,X2,X3,X4),X2,X4),compose_function(inverse_function(X0,X2,X3),inverse_function(X1,X3,X4),X4,X3,X2),X4,X2)
& maps(X0,X2,X3)
& maps(X1,X3,X4)
& one_to_one(X0,X2,X3)
& one_to_one(X1,X3,X4) ),
inference(flattening,[],[f51]) ).
fof(f73,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,[],[f42]) ).
fof(f74,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,[],[f73]) ).
fof(f75,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))],[f74]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
& apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
& apply(X1,sK5(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& member(sK5(X0,X1,X2,X3),X2)
& member(sK6(X0,X1,X2,X3),X3)
& member(sK7(X0,X1,X2,X3),X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X4,sK5(X0,X1,X2,X3)),skolemize(X5,sK6(X0,X1,X2,X3)),skolemize(X6,sK7(X0,X1,X2,X3))],[f44]) ).
fof(f78,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,[],[f50]) ).
fof(f93,plain,
( ~ equal_maps(inverse_function(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK17),compose_function(inverse_function(sK13,sK15,sK16),inverse_function(sK14,sK16,sK17),sK17,sK16,sK15),sK17,sK15)
& maps(sK13,sK15,sK16)
& maps(sK14,sK16,sK17)
& one_to_one(sK13,sK15,sK16)
& one_to_one(sK14,sK16,sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16),skolemize(X4,sK17)],[f52]) ).
fof(f123,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,[],[f75]) ).
fof(f124,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,[],[f75]) ).
fof(f125,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,[],[f75]) ).
fof(f127,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( member(sK6(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( member(sK5(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK5(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f133,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ injective(X0,X1,X2)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X2)
| X3 = X4 ),
inference(cnf_transformation,[],[f46]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f139,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,[],[f78]) ).
fof(f154,plain,
one_to_one(sK14,sK16,sK17),
inference(cnf_transformation,[],[f93]) ).
fof(f155,plain,
one_to_one(sK13,sK15,sK16),
inference(cnf_transformation,[],[f93]) ).
fof(f158,plain,
~ equal_maps(inverse_function(compose_function(sK14,sK13,sK15,sK16,sK17),sK15,sK17),compose_function(inverse_function(sK13,sK15,sK16),inverse_function(sK14,sK16,sK17),sK17,sK16,sK15),sK17,sK15),
inference(cnf_transformation,[],[f93]) ).
fof(f162,definition,
sF18 = compose_function(sK14,sK13,sK15,sK16,sK17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f163,plain,
compose_function(sK14,sK13,sK15,sK16,sK17) = sF18,
inference(reorient_equations,[],[f162]) ).
fof(f164,definition,
sF19 = inverse_function(sF18,sK15,sK17),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f165,plain,
inverse_function(sF18,sK15,sK17) = sF19,
inference(reorient_equations,[],[f164]) ).
fof(f166,definition,
sF20 = inverse_function(sK13,sK15,sK16),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f167,plain,
inverse_function(sK13,sK15,sK16) = sF20,
inference(reorient_equations,[],[f166]) ).
fof(f168,definition,
sF21 = inverse_function(sK14,sK16,sK17),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f169,plain,
inverse_function(sK14,sK16,sK17) = sF21,
inference(reorient_equations,[],[f168]) ).
fof(f170,definition,
sF22 = compose_function(sF20,sF21,sK17,sK16,sK15),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f171,plain,
compose_function(sF20,sF21,sK17,sK16,sK15) = sF22,
inference(reorient_equations,[],[f170]) ).
fof(f172,plain,
~ equal_maps(sF19,sF22,sK17,sK15),
inference(definition_folding,[],[f158,f171,f169,f167,f165,f163]) ).
fof(f173,plain,
! [X0,X1] :
( apply(sF21,X0,sK4(sF20,sF21,sK16,X0,X1))
| ~ apply(sF22,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK15) ),
inference(superposition,[],[f124,f171]) ).
fof(f174,plain,
! [X0,X1] :
( apply(sK13,X0,sK4(sK14,sK13,sK16,X0,X1))
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK17) ),
inference(superposition,[],[f124,f163]) ).
fof(f175,plain,
! [X0,X1] :
( apply(sF20,sK4(sF20,sF21,sK16,X0,X1),X1)
| ~ apply(sF22,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK15) ),
inference(superposition,[],[f123,f171]) ).
fof(f176,plain,
! [X0,X1] :
( apply(sK14,sK4(sK14,sK13,sK16,X0,X1),X1)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK17) ),
inference(superposition,[],[f123,f163]) ).
fof(f185,plain,
! [X0,X1] :
( ~ apply(sF19,X0,X1)
| apply(sF18,X1,X0)
| ~ member(X1,sK15)
| ~ member(X0,sK17) ),
inference(superposition,[],[f139,f165]) ).
