%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET761+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:41:51 PM UTC 2026
% Result : Theorem 10.99s 2.58s
% Output : Refutation 12.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 23
% Syntax : Number of formulae : 217 ( 35 unt; 16 def)
% Number of atoms : 674 ( 44 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 784 ( 327 ~; 347 |; 72 &)
% ( 19 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 12 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 302 ( 0 sgn 281 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
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/sandbox/benchmark/theBenchmark.p',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/sandbox/benchmark/theBenchmark.p',injective) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( member(X3,image3(X0,X1,X2))
<=> ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image3) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& injective(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1) )
=> equal_set(image3(X0,intersection(X3,X4),X2),intersection(image3(X0,X3,X2),image3(X0,X4,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa11) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& injective(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1) )
=> equal_set(image3(X0,intersection(X3,X4),X2),intersection(image3(X0,X3,X2),image3(X0,X4,X2))) ),
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] :
( 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(f34,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f36]) ).
fof(f39,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(f40,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,[],[f39]) ).
fof(f43,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,[],[f33]) ).
fof(f44,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,[],[f43]) ).
fof(f47,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_set(image3(X0,intersection(X3,X4),X2),intersection(image3(X0,X3,X2),image3(X0,X4,X2)))
& maps(X0,X1,X2)
& injective(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f48,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_set(image3(X0,intersection(X3,X4),X2),intersection(image3(X0,X3,X2),image3(X0,X4,X2)))
& maps(X0,X1,X2)
& injective(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f50,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f50]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f53]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK3(X0,X2,X3),X2)
& apply(X0,X3,sK3(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,[sK3]),skolemize(X4,sK3(X0,X2,X3))],[f40]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& ? [X5] :
( member(X5,X1)
& apply(X0,X5,X3) ) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ( member(X3,image3(X0,X1,X2))
| ~ member(X3,X2)
| ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) ) )
& ( ( member(X3,X2)
& member(sK6(X0,X1,X3),X1)
& apply(X0,sK6(X0,X1,X3),X3) )
| ~ member(X3,image3(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X5,sK6(X0,X1,X3))],[f78]) ).
fof(f87,plain,
( ~ equal_set(image3(sK9,intersection(sK12,sK13),sK11),intersection(image3(sK9,sK12,sK11),image3(sK9,sK13,sK11)))
& maps(sK9,sK10,sK11)
& injective(sK9,sK10,sK11)
& subset(sK12,sK10)
& subset(sK13,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12),skolemize(X4,sK13)],[f48]) ).
fof(f88,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f89,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f90,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f91,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f96,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f115,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f122,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,[],[f44]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| apply(X0,sK6(X0,X1,X3),X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| member(sK6(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,image3(X0,X1,X2))
| member(X3,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f131,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(X0,X4,X3)
| ~ member(X3,X2)
| ~ member(X4,X1)
| member(X3,image3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f139,plain,
subset(sK13,sK10),
inference(cnf_transformation,[],[f87]) ).
fof(f140,plain,
subset(sK12,sK10),
inference(cnf_transformation,[],[f87]) ).
fof(f141,plain,
injective(sK9,sK10,sK11),
inference(cnf_transformation,[],[f87]) ).
fof(f142,plain,
maps(sK9,sK10,sK11),
inference(cnf_transformation,[],[f87]) ).
fof(f143,plain,
~ equal_set(image3(sK9,intersection(sK12,sK13),sK11),intersection(image3(sK9,sK12,sK11),image3(sK9,sK13,sK11))),
inference(cnf_transformation,[],[f87]) ).
fof(f147,definition,
sF14 = intersection(sK12,sK13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f148,plain,
intersection(sK12,sK13) = sF14,
inference(reorient_equations,[],[f147]) ).
fof(f149,definition,
sF15 = image3(sK9,sF14,sK11),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f150,plain,
image3(sK9,sF14,sK11) = sF15,
inference(reorient_equations,[],[f149]) ).
fof(f151,definition,
sF16 = image3(sK9,sK12,sK11),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f152,plain,
image3(sK9,sK12,sK11) = sF16,
inference(reorient_equations,[],[f151]) ).
fof(f153,definition,
sF17 = image3(sK9,sK13,sK11),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f154,plain,
image3(sK9,sK13,sK11) = sF17,
inference(reorient_equations,[],[f153]) ).
fof(f155,definition,
sF18 = intersection(sF16,sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f156,plain,
intersection(sF16,sF17) = sF18,
inference(reorient_equations,[],[f155]) ).
fof(f157,plain,
~ equal_set(sF15,sF18),
inference(definition_folding,[],[f143,f156,f154,f152,f150,f148]) ).
fof(f158,plain,
! [X0] :
( ~ member(X0,sF14)
| member(X0,sK12) ),
inference(superposition,[],[f95,f148]) ).
fof(f159,plain,
! [X0] :
( ~ member(X0,sF18)
| member(X0,sF16) ),
inference(superposition,[],[f95,f156]) ).
fof(f160,plain,
! [X0] :
( ~ member(X0,sF14)
| member(X0,sK13) ),
inference(superposition,[],[f94,f148]) ).
fof(f161,plain,
! [X0] :
( ~ member(X0,sF18)
| member(X0,sF17) ),
inference(superposition,[],[f94,f156]) ).
