%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET806+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:41:58 PM UTC 2026
% Result : Theorem 2.67s 1.26s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 122 ( 13 unt; 9 def)
% Number of atoms : 379 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 399 ( 142 ~; 148 |; 77 &)
% ( 15 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 9 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 124 !; 27 ?)
% 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(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
fof(f14,axiom,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X2,X3] :
( ( member(X2,X0)
& member(X3,X0) )
=> ( apply(X1,X2,X3)
=> apply(X1,X3,X2) ) )
& ! [X2,X3,X4] :
( ( member(X2,X0)
& member(X3,X0)
& member(X4,X0) )
=> ( ( apply(X1,X2,X3)
& apply(X1,X3,X4) )
=> apply(X1,X2,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence) ).
fof(f17,axiom,
! [X0,X1] :
( apply(equal_set_predicate,X0,X1)
<=> equal_set(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_equal_set) ).
fof(f18,conjecture,
! [X0] : equivalence(equal_set_predicate,power_set(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII13) ).
fof(f19,negated_conjecture,
~ ! [X0] : equivalence(equal_set_predicate,power_set(X0)),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X5,X6,X7] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X1,X6,X7) )
=> apply(X1,X5,X7) ) ) ) ),
inference(rectify,[],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X5,X6,X7] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X1,X6,X7) )
=> apply(X1,X5,X7) ) ) )
=> equivalence(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f24,plain,
? [X0] : ~ equivalence(equal_set_predicate,power_set(X0)),
inference(ennf_transformation,[],[f19]) ).
fof(f25,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2] :
( ~ apply(X1,X2,X2)
& member(X2,X0) )
| ? [X3,X4] :
( ~ apply(X1,X4,X3)
& apply(X1,X3,X4)
& member(X3,X0)
& member(X4,X0) )
| ? [X5,X6,X7] :
( ~ apply(X1,X5,X7)
& apply(X1,X5,X6)
& apply(X1,X6,X7)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2] :
( ~ apply(X1,X2,X2)
& member(X2,X0) )
| ? [X3,X4] :
( ~ apply(X1,X4,X3)
& apply(X1,X3,X4)
& member(X3,X0)
& member(X4,X0) )
| ? [X5,X6,X7] :
( ~ apply(X1,X5,X7)
& apply(X1,X5,X6)
& apply(X1,X6,X7)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,definition,
! [X1,X0] :
( ? [X5,X6,X7] :
( ~ apply(X1,X5,X7)
& apply(X1,X5,X6)
& apply(X1,X6,X7)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
| ~ sP0(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f29,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2] :
( ~ apply(X1,X2,X2)
& member(X2,X0) )
| ? [X3,X4] :
( ~ apply(X1,X4,X3)
& apply(X1,X3,X4)
& member(X3,X0)
& member(X4,X0) )
| sP0(X1,X0) ),
inference(definition_folding,[],[f26,f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( apply(equal_set_predicate,X0,X1)
| ~ equal_set(X0,X1) )
& ( equal_set(X0,X1)
| ~ apply(equal_set_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f31,plain,
~ equivalence(equal_set_predicate,power_set(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f24]) ).
fof(f32,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f32]) ).
fof(f36,plain,
! [X1,X0] :
( ? [X5,X6,X7] :
( ~ apply(X1,X5,X7)
& apply(X1,X5,X6)
& apply(X1,X6,X7)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f28]) ).
fof(f37,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X2,X3)
& apply(X0,X3,X4)
& member(X2,X1)
& member(X3,X1)
& member(X4,X1) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ( ~ apply(X0,sK2(X0,X1),sK4(X0,X1))
& apply(X0,sK2(X0,X1),sK3(X0,X1))
& apply(X0,sK3(X0,X1),sK4(X0,X1))
& member(sK2(X0,X1),X1)
& member(sK3(X0,X1),X1)
& member(sK4(X0,X1),X1) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1)),skolemize(X4,sK4(X0,X1))],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ( ~ apply(X1,sK5(X0,X1),sK5(X0,X1))
& member(sK5(X0,X1),X0) )
| ( ~ apply(X1,sK7(X0,X1),sK6(X0,X1))
& apply(X1,sK6(X0,X1),sK7(X0,X1))
& member(sK6(X0,X1),X0)
& member(sK7(X0,X1),X0) )
| sP0(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1)),skolemize(X4,sK7(X0,X1))],[f29]) ).
fof(f40,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f41,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,[],[f27]) ).
fof(f42,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,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK8(X0,X1),X1)
& member(sK8(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| apply(equal_set_predicate,X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
~ equivalence(equal_set_predicate,power_set(sK1)),
inference(cnf_transformation,[],[f31]) ).