fof(f186,plain,
! [X0,X1] :
( ~ apply(sF21,X0,X1)
| apply(sK14,X1,X0)
| ~ member(X1,sK16)
| ~ member(X0,sK17) ),
inference(superposition,[],[f139,f169]) ).
fof(f187,plain,
! [X0,X1] :
( ~ apply(sF20,X0,X1)
| apply(sK13,X1,X0)
| ~ member(X1,sK15)
| ~ member(X0,sK16) ),
inference(superposition,[],[f139,f167]) ).
fof(f189,plain,
! [X0,X1] :
( member(sK4(sF20,sF21,sK16,X0,X1),sK16)
| ~ apply(sF22,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK15) ),
inference(superposition,[],[f125,f171]) ).
fof(f190,plain,
! [X0,X1] :
( member(sK4(sK14,sK13,sK16,X0,X1),sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK17) ),
inference(superposition,[],[f125,f163]) ).
fof(f191,plain,
! [X0,X1] :
( apply(sK13,X0,sK4(sF20,sF21,sK16,X1,X0))
| ~ member(X0,sK15)
| ~ member(sK4(sF20,sF21,sK16,X1,X0),sK16)
| ~ apply(sF22,X1,X0)
| ~ member(X1,sK17)
| ~ member(X0,sK15) ),
inference(resolution,[],[f187,f175]) ).
fof(f192,plain,
! [X0,X1] :
( apply(sK13,X0,sK4(sF20,sF21,sK16,X1,X0))
| ~ member(X0,sK15)
| ~ member(sK4(sF20,sF21,sK16,X1,X0),sK16)
| ~ apply(sF22,X1,X0)
| ~ member(X1,sK17) ),
inference(duplicate_literal_removal,[],[f191]) ).
fof(f193,plain,
! [X0,X1] :
( apply(sK13,X0,sK4(sF20,sF21,sK16,X1,X0))
| ~ member(X0,sK15)
| ~ apply(sF22,X1,X0)
| ~ member(X1,sK17) ),
inference(forward_subsumption_resolution,[],[f192,f189]) ).
fof(f194,plain,
! [X0,X1] :
( apply(sK14,sK4(sF20,sF21,sK16,X0,X1),X0)
| ~ member(sK4(sF20,sF21,sK16,X0,X1),sK16)
| ~ member(X0,sK17)
| ~ apply(sF22,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK15) ),
inference(resolution,[],[f186,f173]) ).
fof(f195,plain,
! [X0,X1] :
( apply(sK14,sK4(sF20,sF21,sK16,X0,X1),X0)
| ~ member(sK4(sF20,sF21,sK16,X0,X1),sK16)
| ~ member(X0,sK17)
| ~ apply(sF22,X0,X1)
| ~ member(X1,sK15) ),
inference(duplicate_literal_removal,[],[f194]) ).
fof(f196,plain,
! [X0,X1] :
( apply(sK14,sK4(sF20,sF21,sK16,X0,X1),X0)
| ~ member(X0,sK17)
| ~ apply(sF22,X0,X1)
| ~ member(X1,sK15) ),
inference(forward_subsumption_resolution,[],[f195,f189]) ).
fof(f197,plain,
injective(sK13,sK15,sK16),
inference(resolution,[],[f155,f137]) ).
fof(f199,plain,
injective(sK14,sK16,sK17),
inference(resolution,[],[f154,f137]) ).
fof(f208,plain,
! [X2,X0,X1] :
( apply(sF18,sK6(sF19,X0,X1,X2),sK5(sF19,X0,X1,X2))
| equal_maps(sF19,X0,X1,X2)
| ~ member(sK6(sF19,X0,X1,X2),sK15)
| ~ member(sK5(sF19,X0,X1,X2),sK17) ),
inference(resolution,[],[f131,f185]) ).
fof(f288,plain,
! [X2,X0,X1] :
( ~ apply(sK13,X2,X1)
| ~ apply(sK13,X0,X1)
| ~ member(X0,sK15)
| ~ member(X2,sK15)
| ~ member(X1,sK16)
| X0 = X2 ),
inference(resolution,[],[f133,f197]) ).
fof(f289,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,[],[f133,f199]) ).
fof(f291,plain,
! [X2,X0,X1] :
( ~ apply(sK13,X0,sK4(sF20,sF21,sK16,X1,X2))
| ~ member(X0,sK15)
| ~ member(X2,sK15)
| ~ member(sK4(sF20,sF21,sK16,X1,X2),sK16)
| X0 = X2
| ~ member(X2,sK15)
| ~ apply(sF22,X1,X2)
| ~ member(X1,sK17) ),
inference(resolution,[],[f288,f193]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ apply(sK13,X0,sK4(sF20,sF21,sK16,X1,X2))
| ~ member(X0,sK15)
| ~ member(X2,sK15)
| ~ member(sK4(sF20,sF21,sK16,X1,X2),sK16)
| X0 = X2
| ~ apply(sF22,X1,X2)
| ~ member(X1,sK17) ),
inference(duplicate_literal_removal,[],[f291]) ).