fof(f162,plain,
! [X0] :
( ~ member(X0,sF15)
| member(X0,sK11) ),
inference(superposition,[],[f130,f150]) ).
fof(f163,plain,
! [X0] :
( ~ member(X0,sF16)
| member(X0,sK11) ),
inference(superposition,[],[f130,f152]) ).
fof(f164,plain,
! [X0] :
( ~ member(X0,sF17)
| member(X0,sK11) ),
inference(superposition,[],[f130,f154]) ).
fof(f167,plain,
! [X0] :
( ~ member(X0,sK13)
| ~ member(X0,sK12)
| member(X0,sF14) ),
inference(superposition,[],[f96,f148]) ).
fof(f168,plain,
! [X0] :
( ~ member(X0,sF17)
| ~ member(X0,sF16)
| member(X0,sF18) ),
inference(superposition,[],[f96,f156]) ).
fof(f169,plain,
! [X0] :
( member(sK6(sK9,sF14,X0),sF14)
| ~ member(X0,sF15) ),
inference(superposition,[],[f129,f150]) ).
fof(f170,plain,
! [X0] :
( member(sK6(sK9,sK12,X0),sK12)
| ~ member(X0,sF16) ),
inference(superposition,[],[f129,f152]) ).
fof(f171,plain,
! [X0] :
( member(sK6(sK9,sK13,X0),sK13)
| ~ member(X0,sF17) ),
inference(superposition,[],[f129,f154]) ).
fof(f172,plain,
! [X0] :
( apply(sK9,sK6(sK9,sF14,X0),X0)
| ~ member(X0,sF15) ),
inference(superposition,[],[f128,f150]) ).
fof(f173,plain,
! [X0] :
( apply(sK9,sK6(sK9,sK12,X0),X0)
| ~ member(X0,sF16) ),
inference(superposition,[],[f128,f152]) ).
fof(f174,plain,
! [X0] :
( apply(sK9,sK6(sK9,sK13,X0),X0)
| ~ member(X0,sF17) ),
inference(superposition,[],[f128,f154]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ member(sK6(sK9,sF14,X0),X2)
| ~ member(X0,X1)
| member(X0,image3(sK9,X2,X1))
| ~ member(X0,sF15) ),
inference(resolution,[],[f131,f172]) ).
fof(f178,plain,
! [X0] :
( apply(sK9,X0,sK3(sK9,sK11,X0))
| ~ member(X0,sK10) ),
inference(resolution,[],[f116,f142]) ).
fof(f179,plain,
! [X2,X0,X1] :
( member(sK3(sK9,sK11,X0),image3(sK9,X2,X1))
| ~ member(sK3(sK9,sK11,X0),X1)
| ~ member(X0,X2)
| ~ member(X0,sK10) ),
inference(resolution,[],[f178,f131]) ).
fof(f181,plain,
! [X0] :
( member(sK6(sK9,sF14,X0),sK13)
| ~ member(X0,sF15) ),
inference(resolution,[],[f169,f160]) ).
fof(f182,plain,
! [X0] :
( member(sK6(sK9,sF14,X0),sK12)
| ~ member(X0,sF15) ),
inference(resolution,[],[f169,f158]) ).
fof(f184,plain,
! [X0] :
( subset(X0,X0)
| subset(X0,X0) ),
inference(resolution,[],[f89,f90]) ).
fof(f195,plain,
! [X0] :
( member(sK0(sF18,X0),sF17)
| subset(sF18,X0) ),
inference(resolution,[],[f89,f161]) ).
fof(f196,plain,
! [X0] :
( member(sK0(sF18,X0),sF16)
| subset(sF18,X0) ),
inference(resolution,[],[f89,f159]) ).
fof(f197,plain,
! [X0] : subset(X0,X0),
inference(duplicate_literal_removal,[],[f184]) ).
fof(f198,plain,
! [X0] :
( ~ member(sK6(sK9,sK13,X0),sK12)
| ~ member(X0,sF17)
| member(sK6(sK9,sK13,X0),sF14) ),
inference(resolution,[],[f171,f167]) ).
fof(f219,plain,
( subset(sF18,sF16)
| subset(sF18,sF16) ),
inference(resolution,[],[f196,f90]) ).
fof(f220,plain,
subset(sF18,sF16),
inference(duplicate_literal_removal,[],[f219]) ).
fof(f221,plain,
( subset(sF18,sF17)
| subset(sF18,sF17) ),
inference(resolution,[],[f195,f90]) ).
fof(f223,plain,
subset(sF18,sF17),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f228,plain,
! [X0,X1] :
( member(sK6(sK9,sK12,X0),X1)
| ~ subset(sK12,X1)
| ~ member(X0,sF16) ),
inference(resolution,[],[f88,f170]) ).
fof(f229,plain,
! [X0,X1] :
( member(sK6(sK9,sK13,X0),X1)
| ~ subset(sK13,X1)
| ~ member(X0,sF17) ),
inference(resolution,[],[f88,f171]) ).
fof(f230,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[],[f88,f89]) ).
fof(f241,plain,
! [X0] :
( ~ member(sK3(sK9,sK11,X0),sK11)
| member(sK3(sK9,sK11,X0),sF15)
| ~ member(X0,sF14)
| ~ member(X0,sK10) ),
inference(superposition,[],[f179,f150]) ).