fof(f50,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f59,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK3(X0,X1),sK4(X0,X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f60,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK2(X0,X1),sK3(X0,X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK2(X0,X1),sK4(X0,X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f68,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ~ apply(X1,sK5(X0,X1),sK5(X0,X1))
| apply(X1,sK6(X0,X1),sK7(X0,X1))
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f69,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ~ apply(X1,sK5(X0,X1),sK5(X0,X1))
| ~ apply(X1,sK7(X0,X1),sK6(X0,X1))
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f70,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f71,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f72,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f73,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f74,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f88,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(resolution,[],[f47,f51]) ).
fof(f89,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(resolution,[],[f47,f50]) ).
fof(f94,plain,
! [X0,X1] :
( member(sK8(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f73,f71]) ).
fof(f95,plain,
! [X0,X1] :
( ~ member(sK8(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f74,f71]) ).
fof(f96,plain,
! [X0,X1] :
( apply(equal_set_predicate,X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(resolution,[],[f52,f48]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ apply(equal_set_predicate,X2,X1)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[],[f72,f89]) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ apply(equal_set_predicate,X1,X2)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[],[f72,f88]) ).
fof(f107,plain,
! [X0] :
( member(X0,power_set(X0))
| member(X0,power_set(X0)) ),
inference(resolution,[],[f95,f94]) ).
fof(f108,plain,
! [X0] : member(X0,power_set(X0)),
inference(duplicate_literal_removal,[],[f107]) ).
fof(f119,definition,
( spl10_1
<=> sP0(equal_set_predicate,power_set(sK1)) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f120,plain,
( sP0(equal_set_predicate,power_set(sK1))
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f152,definition,
( spl10_5
<=> apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
fof(f153,plain,
( ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| spl10_5 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( ~ subset(sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| ~ subset(sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| spl10_5 ),
inference(resolution,[],[f153,f96]) ).
fof(f157,plain,
( ~ subset(sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| spl10_5 ),
inference(duplicate_literal_removal,[],[f155]) ).
fof(f166,plain,
( ~ member(sK5(power_set(sK1),equal_set_predicate),power_set(sK5(power_set(sK1),equal_set_predicate)))
| spl10_5 ),
inference(resolution,[],[f157,f70]) ).
fof(f167,plain,
( $false
| spl10_5 ),
inference(resolution,[],[f166,f108]) ).
fof(f171,plain,
spl10_5,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f172,plain,
( ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| sP0(equal_set_predicate,power_set(sK1)) ),
inference(resolution,[],[f68,f49]) ).
fof(f174,definition,
( spl10_6
<=> apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate)) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f175,plain,
( apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f176,plain,
( spl10_1
| spl10_6
| ~ spl10_5 ),
inference(avatar_split_clause,[],[f172,f152,f174,f119]) ).
fof(f178,plain,
( apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK3(equal_set_predicate,power_set(sK1)))
| ~ spl10_1 ),
inference(resolution,[],[f120,f60]) ).
fof(f179,plain,
( apply(equal_set_predicate,sK3(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1)))
| ~ spl10_1 ),
inference(resolution,[],[f120,f59]) ).
fof(f186,definition,
( spl10_7
<=> subset(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
fof(f187,plain,
( ~ subset(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1)))
| spl10_7 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f189,definition,
( spl10_8
<=> subset(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
fof(f190,plain,
( ~ subset(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1)))
| spl10_8 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f192,plain,
( ! [X0] :
( member(X0,sK3(equal_set_predicate,power_set(sK1)))
| ~ member(X0,sK2(equal_set_predicate,power_set(sK1))) )
| ~ spl10_1 ),
inference(resolution,[],[f178,f102]) ).
fof(f197,plain,
( ~ member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| spl10_7 ),
inference(resolution,[],[f187,f74]) ).
fof(f198,plain,
( member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| spl10_7 ),
inference(resolution,[],[f187,f73]) ).
fof(f202,plain,
( ! [X0] :
( member(X0,sK4(equal_set_predicate,power_set(sK1)))
| ~ member(X0,sK3(equal_set_predicate,power_set(sK1))) )
| ~ spl10_1 ),
inference(resolution,[],[f179,f102]) ).
fof(f247,plain,
( ~ member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK3(equal_set_predicate,power_set(sK1)))
| ~ spl10_1
| spl10_7 ),
inference(resolution,[],[f197,f202]) ).
fof(f266,plain,
( ~ member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| ~ spl10_1
| spl10_7 ),
inference(resolution,[],[f247,f192]) ).
fof(f272,plain,
( ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| sP0(equal_set_predicate,power_set(sK1)) ),
inference(resolution,[],[f69,f49]) ).
fof(f273,plain,
( $false
| ~ spl10_1
| spl10_7 ),
inference(resolution,[],[f266,f198]) ).