fof(f300,plain,
! [X2,X0,X1] :
( ~ apply(sK13,X0,sK4(sF20,sF21,sK16,X1,X2))
| ~ member(X0,sK15)
| ~ member(X2,sK15)
| X0 = X2
| ~ apply(sF22,X1,X2)
| ~ member(X1,sK17) ),
inference(forward_subsumption_resolution,[],[f298,f189]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ apply(sK14,X0,X1)
| ~ member(X0,sK16)
| ~ member(sK4(sK14,sK13,sK16,X2,X1),sK16)
| ~ member(X1,sK17)
| sK4(sK14,sK13,sK16,X2,X1) = X0
| ~ apply(sF18,X2,X1)
| ~ member(X2,sK15)
| ~ member(X1,sK17) ),
inference(resolution,[],[f289,f176]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ apply(sK14,X0,X1)
| ~ member(X0,sK16)
| ~ member(sK4(sK14,sK13,sK16,X2,X1),sK16)
| ~ member(X1,sK17)
| sK4(sK14,sK13,sK16,X2,X1) = X0
| ~ apply(sF18,X2,X1)
| ~ member(X2,sK15) ),
inference(duplicate_literal_removal,[],[f302]) ).
fof(f313,plain,
! [X2,X0,X1] :
( ~ apply(sF18,X2,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| sK4(sK14,sK13,sK16,X2,X1) = X0
| ~ apply(sK14,X0,X1)
| ~ member(X2,sK15) ),
inference(forward_subsumption_resolution,[],[f311,f190]) ).
fof(f316,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,sK16)
| ~ member(sK5(sF19,X1,X2,X3),sK17)
| sK4(sK14,sK13,sK16,sK6(sF19,X1,X2,X3),sK5(sF19,X1,X2,X3)) = X0
| ~ apply(sK14,X0,sK5(sF19,X1,X2,X3))
| ~ member(sK6(sF19,X1,X2,X3),sK15)
| equal_maps(sF19,X1,X2,X3)
| ~ member(sK6(sF19,X1,X2,X3),sK15)
| ~ member(sK5(sF19,X1,X2,X3),sK17) ),
inference(resolution,[],[f313,f208]) ).
fof(f321,plain,
! [X2,X3,X0,X1] :
( ~ apply(sK14,X0,sK5(sF19,X1,X2,X3))
| ~ member(sK5(sF19,X1,X2,X3),sK17)
| sK4(sK14,sK13,sK16,sK6(sF19,X1,X2,X3),sK5(sF19,X1,X2,X3)) = X0
| ~ member(X0,sK16)
| ~ member(sK6(sF19,X1,X2,X3),sK15)
| equal_maps(sF19,X1,X2,X3) ),
inference(duplicate_literal_removal,[],[f316]) ).
fof(f323,plain,
! [X2,X3,X0,X1] :
( ~ member(sK5(sF19,X0,X1,X2),sK17)
| sK4(sK14,sK13,sK16,sK6(sF19,X0,X1,X2),sK5(sF19,X0,X1,X2)) = sK4(sF20,sF21,sK16,sK5(sF19,X0,X1,X2),X3)
| ~ member(sK4(sF20,sF21,sK16,sK5(sF19,X0,X1,X2),X3),sK16)
| ~ member(sK6(sF19,X0,X1,X2),sK15)
| equal_maps(sF19,X0,X1,X2)
| ~ member(sK5(sF19,X0,X1,X2),sK17)
| ~ apply(sF22,sK5(sF19,X0,X1,X2),X3)
| ~ member(X3,sK15) ),
inference(resolution,[],[f321,f196]) ).
fof(f326,plain,
! [X2,X3,X0,X1] :
( ~ member(sK5(sF19,X0,X1,X2),sK17)
| sK4(sK14,sK13,sK16,sK6(sF19,X0,X1,X2),sK5(sF19,X0,X1,X2)) = sK4(sF20,sF21,sK16,sK5(sF19,X0,X1,X2),X3)
| ~ member(sK4(sF20,sF21,sK16,sK5(sF19,X0,X1,X2),X3),sK16)
| ~ member(sK6(sF19,X0,X1,X2),sK15)
| equal_maps(sF19,X0,X1,X2)
| ~ apply(sF22,sK5(sF19,X0,X1,X2),X3)
| ~ member(X3,sK15) ),
inference(duplicate_literal_removal,[],[f323]) ).