fof(f247,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(sK9,sK11,X0),X3)
| sK3(sK9,sK11,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ apply(sK9,X0,X1)
| ~ maps(sK9,X2,X3)
| ~ member(X0,sK10) ),
inference(resolution,[],[f115,f178]) ).
fof(f248,plain,
! [X2,X0,X1] :
( ~ apply(sK9,X2,X1)
| ~ apply(sK9,X0,X1)
| ~ member(X0,sK10)
| ~ member(X2,sK10)
| ~ member(X1,sK11)
| X0 = X2 ),
inference(resolution,[],[f122,f141]) ).
fof(f252,plain,
! [X0,X1] :
( ~ apply(sK9,X0,sK3(sK9,sK11,X1))
| ~ member(X0,sK10)
| ~ member(X1,sK10)
| ~ member(sK3(sK9,sK11,X1),sK11)
| X0 = X1
| ~ member(X1,sK10) ),
inference(resolution,[],[f248,f178]) ).
fof(f253,plain,
! [X0,X1] :
( ~ apply(sK9,X0,sK3(sK9,sK11,X1))
| ~ member(X0,sK10)
| ~ member(X1,sK10)
| ~ member(sK3(sK9,sK11,X1),sK11)
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f252]) ).
fof(f285,plain,
! [X0] :
( ~ member(sK6(sK9,sK13,sK3(sK9,sK11,X0)),sK10)
| ~ member(X0,sK10)
| ~ member(sK3(sK9,sK11,X0),sK11)
| sK6(sK9,sK13,sK3(sK9,sK11,X0)) = X0
| ~ member(sK3(sK9,sK11,X0),sF17) ),
inference(resolution,[],[f253,f174]) ).
fof(f288,plain,
! [X0] :
( ~ member(sK6(sK9,sK13,sK3(sK9,sK11,X0)),sK10)
| ~ member(X0,sK10)
| sK6(sK9,sK13,sK3(sK9,sK11,X0)) = X0
| ~ member(sK3(sK9,sK11,X0),sF17) ),
inference(forward_subsumption_resolution,[],[f285,f164]) ).
fof(f291,plain,
! [X0] :
( member(sK3(sK9,sK11,X0),sK11)
| ~ member(X0,sK10) ),
inference(resolution,[],[f117,f142]) ).
fof(f294,plain,
! [X0] :
( ~ member(X0,sK10)
| member(sK3(sK9,sK11,X0),sF15)
| ~ member(X0,sF14)
| ~ member(X0,sK10) ),
inference(resolution,[],[f291,f241]) ).
fof(f295,plain,
! [X2,X0,X1] :
( ~ member(X0,sK10)
| sK3(sK9,sK11,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK11)
| ~ apply(sK9,X0,X1)
| ~ maps(sK9,X2,sK11)
| ~ member(X0,sK10) ),
inference(resolution,[],[f291,f247]) ).
fof(f297,plain,
! [X2,X0,X1] :
( ~ apply(sK9,X0,X1)
| sK3(sK9,sK11,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK11)
| ~ member(X0,sK10)
| ~ maps(sK9,X2,sK11) ),
inference(duplicate_literal_removal,[],[f295]) ).
fof(f298,plain,
! [X0] :
( member(sK3(sK9,sK11,X0),sF15)
| ~ member(X0,sK10)
| ~ member(X0,sF14) ),
inference(duplicate_literal_removal,[],[f294]) ).
fof(f302,plain,
! [X0,X1] :
( sK3(sK9,sK11,sK6(sK9,sK12,X0)) = X0
| ~ member(sK6(sK9,sK12,X0),X1)
| ~ member(X0,sK11)
| ~ member(sK6(sK9,sK12,X0),sK10)
| ~ maps(sK9,X1,sK11)
| ~ member(X0,sF16) ),
inference(resolution,[],[f297,f173]) ).
fof(f307,plain,
! [X0,X1] :
( ~ member(sK6(sK9,sK12,X0),sK10)
| ~ member(sK6(sK9,sK12,X0),X1)
| sK3(sK9,sK11,sK6(sK9,sK12,X0)) = X0
| ~ maps(sK9,X1,sK11)
| ~ member(X0,sF16) ),
inference(forward_subsumption_resolution,[],[f302,f163]) ).
fof(f323,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,image3(sK9,sK13,X1))
| ~ member(X0,sF15)
| ~ member(X0,sF15) ),
inference(resolution,[],[f175,f181]) ).
fof(f324,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,image3(sK9,sK12,X1))
| ~ member(X0,sF15)
| ~ member(X0,sF15) ),
inference(resolution,[],[f175,f182]) ).
fof(f326,plain,
! [X0,X1] :
( member(X0,image3(sK9,sK12,X1))
| ~ member(X0,X1)
| ~ member(X0,sF15) ),
inference(duplicate_literal_removal,[],[f324]) ).
fof(f327,plain,
! [X0,X1] :
( member(X0,image3(sK9,sK13,X1))
| ~ member(X0,X1)
| ~ member(X0,sF15) ),
inference(duplicate_literal_removal,[],[f323]) ).
fof(f344,plain,
! [X0] :
( member(X0,sF16)
| ~ member(X0,sK11)
| ~ member(X0,sF15) ),
inference(superposition,[],[f326,f152]) ).
fof(f345,plain,
! [X0] :
( ~ member(X0,sF15)
| member(X0,sF16) ),
inference(forward_subsumption_resolution,[],[f344,f162]) ).