fof(f281,plain,
( ~ spl10_1
| spl10_7 ),
inference(avatar_contradiction_clause,[],[f273]) ).
fof(f283,definition,
( spl10_9
<=> apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate)) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
fof(f284,plain,
( ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| spl10_9 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f285,plain,
( spl10_1
| ~ spl10_9
| ~ spl10_5 ),
inference(avatar_split_clause,[],[f272,f152,f283,f119]) ).
fof(f291,plain,
( ~ subset(sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| ~ subset(sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| spl10_9 ),
inference(resolution,[],[f284,f96]) ).
fof(f294,definition,
( spl10_10
<=> subset(sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate)) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
fof(f295,plain,
( ~ subset(sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| spl10_10 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f297,definition,
( spl10_11
<=> subset(sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate)) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
fof(f298,plain,
( ~ subset(sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| spl10_11 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( ~ spl10_10
| ~ spl10_11
| spl10_9 ),
inference(avatar_split_clause,[],[f291,f283,f297,f294]) ).
fof(f302,plain,
( ~ apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| spl10_10 ),
inference(resolution,[],[f295,f89]) ).
fof(f312,plain,
( $false
| ~ spl10_6
| spl10_10 ),
inference(resolution,[],[f302,f175]) ).
fof(f315,plain,
( ~ spl10_6
| spl10_10 ),
inference(avatar_contradiction_clause,[],[f312]) ).
fof(f319,plain,
( ~ apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| spl10_11 ),
inference(resolution,[],[f298,f88]) ).
fof(f321,plain,
( $false
| ~ spl10_6
| spl10_11 ),
inference(resolution,[],[f319,f175]) ).
fof(f324,plain,
( ~ spl10_6
| spl10_11 ),
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f325,plain,
( ~ apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1)))
| ~ spl10_1 ),
inference(resolution,[],[f120,f61]) ).
fof(f326,plain,
( apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK3(equal_set_predicate,power_set(sK1)))
| ~ spl10_1 ),
inference(resolution,[],[f120,f60]) ).
fof(f327,plain,
( apply(equal_set_predicate,sK3(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1)))
| ~ spl10_1 ),
inference(resolution,[],[f120,f59]) ).
fof(f331,plain,
( ~ subset(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1)))
| ~ subset(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1)))
| ~ spl10_1 ),
inference(resolution,[],[f325,f96]) ).
fof(f333,plain,
( ~ spl10_7
| ~ spl10_8
| ~ spl10_1 ),
inference(avatar_split_clause,[],[f331,f119,f189,f186]) ).
fof(f338,plain,
( ~ member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| spl10_8 ),
inference(resolution,[],[f190,f74]) ).
fof(f339,plain,
( member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| spl10_8 ),
inference(resolution,[],[f190,f73]) ).
fof(f344,plain,
( ! [X0] :
( ~ member(X0,sK3(equal_set_predicate,power_set(sK1)))
| member(X0,sK2(equal_set_predicate,power_set(sK1))) )
| ~ spl10_1 ),
inference(resolution,[],[f326,f101]) ).
fof(f349,plain,
( ! [X0] :
( ~ member(X0,sK4(equal_set_predicate,power_set(sK1)))
| member(X0,sK3(equal_set_predicate,power_set(sK1))) )
| ~ spl10_1 ),
inference(resolution,[],[f327,f101]) ).
fof(f414,plain,
( member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK3(equal_set_predicate,power_set(sK1)))
| ~ spl10_1
| spl10_8 ),
inference(resolution,[],[f339,f349]) ).
fof(f432,plain,
( member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| ~ spl10_1
| spl10_8 ),
inference(resolution,[],[f414,f344]) ).
fof(f435,plain,
( $false
| ~ spl10_1
| spl10_8 ),
inference(resolution,[],[f432,f338]) ).
fof(f437,plain,
( ~ spl10_1
| spl10_8 ),
inference(avatar_contradiction_clause,[],[f435]) ).
cnf(s4,plain,
spl10_5,
inference(sat_conversion,[],[f171]) ).
cnf(s5,plain,
( spl10_1
| ~ spl10_5
| spl10_6 ),
inference(sat_conversion,[],[f176]) ).
cnf(s7,plain,
( ~ spl10_1
| spl10_7 ),
inference(sat_conversion,[],[f281]) ).
cnf(s8,plain,
( spl10_1
| ~ spl10_5
| ~ spl10_9 ),
inference(sat_conversion,[],[f285]) ).
cnf(s9,plain,
( spl10_9
| ~ spl10_10
| ~ spl10_11 ),
inference(sat_conversion,[],[f299]) ).
cnf(s10,plain,
( ~ spl10_6
| spl10_10 ),
inference(sat_conversion,[],[f315]) ).