fof(f328,plain,
! [X2,X3,X0,X1] :
( ~ apply(sF22,sK5(sF19,X0,X1,X2),X3)
| sK4(sK14,sK13,sK16,sK6(sF19,X0,X1,X2),sK5(sF19,X0,X1,X2)) = sK4(sF20,sF21,sK16,sK5(sF19,X0,X1,X2),X3)
| ~ member(sK6(sF19,X0,X1,X2),sK15)
| equal_maps(sF19,X0,X1,X2)
| ~ member(sK5(sF19,X0,X1,X2),sK17)
| ~ member(X3,sK15) ),
inference(forward_subsumption_resolution,[],[f326,f189]) ).
fof(f435,plain,
! [X0,X1] :
( sK4(sK14,sK13,sK16,sK6(sF19,sF22,X0,X1),sK5(sF19,sF22,X0,X1)) = sK4(sF20,sF21,sK16,sK5(sF19,sF22,X0,X1),sK7(sF19,sF22,X0,X1))
| ~ member(sK6(sF19,sF22,X0,X1),sK15)
| equal_maps(sF19,sF22,X0,X1)
| ~ member(sK5(sF19,sF22,X0,X1),sK17)
| ~ member(sK7(sF19,sF22,X0,X1),sK15)
| equal_maps(sF19,sF22,X0,X1) ),
inference(resolution,[],[f328,f130]) ).
fof(f436,plain,
! [X0,X1] :
( ~ member(sK7(sF19,sF22,X0,X1),sK15)
| ~ member(sK6(sF19,sF22,X0,X1),sK15)
| equal_maps(sF19,sF22,X0,X1)
| ~ member(sK5(sF19,sF22,X0,X1),sK17)
| sK4(sK14,sK13,sK16,sK6(sF19,sF22,X0,X1),sK5(sF19,sF22,X0,X1)) = sK4(sF20,sF21,sK16,sK5(sF19,sF22,X0,X1),sK7(sF19,sF22,X0,X1)) ),
inference(duplicate_literal_removal,[],[f435]) ).
fof(f437,plain,
! [X0] :
( ~ member(sK6(sF19,sF22,X0,sK15),sK15)
| equal_maps(sF19,sF22,X0,sK15)
| ~ member(sK5(sF19,sF22,X0,sK15),sK17)
| sK4(sK14,sK13,sK16,sK6(sF19,sF22,X0,sK15),sK5(sF19,sF22,X0,sK15)) = sK4(sF20,sF21,sK16,sK5(sF19,sF22,X0,sK15),sK7(sF19,sF22,X0,sK15))
| equal_maps(sF19,sF22,X0,sK15) ),
inference(resolution,[],[f436,f127]) ).
fof(f438,plain,
! [X0] :
( ~ member(sK6(sF19,sF22,X0,sK15),sK15)
| equal_maps(sF19,sF22,X0,sK15)
| ~ member(sK5(sF19,sF22,X0,sK15),sK17)
| sK4(sK14,sK13,sK16,sK6(sF19,sF22,X0,sK15),sK5(sF19,sF22,X0,sK15)) = sK4(sF20,sF21,sK16,sK5(sF19,sF22,X0,sK15),sK7(sF19,sF22,X0,sK15)) ),
inference(duplicate_literal_removal,[],[f437]) ).
fof(f439,plain,
! [X0] :
( ~ member(sK5(sF19,sF22,X0,sK15),sK17)
| equal_maps(sF19,sF22,X0,sK15)
| sK4(sK14,sK13,sK16,sK6(sF19,sF22,X0,sK15),sK5(sF19,sF22,X0,sK15)) = sK4(sF20,sF21,sK16,sK5(sF19,sF22,X0,sK15),sK7(sF19,sF22,X0,sK15)) ),
inference(forward_subsumption_resolution,[],[f438,f128]) ).
fof(f440,plain,
( equal_maps(sF19,sF22,sK17,sK15)
| sK4(sK14,sK13,sK16,sK6(sF19,sF22,sK17,sK15),sK5(sF19,sF22,sK17,sK15)) = sK4(sF20,sF21,sK16,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15))
| equal_maps(sF19,sF22,sK17,sK15) ),
inference(resolution,[],[f439,f129]) ).
fof(f441,plain,
( equal_maps(sF19,sF22,sK17,sK15)
| sK4(sK14,sK13,sK16,sK6(sF19,sF22,sK17,sK15),sK5(sF19,sF22,sK17,sK15)) = sK4(sF20,sF21,sK16,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15)) ),
inference(duplicate_literal_removal,[],[f440]) ).
fof(f442,plain,
sK4(sK14,sK13,sK16,sK6(sF19,sF22,sK17,sK15),sK5(sF19,sF22,sK17,sK15)) = sK4(sF20,sF21,sK16,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15)),
inference(forward_subsumption_resolution,[],[f441,f172]) ).
fof(f446,plain,
( apply(sK13,sK6(sF19,sF22,sK17,sK15),sK4(sF20,sF21,sK16,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15)))
| ~ apply(sF18,sK6(sF19,sF22,sK17,sK15),sK5(sF19,sF22,sK17,sK15))
| ~ member(sK6(sF19,sF22,sK17,sK15),sK15)
| ~ member(sK5(sF19,sF22,sK17,sK15),sK17) ),
inference(superposition,[],[f174,f442]) ).