fof(f346,plain,
! [X0] :
( member(sK0(sF15,X0),sF16)
| subset(sF15,X0) ),
inference(resolution,[],[f345,f89]) ).
fof(f360,plain,
! [X0] :
( member(X0,sF17)
| ~ member(X0,sK11)
| ~ member(X0,sF15) ),
inference(superposition,[],[f327,f154]) ).
fof(f361,plain,
! [X0] :
( ~ member(X0,sF15)
| member(X0,sF17) ),
inference(forward_subsumption_resolution,[],[f360,f162]) ).
fof(f362,plain,
! [X0] :
( member(sK0(sF15,X0),sF17)
| subset(sF15,X0) ),
inference(resolution,[],[f361,f89]) ).
fof(f367,plain,
! [X0] :
( subset(sF15,X0)
| ~ member(sK0(sF15,X0),sF16)
| member(sK0(sF15,X0),sF18) ),
inference(resolution,[],[f362,f168]) ).
fof(f370,plain,
! [X0] :
( member(sK0(sF15,X0),sF18)
| subset(sF15,X0) ),
inference(forward_subsumption_resolution,[],[f367,f346]) ).
fof(f371,plain,
( subset(sF15,sF18)
| subset(sF15,sF18) ),
inference(resolution,[],[f370,f90]) ).
fof(f375,plain,
subset(sF15,sF18),
inference(duplicate_literal_removal,[],[f371]) ).
fof(f382,definition,
( spl19_6
<=> subset(sF18,sF15) ),
introduced(definition,[new_symbols(definition,[spl19_6])],[avatar_definition]) ).
fof(f383,plain,
( subset(sF18,sF15)
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f384,plain,
( ~ subset(sF18,sF15)
| spl19_6 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f507,plain,
! [X0,X1] :
( ~ member(sK6(sK9,sK12,X0),X1)
| sK3(sK9,sK11,sK6(sK9,sK12,X0)) = X0
| ~ maps(sK9,X1,sK11)
| ~ member(X0,sF16)
| ~ subset(sK12,sK10)
| ~ member(X0,sF16) ),
inference(resolution,[],[f307,f228]) ).
fof(f508,plain,
! [X0,X1] :
( ~ member(sK6(sK9,sK12,X0),X1)
| sK3(sK9,sK11,sK6(sK9,sK12,X0)) = X0
| ~ maps(sK9,X1,sK11)
| ~ member(X0,sF16)
| ~ subset(sK12,sK10) ),
inference(duplicate_literal_removal,[],[f507]) ).
fof(f509,plain,
! [X0,X1] :
( ~ member(sK6(sK9,sK12,X0),X1)
| sK3(sK9,sK11,sK6(sK9,sK12,X0)) = X0
| ~ maps(sK9,X1,sK11)
| ~ member(X0,sF16) ),
inference(forward_subsumption_resolution,[],[f508,f140]) ).
fof(f511,plain,
! [X0,X1] :
( sK3(sK9,sK11,sK6(sK9,sK12,X0)) = X0
| ~ maps(sK9,X1,sK11)
| ~ member(X0,sF16)
| ~ subset(sK12,X1)
| ~ member(X0,sF16) ),
inference(resolution,[],[f509,f228]) ).
fof(f516,plain,
! [X0,X1] :
( sK3(sK9,sK11,sK6(sK9,sK12,X0)) = X0
| ~ maps(sK9,X1,sK11)
| ~ member(X0,sF16)
| ~ subset(sK12,X1) ),
inference(duplicate_literal_removal,[],[f511]) ).
fof(f519,definition,
( spl19_21
<=> ! [X1] :
( ~ maps(sK9,X1,sK11)
| ~ subset(sK12,X1) ) ),
introduced(definition,[new_symbols(definition,[spl19_21])],[avatar_definition]) ).
fof(f520,plain,
( ! [X1] :
( ~ maps(sK9,X1,sK11)
| ~ subset(sK12,X1) )
| ~ spl19_21 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f522,definition,
( spl19_22
<=> ! [X0] :
( sK3(sK9,sK11,sK6(sK9,sK12,X0)) = X0
| ~ member(X0,sF16) ) ),
introduced(definition,[new_symbols(definition,[spl19_22])],[avatar_definition]) ).
fof(f523,plain,
( ! [X0] :
( ~ member(X0,sF16)
| sK3(sK9,sK11,sK6(sK9,sK12,X0)) = X0 )
| ~ spl19_22 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f524,plain,
( spl19_21
| spl19_22 ),
inference(avatar_split_clause,[],[f516,f522,f519]) ).
fof(f530,plain,
( ~ subset(sK12,sK10)
| ~ spl19_21 ),
inference(resolution,[],[f520,f142]) ).
fof(f531,plain,
( $false
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f530,f140]) ).
fof(f532,plain,
~ spl19_21,
inference(avatar_contradiction_clause,[],[f531]) ).
fof(f533,plain,
( ! [X0] :
( subset(sF18,X0)
| sK0(sF18,X0) = sK3(sK9,sK11,sK6(sK9,sK12,sK0(sF18,X0))) )
| ~ spl19_22 ),
inference(resolution,[],[f523,f196]) ).