cnf(s11,plain,
( ~ spl10_6
| spl10_11 ),
inference(sat_conversion,[],[f324]) ).
cnf(s12,plain,
( ~ spl10_1
| ~ spl10_7
| ~ spl10_8 ),
inference(sat_conversion,[],[f333]) ).
cnf(s13,plain,
( ~ spl10_1
| spl10_8 ),
inference(sat_conversion,[],[f437]) ).
cnf(s15,plain,
spl10_1,
inference(rat,[],[s9,s10,s11,s5,s8,s4]) ).
cnf(s16,plain,
spl10_8,
inference(rat,[],[s13,s15]) ).
cnf(s17,plain,
~ spl10_7,
inference(rat,[],[s12,s16,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s7,s17,s15]) ).
fof(f438,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET806+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.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 02:53:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.67/1.26 % (2947128)Detected formulas, will run a generic FOF schedule.
% 2.67/1.26 % (2947134)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=3434214681:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.26 % (2947133)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=2610779010:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.26 % (2947138)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2787888337:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.26 % (2947137)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=577737256:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.26 % (2947139)dis-21_1_sil=8000:lcm=predicate:random_seed=1760746222:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.67/1.26 % (2947136)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=66453781:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.26 % (2947135)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=2132899139:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.26 % (2947136)Refutation not found, incomplete strategy
% 2.67/1.26 % (2947136)------------------------------
% 2.67/1.26 % (2947136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.26 % (2947136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.26 % (2947136)CaDiCaL version: 2.1.3
% 2.67/1.26 % (2947136)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.26 % (2947136)Time elapsed: 0.002 s
% 2.67/1.26 % (2947136)Peak memory usage: 88 MB
% 2.67/1.26 % (2947136)Instructions burned: 3 (million)
% 2.67/1.26 % (2947139)First to succeed.
% 2.67/1.26 % (2947139)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2947128"
% 2.67/1.26 % (2947137)Instruction limit reached!
% 2.67/1.26 % (2947137)------------------------------
% 2.67/1.26 % (2947137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.26 % (2947137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.26 % (2947137)CaDiCaL version: 2.1.3
% 2.67/1.26 % (2947137)Termination reason: Instruction limit
% 2.67/1.26 % (2947137)Termination phase: Saturation
% 2.67/1.26 % (2947137)Time elapsed: 0.066 s
% 2.67/1.26 % (2947137)Peak memory usage: 88 MB
% 2.67/1.26 % (2947137)Instructions burned: 120 (million)
% 2.67/1.26 % (2947138)Instruction limit reached!
% 2.67/1.26 % (2947138)------------------------------
% 2.67/1.26 % (2947138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.26 % (2947138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.26 % (2947138)CaDiCaL version: 2.1.3
% 2.67/1.26 % (2947138)Termination reason: Instruction limit
% 2.67/1.26 % (2947138)Termination phase: Saturation
% 2.67/1.26 % (2947138)Time elapsed: 0.099 s
% 2.67/1.26 % (2947138)Peak memory usage: 89 MB
% 2.67/1.26 % (2947138)Instructions burned: 139 (million)
% 2.67/1.26 % (2947147)lrs+10_1_sil=8000:sp=occurrence:random_seed=2025156400:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.67/1.26 % (2947148)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2300821254:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.67/1.26 % (2947148)Refutation not found, incomplete strategy
% 2.67/1.26 % (2947148)------------------------------
% 2.67/1.26 % (2947148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.26 % (2947148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.26 % (2947148)CaDiCaL version: 2.1.3
% 2.67/1.26 % (2947148)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.26 % (2947148)Time elapsed: 0.001 s
% 2.67/1.26 % (2947148)Peak memory usage: 88 MB
% 2.67/1.26 % (2947148)Instructions burned: 1 (million)
% 2.67/1.26 % (2947136)------------------------------
% 2.67/1.26 % (2947136)------------------------------
% 2.67/1.26 % (2947139)Refutation found. Thanks to Tanya!
% 2.67/1.26 % SZS status Theorem for theBenchmark
% 2.67/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.36 % (2947139)------------------------------
% 3.42/1.36 % (2947139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.36 % (2947139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.36 % (2947139)CaDiCaL version: 2.1.3
% 3.42/1.36 % (2947139)Termination reason: Refutation
% 3.42/1.36 % (2947139)Time elapsed: 0.010 s
% 3.42/1.36 % (2947139)Peak memory usage: 89 MB
% 3.42/1.36 % (2947139)Instructions burned: 13 (million)
% 3.42/1.36 % (2947139)------------------------------
% 3.42/1.36 % (2947139)------------------------------
% 3.42/1.36 % (2947128)Success in time 0.414 s
% 3.42/1.36 % Vampire exiting
%------------------------------------------------------------------------------