fof(f448,definition,
( spl23_11
<=> member(sK5(sF19,sF22,sK17,sK15),sK17) ),
introduced(definition,[new_symbols(definition,[spl23_11])],[avatar_definition]) ).
fof(f449,plain,
( member(sK5(sF19,sF22,sK17,sK15),sK17)
| ~ spl23_11 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f450,plain,
( ~ member(sK5(sF19,sF22,sK17,sK15),sK17)
| spl23_11 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f452,definition,
( spl23_12
<=> member(sK6(sF19,sF22,sK17,sK15),sK15) ),
introduced(definition,[new_symbols(definition,[spl23_12])],[avatar_definition]) ).
fof(f453,plain,
( member(sK6(sF19,sF22,sK17,sK15),sK15)
| ~ spl23_12 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f454,plain,
( ~ member(sK6(sF19,sF22,sK17,sK15),sK15)
| spl23_12 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f456,definition,
( spl23_13
<=> apply(sF18,sK6(sF19,sF22,sK17,sK15),sK5(sF19,sF22,sK17,sK15)) ),
introduced(definition,[new_symbols(definition,[spl23_13])],[avatar_definition]) ).
fof(f458,plain,
( ~ apply(sF18,sK6(sF19,sF22,sK17,sK15),sK5(sF19,sF22,sK17,sK15))
| spl23_13 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f460,definition,
( spl23_14
<=> apply(sK13,sK6(sF19,sF22,sK17,sK15),sK4(sF20,sF21,sK16,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15))) ),
introduced(definition,[new_symbols(definition,[spl23_14])],[avatar_definition]) ).
fof(f462,plain,
( apply(sK13,sK6(sF19,sF22,sK17,sK15),sK4(sF20,sF21,sK16,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15)))
| ~ spl23_14 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f463,plain,
( ~ spl23_11
| ~ spl23_12
| ~ spl23_13
| spl23_14 ),
inference(avatar_split_clause,[],[f446,f460,f456,f452,f448]) ).
fof(f478,plain,
( equal_maps(sF19,sF22,sK17,sK15)
| spl23_11 ),
inference(resolution,[],[f450,f129]) ).
fof(f479,plain,
( $false
| spl23_11 ),
inference(forward_subsumption_resolution,[],[f478,f172]) ).
fof(f480,plain,
spl23_11,
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f482,plain,
( equal_maps(sF19,sF22,sK17,sK15)
| spl23_12 ),
inference(resolution,[],[f454,f128]) ).
fof(f483,plain,
( $false
| spl23_12 ),
inference(forward_subsumption_resolution,[],[f482,f172]) ).
fof(f484,plain,
spl23_12,
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f485,plain,
( equal_maps(sF19,sF22,sK17,sK15)
| ~ member(sK6(sF19,sF22,sK17,sK15),sK15)
| ~ member(sK5(sF19,sF22,sK17,sK15),sK17)
| spl23_13 ),
inference(resolution,[],[f458,f208]) ).
fof(f486,plain,
( ~ member(sK6(sF19,sF22,sK17,sK15),sK15)
| ~ member(sK5(sF19,sF22,sK17,sK15),sK17)
| spl23_13 ),
inference(forward_subsumption_resolution,[],[f485,f172]) ).
fof(f487,plain,
( ~ member(sK5(sF19,sF22,sK17,sK15),sK17)
| ~ spl23_12
| spl23_13 ),
inference(forward_subsumption_resolution,[],[f486,f453]) ).
fof(f488,plain,
( $false
| ~ spl23_11
| ~ spl23_12
| spl23_13 ),
inference(forward_subsumption_resolution,[],[f487,f449]) ).
fof(f489,plain,
( ~ spl23_11
| ~ spl23_12
| spl23_13 ),
inference(avatar_contradiction_clause,[],[f488]) ).
fof(f516,plain,
( ~ member(sK6(sF19,sF22,sK17,sK15),sK15)
| ~ member(sK7(sF19,sF22,sK17,sK15),sK15)
| sK6(sF19,sF22,sK17,sK15) = sK7(sF19,sF22,sK17,sK15)
| ~ apply(sF22,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15))
| ~ member(sK5(sF19,sF22,sK17,sK15),sK17)
| ~ spl23_14 ),
inference(resolution,[],[f462,f300]) ).
fof(f522,plain,
( ~ member(sK7(sF19,sF22,sK17,sK15),sK15)
| sK6(sF19,sF22,sK17,sK15) = sK7(sF19,sF22,sK17,sK15)
| ~ apply(sF22,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15))
| ~ member(sK5(sF19,sF22,sK17,sK15),sK17)
| ~ spl23_12
| ~ spl23_14 ),
inference(forward_subsumption_resolution,[],[f516,f453]) ).