fof(f804,plain,
( sK0(sF18,sF15) = sK3(sK9,sK11,sK6(sK9,sK12,sK0(sF18,sF15)))
| spl19_6
| ~ spl19_22 ),
inference(resolution,[],[f533,f384]) ).
fof(f813,plain,
( ~ member(sK6(sK9,sK13,sK0(sF18,sF15)),sK10)
| ~ member(sK6(sK9,sK12,sK0(sF18,sF15)),sK10)
| sK6(sK9,sK12,sK0(sF18,sF15)) = sK6(sK9,sK13,sK0(sF18,sF15))
| ~ member(sK0(sF18,sF15),sF17)
| spl19_6
| ~ spl19_22 ),
inference(superposition,[],[f288,f804]) ).
fof(f816,plain,
( member(sK0(sF18,sF15),sF15)
| ~ member(sK6(sK9,sK12,sK0(sF18,sF15)),sK10)
| ~ member(sK6(sK9,sK12,sK0(sF18,sF15)),sF14)
| spl19_6
| ~ spl19_22 ),
inference(superposition,[],[f298,f804]) ).
fof(f824,definition,
( spl19_50
<=> member(sK6(sK9,sK12,sK0(sF18,sF15)),sK10) ),
introduced(definition,[new_symbols(definition,[spl19_50])],[avatar_definition]) ).
fof(f826,plain,
( ~ member(sK6(sK9,sK12,sK0(sF18,sF15)),sK10)
| spl19_50 ),
inference(avatar_component_clause,[],[f824]) ).
fof(f828,definition,
( spl19_51
<=> member(sK0(sF18,sF15),sF17) ),
introduced(definition,[new_symbols(definition,[spl19_51])],[avatar_definition]) ).
fof(f829,plain,
( ~ member(sK0(sF18,sF15),sF17)
| spl19_51 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f830,plain,
( member(sK0(sF18,sF15),sF17)
| ~ spl19_51 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f833,definition,
( spl19_52
<=> member(sK6(sK9,sK12,sK0(sF18,sF15)),sK12) ),
introduced(definition,[new_symbols(definition,[spl19_52])],[avatar_definition]) ).
fof(f835,plain,
( ~ member(sK6(sK9,sK12,sK0(sF18,sF15)),sK12)
| spl19_52 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f837,definition,
( spl19_53
<=> member(sK0(sF18,sF15),sF16) ),
introduced(definition,[new_symbols(definition,[spl19_53])],[avatar_definition]) ).
fof(f838,plain,
( ~ member(sK0(sF18,sF15),sF16)
| spl19_53 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f839,plain,
( member(sK0(sF18,sF15),sF16)
| ~ spl19_53 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f842,definition,
( spl19_54
<=> member(sK6(sK9,sK12,sK0(sF18,sF15)),sF14) ),
introduced(definition,[new_symbols(definition,[spl19_54])],[avatar_definition]) ).
fof(f844,plain,
( ~ member(sK6(sK9,sK12,sK0(sF18,sF15)),sF14)
| spl19_54 ),
inference(avatar_component_clause,[],[f842]) ).
fof(f846,definition,
( spl19_55
<=> member(sK0(sF18,sF15),sF15) ),
introduced(definition,[new_symbols(definition,[spl19_55])],[avatar_definition]) ).
fof(f848,plain,
( member(sK0(sF18,sF15),sF15)
| ~ spl19_55 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f849,plain,
( ~ spl19_54
| ~ spl19_50
| spl19_55
| spl19_6
| ~ spl19_22 ),
inference(avatar_split_clause,[],[f816,f522,f382,f846,f824,f842]) ).
fof(f856,definition,
( spl19_57
<=> sK6(sK9,sK12,sK0(sF18,sF15)) = sK6(sK9,sK13,sK0(sF18,sF15)) ),
introduced(definition,[new_symbols(definition,[spl19_57])],[avatar_definition]) ).
fof(f858,plain,
( sK6(sK9,sK12,sK0(sF18,sF15)) = sK6(sK9,sK13,sK0(sF18,sF15))
| ~ spl19_57 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f860,definition,
( spl19_58
<=> member(sK6(sK9,sK13,sK0(sF18,sF15)),sK10) ),
introduced(definition,[new_symbols(definition,[spl19_58])],[avatar_definition]) ).
fof(f862,plain,
( ~ member(sK6(sK9,sK13,sK0(sF18,sF15)),sK10)
| spl19_58 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f863,plain,
( ~ spl19_51
| spl19_57
| ~ spl19_50
| ~ spl19_58
| spl19_6
| ~ spl19_22 ),
inference(avatar_split_clause,[],[f813,f522,f382,f860,f824,f856,f828]) ).
fof(f884,plain,
( ~ subset(sK12,sK10)
| ~ member(sK0(sF18,sF15),sF16)
| spl19_50 ),
inference(resolution,[],[f826,f228]) ).
fof(f885,plain,
( ~ member(sK0(sF18,sF15),sF16)
| spl19_50 ),
inference(forward_subsumption_resolution,[],[f884,f140]) ).
fof(f886,plain,
( ~ spl19_53
| spl19_50 ),
inference(avatar_split_clause,[],[f885,f824,f837]) ).
fof(f888,plain,
( ~ subset(sF18,sF16)
| subset(sF18,sF15)
| spl19_53 ),
inference(resolution,[],[f838,f230]) ).
fof(f889,plain,
( subset(sF18,sF15)
| spl19_53 ),
inference(forward_subsumption_resolution,[],[f888,f220]) ).
fof(f892,plain,
( $false
| spl19_6
| spl19_53 ),
inference(forward_subsumption_resolution,[],[f889,f384]) ).
fof(f893,plain,
( spl19_6
| spl19_53 ),
inference(avatar_contradiction_clause,[],[f892]) ).
fof(f895,plain,
( ~ subset(sF15,sF18)
| equal_set(sF15,sF18)
| ~ spl19_6 ),
inference(resolution,[],[f383,f91]) ).
fof(f896,plain,
( equal_set(sF15,sF18)
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f895,f375]) ).
fof(f897,plain,
( $false
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f896,f157]) ).
fof(f898,plain,
~ spl19_6,
inference(avatar_contradiction_clause,[],[f897]) ).
fof(f903,plain,
( ~ subset(sK13,sK10)
| ~ member(sK0(sF18,sF15),sF17)
| spl19_58 ),
inference(resolution,[],[f862,f229]) ).
fof(f904,plain,
( ~ member(sK0(sF18,sF15),sF17)
| spl19_58 ),
inference(forward_subsumption_resolution,[],[f903,f139]) ).
fof(f905,plain,
( ~ spl19_51
| spl19_58 ),
inference(avatar_split_clause,[],[f904,f860,f828]) ).
fof(f907,plain,
( ~ subset(sF18,sF17)
| subset(sF18,sF15)
| spl19_51 ),
inference(resolution,[],[f829,f230]) ).
fof(f908,plain,
( subset(sF18,sF15)
| spl19_51 ),
inference(forward_subsumption_resolution,[],[f907,f223]) ).
fof(f911,plain,
( $false
| spl19_6
| spl19_51 ),
inference(forward_subsumption_resolution,[],[f908,f384]) ).
fof(f912,plain,
( spl19_6
| spl19_51 ),
inference(avatar_contradiction_clause,[],[f911]) ).
fof(f917,plain,
( ~ member(sK6(sK9,sK12,sK0(sF18,sF15)),sK12)
| ~ member(sK0(sF18,sF15),sF17)
| member(sK6(sK9,sK12,sK0(sF18,sF15)),sF14)
| ~ spl19_57 ),
inference(superposition,[],[f198,f858]) ).
fof(f923,plain,
( ~ member(sK6(sK9,sK12,sK0(sF18,sF15)),sK12)
| member(sK6(sK9,sK12,sK0(sF18,sF15)),sF14)
| ~ spl19_51
| ~ spl19_57 ),
inference(forward_subsumption_resolution,[],[f917,f830]) ).
fof(f925,plain,
( ~ member(sK6(sK9,sK12,sK0(sF18,sF15)),sK12)
| ~ spl19_51
| spl19_54
| ~ spl19_57 ),
inference(forward_subsumption_resolution,[],[f923,f844]) ).
fof(f928,plain,
( ~ spl19_52
| ~ spl19_51
| spl19_54
| ~ spl19_57 ),
inference(avatar_split_clause,[],[f925,f856,f842,f828,f833]) ).
fof(f1010,plain,
( ~ subset(sK12,sK12)
| ~ member(sK0(sF18,sF15),sF16)
| spl19_52 ),
inference(resolution,[],[f835,f228]) ).
fof(f1011,plain,
( ~ member(sK0(sF18,sF15),sF16)
| spl19_52 ),
inference(forward_subsumption_resolution,[],[f1010,f197]) ).
fof(f1014,plain,
( $false
| spl19_52
| ~ spl19_53 ),
inference(forward_subsumption_resolution,[],[f1011,f839]) ).
fof(f1015,plain,
( spl19_52
| ~ spl19_53 ),
inference(avatar_contradiction_clause,[],[f1014]) ).
fof(f1016,plain,
( subset(sF18,sF15)
| ~ spl19_55 ),
inference(resolution,[],[f848,f90]) ).
fof(f1021,plain,
( $false
| spl19_6
| ~ spl19_55 ),
inference(forward_subsumption_resolution,[],[f1016,f384]) ).
fof(f1022,plain,
( spl19_6
| ~ spl19_55 ),
inference(avatar_contradiction_clause,[],[f1021]) ).
cnf(s15,plain,
( spl19_21
| spl19_22 ),
inference(sat_conversion,[],[f524]) ).
cnf(s17,plain,
~ spl19_21,
inference(sat_conversion,[],[f532]) ).
cnf(s39,plain,
( spl19_6
| ~ spl19_22
| ~ spl19_50
| ~ spl19_54
| spl19_55 ),
inference(sat_conversion,[],[f849]) ).
cnf(s41,plain,
( spl19_6
| ~ spl19_22
| ~ spl19_50
| ~ spl19_51
| spl19_57
| ~ spl19_58 ),
inference(sat_conversion,[],[f863]) ).
cnf(s49,plain,
( spl19_50
| ~ spl19_53 ),
inference(sat_conversion,[],[f886]) ).
cnf(s51,plain,
( spl19_6
| spl19_53 ),
inference(sat_conversion,[],[f893]) ).
cnf(s52,plain,
~ spl19_6,
inference(sat_conversion,[],[f898]) ).
cnf(s53,plain,
( ~ spl19_51
| spl19_58 ),
inference(sat_conversion,[],[f905]) ).