fof(f524,plain,
( ~ member(sK7(sF19,sF22,sK17,sK15),sK15)
| sK6(sF19,sF22,sK17,sK15) = sK7(sF19,sF22,sK17,sK15)
| ~ apply(sF22,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15))
| ~ spl23_11
| ~ spl23_12
| ~ spl23_14 ),
inference(forward_subsumption_resolution,[],[f522,f449]) ).
fof(f526,definition,
( spl23_18
<=> apply(sF22,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15)) ),
introduced(definition,[new_symbols(definition,[spl23_18])],[avatar_definition]) ).
fof(f528,plain,
( ~ apply(sF22,sK5(sF19,sF22,sK17,sK15),sK7(sF19,sF22,sK17,sK15))
| spl23_18 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f530,definition,
( spl23_19
<=> sK6(sF19,sF22,sK17,sK15) = sK7(sF19,sF22,sK17,sK15) ),
introduced(definition,[new_symbols(definition,[spl23_19])],[avatar_definition]) ).
fof(f532,plain,
( sK6(sF19,sF22,sK17,sK15) = sK7(sF19,sF22,sK17,sK15)
| ~ spl23_19 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f534,definition,
( spl23_20
<=> member(sK7(sF19,sF22,sK17,sK15),sK15) ),
introduced(definition,[new_symbols(definition,[spl23_20])],[avatar_definition]) ).
fof(f536,plain,
( ~ member(sK7(sF19,sF22,sK17,sK15),sK15)
| spl23_20 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f537,plain,
( ~ spl23_18
| spl23_19
| ~ spl23_20
| ~ spl23_11
| ~ spl23_12
| ~ spl23_14 ),
inference(avatar_split_clause,[],[f524,f460,f452,f448,f534,f530,f526]) ).
fof(f577,plain,
( equal_maps(sF19,sF22,sK17,sK15)
| spl23_18 ),
inference(resolution,[],[f528,f130]) ).
fof(f578,plain,
( $false
| spl23_18 ),
inference(forward_subsumption_resolution,[],[f577,f172]) ).
fof(f579,plain,
spl23_18,
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f580,plain,
( equal_maps(sF19,sF22,sK17,sK15)
| spl23_20 ),
inference(resolution,[],[f536,f127]) ).
fof(f581,plain,
( $false
| spl23_20 ),
inference(forward_subsumption_resolution,[],[f580,f172]) ).
fof(f582,plain,
spl23_20,
inference(avatar_contradiction_clause,[],[f581]) ).
fof(f593,plain,
( sK6(sF19,sF22,sK17,sK15) != sK6(sF19,sF22,sK17,sK15)
| equal_maps(sF19,sF22,sK17,sK15)
| ~ spl23_19 ),
inference(superposition,[],[f132,f532]) ).
fof(f594,plain,
( equal_maps(sF19,sF22,sK17,sK15)
| ~ spl23_19 ),
inference(trivial_inequality_removal,[],[f593]) ).
fof(f596,plain,
( $false
| ~ spl23_19 ),
inference(forward_subsumption_resolution,[],[f594,f172]) ).
fof(f597,plain,
~ spl23_19,
inference(avatar_contradiction_clause,[],[f596]) ).
cnf(s7,plain,
( ~ spl23_11
| ~ spl23_12
| ~ spl23_13
| spl23_14 ),
inference(sat_conversion,[],[f463]) ).
cnf(s11,plain,
spl23_11,
inference(sat_conversion,[],[f480]) ).
cnf(s12,plain,
spl23_12,
inference(sat_conversion,[],[f484]) ).
cnf(s13,plain,
( ~ spl23_11
| ~ spl23_12
| spl23_13 ),
inference(sat_conversion,[],[f489]) ).
cnf(s14,plain,
( ~ spl23_11
| ~ spl23_12
| ~ spl23_14
| ~ spl23_18
| spl23_19
| ~ spl23_20 ),
inference(sat_conversion,[],[f537]) ).
cnf(s17,plain,
spl23_18,
inference(sat_conversion,[],[f579]) ).
cnf(s18,plain,
spl23_20,
inference(sat_conversion,[],[f582]) ).
cnf(s19,plain,
~ spl23_19,
inference(sat_conversion,[],[f597]) ).
cnf(s20,plain,
( ~ spl23_11
| ~ spl23_12
| ~ spl23_14 ),
inference(rat,[],[s14,s18,s19,s17]) ).
cnf(s21,plain,
~ spl23_14,
inference(rat,[],[s20,s12,s11]) ).
cnf(s22,plain,
spl23_13,
inference(rat,[],[s13,s12,s11]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s7,s21,s22,s12,s11]) ).
fof(f603,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET719+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.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 02:38:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 6.56/1.97 % (3611258)Detected formulas, will run a generic FOF schedule.