cnf(s55,plain,
( spl19_6
| spl19_51 ),
inference(sat_conversion,[],[f912]) ).
cnf(s57,plain,
( ~ spl19_51
| ~ spl19_52
| spl19_54
| ~ spl19_57 ),
inference(sat_conversion,[],[f928]) ).
cnf(s66,plain,
( spl19_52
| ~ spl19_53 ),
inference(sat_conversion,[],[f1015]) ).
cnf(s67,plain,
( spl19_6
| ~ spl19_55 ),
inference(sat_conversion,[],[f1022]) ).
cnf(s68,plain,
~ spl19_55,
inference(rat,[],[s67,s52]) ).
cnf(s69,plain,
spl19_51,
inference(rat,[],[s55,s52]) ).
cnf(s70,plain,
spl19_58,
inference(rat,[],[s53,s69]) ).
cnf(s71,plain,
spl19_53,
inference(rat,[],[s51,s52]) ).
cnf(s72,plain,
spl19_52,
inference(rat,[],[s66,s71]) ).
cnf(s73,plain,
spl19_50,
inference(rat,[],[s49,s71]) ).
cnf(s79,plain,
( ~ spl19_22
| spl19_57 ),
inference(rat,[],[s41,s70,s69,s73,s52]) ).
cnf(s81,plain,
( ~ spl19_22
| ~ spl19_54 ),
inference(rat,[],[s39,s68,s73,s52]) ).
cnf(s83,plain,
spl19_22,
inference(rat,[],[s15,s17]) ).
cnf(s87,plain,
spl19_57,
inference(rat,[],[s79,s83]) ).
cnf(s89,plain,
~ spl19_54,
inference(rat,[],[s81,s83]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s57,s72,s69,s87,s89]) ).
fof(f1023,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET761+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:49:02 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.99/2.58 % (3209168)Detected formulas, will run a generic FOF schedule.
% 10.99/2.58 % (3209278)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=718303111:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.99/2.58 % (3209274)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=4115254402:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.99/2.58 % (3209277)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4165123398:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.99/2.58 % (3209276)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=626818459:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.99/2.58 % (3209277)Refutation not found, incomplete strategy
% 10.99/2.58 % (3209277)------------------------------
% 10.99/2.58 % (3209277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209277)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209277)Termination reason: Refutation not found, incomplete strategy
% 10.99/2.58 % (3209277)Time elapsed: 0.006 s
% 10.99/2.58 % (3209277)Peak memory usage: 88 MB
% 10.99/2.58 % (3209277)Instructions burned: 7 (million)
% 10.99/2.58 % (3209275)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=3721990759:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.99/2.58 % (3209280)dis-21_1_sil=8000:lcm=predicate:random_seed=2903602419: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)
% 10.99/2.58 % (3209278)Instruction limit reached!
% 10.99/2.58 % (3209278)------------------------------
% 10.99/2.58 % (3209278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209278)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209278)Termination reason: Instruction limit
% 10.99/2.58 % (3209278)Termination phase: Saturation
% 10.99/2.58 % (3209278)Time elapsed: 0.058 s
% 10.99/2.58 % (3209278)Peak memory usage: 89 MB
% 10.99/2.58 % (3209278)Instructions burned: 121 (million)
% 10.99/2.58 % (3209279)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1428729747:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.99/2.58 % (3209280)Instruction limit reached!
% 10.99/2.58 % (3209280)------------------------------
% 10.99/2.58 % (3209280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209280)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209280)Termination reason: Instruction limit
% 10.99/2.58 % (3209280)Termination phase: Saturation
% 10.99/2.58 % (3209280)Time elapsed: 0.119 s
% 10.99/2.58 % (3209280)Peak memory usage: 89 MB
% 10.99/2.58 % (3209280)Instructions burned: 130 (million)
% 10.99/2.58 % (3209279)Instruction limit reached!
% 10.99/2.58 % (3209279)------------------------------
% 10.99/2.58 % (3209279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209279)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209279)Termination reason: Instruction limit
% 10.99/2.58 % (3209279)Termination phase: Saturation
% 10.99/2.58 % (3209279)Time elapsed: 0.145 s
% 10.99/2.58 % (3209279)Peak memory usage: 89 MB
% 10.99/2.58 % (3209279)Instructions burned: 140 (million)
% 10.99/2.58 % (3209309)lrs+10_1_sil=8000:sp=occurrence:random_seed=3874075656:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.99/2.58 % (3209309)Instruction limit reached!
% 10.99/2.58 % (3209309)------------------------------
% 10.99/2.58 % (3209309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209309)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209309)Termination reason: Instruction limit
% 10.99/2.58 % (3209309)Termination phase: Saturation
% 10.99/2.58 % (3209309)Time elapsed: 0.137 s
% 10.99/2.58 % (3209309)Peak memory usage: 92 MB
% 10.99/2.58 % (3209309)Instructions burned: 286 (million)
% 10.99/2.58 % (3209277)------------------------------
% 10.99/2.58 % (3209277)------------------------------
% 10.99/2.58 % (3209318)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1659333923:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 10.99/2.58 % (3209322)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3312671947:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 10.99/2.58 % (3209318)Instruction limit reached!