% 6.56/1.97 % (3611269)dis-21_1_sil=8000:lcm=predicate:random_seed=3171100623: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)
% 6.56/1.97 % (3611264)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=3411792552:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.56/1.97 % (3611268)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4256486016:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.56/1.97 % (3611265)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=3235637288:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.56/1.97 % (3611263)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=1793697219:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.56/1.97 % (3611266)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2964338582:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.56/1.97 % (3611267)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1757043437:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.56/1.97 % (3611269)Instruction limit reached!
% 6.56/1.97 % (3611269)------------------------------
% 6.56/1.97 % (3611269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611269)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611269)Termination reason: Instruction limit
% 6.56/1.97 % (3611269)Termination phase: Saturation
% 6.56/1.97 % (3611269)Time elapsed: 0.039 s
% 6.56/1.97 % (3611269)Peak memory usage: 89 MB
% 6.56/1.97 % (3611269)Instructions burned: 133 (million)
% 6.56/1.97 % (3611266)Refutation not found, incomplete strategy
% 6.56/1.97 % (3611266)------------------------------
% 6.56/1.97 % (3611266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611266)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611266)Termination reason: Refutation not found, incomplete strategy
% 6.56/1.97 % (3611266)Time elapsed: 0.007 s
% 6.56/1.97 % (3611266)Peak memory usage: 88 MB
% 6.56/1.97 % (3611266)Instructions burned: 9 (million)
% 6.56/1.97 % (3611267)Instruction limit reached!
% 6.56/1.97 % (3611267)------------------------------
% 6.56/1.97 % (3611267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611267)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611267)Termination reason: Instruction limit
% 6.56/1.97 % (3611267)Termination phase: Saturation
% 6.56/1.97 % (3611267)Time elapsed: 0.069 s
% 6.56/1.97 % (3611267)Peak memory usage: 89 MB
% 6.56/1.97 % (3611267)Instructions burned: 120 (million)
% 6.56/1.97 % (3611277)lrs+10_1_sil=8000:sp=occurrence:random_seed=3033015481:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.56/1.97 % (3611268)Instruction limit reached!
% 6.56/1.97 % (3611268)------------------------------
% 6.56/1.97 % (3611268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611268)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611268)Termination reason: Instruction limit
% 6.56/1.97 % (3611268)Termination phase: Saturation
% 6.56/1.97 % (3611268)Time elapsed: 0.101 s
% 6.56/1.97 % (3611268)Peak memory usage: 89 MB
% 6.56/1.97 % (3611268)Instructions burned: 139 (million)
% 6.56/1.97 % (3611277)Instruction limit reached!
% 6.56/1.97 % (3611277)------------------------------
% 6.56/1.97 % (3611277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611277)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611277)Termination reason: Instruction limit
% 6.56/1.97 % (3611277)Termination phase: Saturation
% 6.56/1.97 % (3611277)Time elapsed: 0.088 s
% 6.56/1.97 % (3611277)Peak memory usage: 92 MB
% 6.56/1.97 % (3611277)Instructions burned: 289 (million)
% 6.56/1.97 % (3611278)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1416942200:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.56/1.97 % (3611280)lrs+1011_1_sil=32000:sp=occurrence:random_seed=910149750:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.56/1.97 % (3611266)------------------------------
% 6.56/1.97 % (3611266)------------------------------
% 6.56/1.97 % (3611281)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=766436035:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.56/1.97 % (3611278)Instruction limit reached!
% 6.56/1.97 % (3611278)------------------------------
% 6.56/1.97 % (3611278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611278)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611278)Termination reason: Instruction limit
% 6.56/1.97 % (3611278)Termination phase: Saturation
% 6.56/1.97 % (3611278)Time elapsed: 0.082 s
% 6.56/1.97 % (3611278)Peak memory usage: 89 MB
% 6.56/1.97 % (3611278)Instructions burned: 157 (million)
% 6.56/1.97 % (3611281)Instruction limit reached!
% 6.56/1.97 % (3611281)------------------------------
% 6.56/1.97 % (3611281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611281)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611281)Termination reason: Instruction limit
% 6.56/1.97 % (3611281)Termination phase: Saturation
% 6.56/1.97 % (3611281)Time elapsed: 0.064 s
% 6.56/1.97 % (3611281)Peak memory usage: 90 MB
% 6.56/1.97 % (3611281)Instructions burned: 249 (million)
% 6.56/1.97 % (3611284)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4282742031:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.56/1.97 % (3611286)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=46245661:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.56/1.97 % (3611287)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1238247923:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 6.56/1.97 % (3611280)Instruction limit reached!