% 10.99/2.58 % (3209318)------------------------------
% 10.99/2.58 % (3209318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209318)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209318)Termination reason: Instruction limit
% 10.99/2.58 % (3209318)Termination phase: Saturation
% 10.99/2.58 % (3209318)Time elapsed: 0.130 s
% 10.99/2.58 % (3209318)Peak memory usage: 90 MB
% 10.99/2.58 % (3209318)Instructions burned: 157 (million)
% 10.99/2.58 % (3209331)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=663954561:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 10.99/2.58 % (3209334)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=340655584:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 10.99/2.58 % (3209331)Instruction limit reached!
% 10.99/2.58 % (3209331)------------------------------
% 10.99/2.58 % (3209331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209331)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209331)Termination reason: Instruction limit
% 10.99/2.58 % (3209331)Termination phase: Saturation
% 10.99/2.58 % (3209331)Time elapsed: 0.118 s
% 10.99/2.58 % (3209331)Peak memory usage: 92 MB
% 10.99/2.58 % (3209331)Instructions burned: 250 (million)
% 10.99/2.58 % (3209322)Instruction limit reached!
% 10.99/2.58 % (3209322)------------------------------
% 10.99/2.58 % (3209322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209322)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209322)Termination reason: Instruction limit
% 10.99/2.58 % (3209322)Termination phase: Saturation
% 10.99/2.58 % (3209322)Time elapsed: 0.361 s
% 10.99/2.58 % (3209322)Peak memory usage: 91 MB
% 10.99/2.58 % (3209322)Instructions burned: 326 (million)
% 10.99/2.58 % (3209337)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3114707370:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 10.99/2.58 % (3209334)Instruction limit reached!
% 10.99/2.58 % (3209334)------------------------------
% 10.99/2.58 % (3209334)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209334)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209334)Termination reason: Instruction limit
% 10.99/2.58 % (3209334)Termination phase: Saturation
% 10.99/2.58 % (3209334)Time elapsed: 0.252 s
% 10.99/2.58 % (3209334)Peak memory usage: 88 MB
% 10.99/2.58 % (3209334)Instructions burned: 295 (million)
% 10.99/2.58 % (3209342)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=264901192:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 10.99/2.58 % (3209342)Instruction limit reached!
% 10.99/2.58 % (3209342)------------------------------
% 10.99/2.58 % (3209342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209342)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209342)Termination reason: Instruction limit
% 10.99/2.58 % (3209342)Termination phase: Saturation
% 10.99/2.58 % (3209342)Time elapsed: 0.065 s
% 10.99/2.58 % (3209342)Peak memory usage: 89 MB
% 10.99/2.58 % (3209342)Instructions burned: 113 (million)
% 10.99/2.58 % (3209344)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1143489322:i=127:av=off:fsr=off:sup=off_2990 on theBenchmark for (2990ds/127Mi)
% 10.99/2.58 % (3209344)Instruction limit reached!
% 10.99/2.58 % (3209344)------------------------------
% 10.99/2.58 % (3209344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209344)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209344)Termination reason: Instruction limit
% 10.99/2.58 % (3209344)Termination phase: Saturation
% 10.99/2.58 % (3209344)Time elapsed: 0.084 s
% 10.99/2.58 % (3209344)Peak memory usage: 89 MB
% 10.99/2.58 % (3209344)Instructions burned: 128 (million)
% 10.99/2.58 % (3209274)First to succeed.
% 10.99/2.58 % (3209274)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3209168"
% 10.99/2.58 % (3209350)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2074164201:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2988 on theBenchmark for (2988ds/114Mi)
% 10.99/2.58 % (3209352)lrs+10_1_sil=8000:sp=occurrence:random_seed=3371995623:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 10.99/2.58 % (3209350)Instruction limit reached!
% 10.99/2.58 % (3209350)------------------------------
% 10.99/2.58 % (3209350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.58 % (3209350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.58 % (3209350)CaDiCaL version: 2.1.3
% 10.99/2.58 % (3209350)Termination reason: Instruction limit
% 10.99/2.58 % (3209350)Termination phase: Saturation
% 10.99/2.58 % (3209350)Time elapsed: 0.122 s
% 10.99/2.58 % (3209350)Peak memory usage: 89 MB
% 10.99/2.58 % (3209350)Instructions burned: 114 (million)
% 10.99/2.58 % (3209353)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1854215298:i=437:sd=1:aac=none:ss=included_2987 on theBenchmark for (2987ds/437Mi)
% 10.99/2.58 % (3209274)Refutation found. Thanks to Tanya!
% 10.99/2.58 % SZS status Theorem for theBenchmark
% 10.99/2.58 % SZS output start Proof for theBenchmark
% See solution above
% 12.71/2.82 % (3209274)------------------------------
% 12.71/2.82 % (3209274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.71/2.82 % (3209274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.71/2.82 % (3209274)CaDiCaL version: 2.1.3
% 12.71/2.82 % (3209274)Termination reason: Refutation
% 12.71/2.82 % (3209274)Time elapsed: 1.131 s
% 12.71/2.82 % (3209274)Peak memory usage: 131 MB
% 12.71/2.82 % (3209274)Instructions burned: 1088 (million)
% 12.71/2.82 % (3209274)------------------------------
% 12.71/2.82 % (3209274)------------------------------
% 12.71/2.82 % (3209168)Success in time 1.706 s
% 12.71/2.82 % Vampire exiting
%------------------------------------------------------------------------------