% 6.56/1.97 % (3611280)------------------------------
% 6.56/1.97 % (3611280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611280)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611280)Termination reason: Instruction limit
% 6.56/1.97 % (3611280)Termination phase: Saturation
% 6.56/1.97 % (3611280)Time elapsed: 0.223 s
% 6.56/1.97 % (3611280)Peak memory usage: 93 MB
% 6.56/1.97 % (3611280)Instructions burned: 325 (million)
% 6.56/1.97 % (3611287)Instruction limit reached!
% 6.56/1.97 % (3611287)------------------------------
% 6.56/1.97 % (3611287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611287)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611287)Termination reason: Instruction limit
% 6.56/1.97 % (3611287)Termination phase: Saturation
% 6.56/1.97 % (3611287)Time elapsed: 0.041 s
% 6.56/1.97 % (3611287)Peak memory usage: 89 MB
% 6.56/1.97 % (3611287)Instructions burned: 113 (million)
% 6.56/1.97 % (3611292)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1624302051:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 6.56/1.97 % (3611284)Instruction limit reached!
% 6.56/1.97 % (3611284)------------------------------
% 6.56/1.97 % (3611284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611284)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611284)Termination reason: Instruction limit
% 6.56/1.97 % (3611284)Termination phase: Saturation
% 6.56/1.97 % (3611284)Time elapsed: 0.173 s
% 6.56/1.97 % (3611284)Peak memory usage: 89 MB
% 6.56/1.97 % (3611284)Instructions burned: 296 (million)
% 6.56/1.97 % (3611292)Instruction limit reached!
% 6.56/1.97 % (3611292)------------------------------
% 6.56/1.97 % (3611292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611292)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611292)Termination reason: Instruction limit
% 6.56/1.97 % (3611292)Termination phase: Saturation
% 6.56/1.97 % (3611292)Time elapsed: 0.038 s
% 6.56/1.97 % (3611292)Peak memory usage: 89 MB
% 6.56/1.97 % (3611292)Instructions burned: 115 (million)
% 6.56/1.97 % (3611291)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2589230494:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.56/1.97 % (3611291)Instruction limit reached!
% 6.56/1.97 % (3611291)------------------------------
% 6.56/1.97 % (3611291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611291)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611291)Termination reason: Instruction limit
% 6.56/1.97 % (3611291)Termination phase: Saturation
% 6.56/1.97 % (3611291)Time elapsed: 0.071 s
% 6.56/1.97 % (3611291)Peak memory usage: 89 MB
% 6.56/1.97 % (3611291)Instructions burned: 128 (million)
% 6.56/1.97 % (3611295)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=772366947:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.56/1.97 % (3611295)Refutation not found, incomplete strategy
% 6.56/1.97 % (3611295)------------------------------
% 6.56/1.97 % (3611295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611295)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611295)Termination reason: Refutation not found, incomplete strategy
% 6.56/1.97 % (3611295)Time elapsed: 0.001 s
% 6.56/1.97 % (3611295)Peak memory usage: 88 MB
% 6.56/1.97 % (3611295)Instructions burned: 1 (million)
% 6.56/1.97 % (3611294)lrs+10_1_sil=8000:sp=occurrence:random_seed=845801580:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 6.56/1.97 % (3611263)First to succeed.
% 6.56/1.97 % (3611263)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3611258"
% 6.56/1.97 % (3611298)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4004824715:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.56/1.97 % (3611295)------------------------------
% 6.56/1.97 % (3611295)------------------------------
% 6.56/1.97 % (3611301)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4060605451:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2990 on theBenchmark for (2990ds/134Mi)
% 6.56/1.97 % (3611301)Instruction limit reached!
% 6.56/1.97 % (3611301)------------------------------
% 6.56/1.97 % (3611301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.97 % (3611301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.97 % (3611301)CaDiCaL version: 2.1.3
% 6.56/1.97 % (3611301)Termination reason: Instruction limit
% 6.56/1.97 % (3611301)Termination phase: Saturation
% 6.56/1.97 % (3611301)Time elapsed: 0.040 s
% 6.56/1.97 % (3611301)Peak memory usage: 90 MB
% 6.56/1.97 % (3611301)Instructions burned: 137 (million)
% 6.56/1.97 % (3611263)Refutation found. Thanks to Tanya!
% 6.56/1.97 % SZS status Theorem for theBenchmark
% 6.56/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 8.54/2.16 % (3611263)------------------------------
% 8.54/2.16 % (3611263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.16 % (3611263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.16 % (3611263)CaDiCaL version: 2.1.3
% 8.54/2.16 % (3611263)Termination reason: Refutation
% 8.54/2.16 % (3611263)Time elapsed: 0.723 s
% 8.54/2.16 % (3611263)Peak memory usage: 130 MB
% 8.54/2.16 % (3611263)Instructions burned: 1083 (million)
% 8.54/2.16 % (3611263)------------------------------
% 8.54/2.16 % (3611263)------------------------------
% 8.54/2.16 % (3611258)Success in time 1.123 s
% 8.54/2.16 % Vampire exiting
%------------------------------------------------------------------------------