%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:41:25 PM UTC 2026
% Result : Theorem 2.16s 1.32s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 138 ( 14 unt; 15 def)
% Number of atoms : 344 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 353 ( 147 ~; 159 |; 25 &)
% ( 21 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 97 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f6,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f15,conjecture,
! [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) = union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th98) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) = union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f18,plain,
? [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) != union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
inference(ennf_transformation,[],[f16]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f25]) ).
fof(f30,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,[],[f17]) ).
fof(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f31]) ).
fof(f33,plain,
difference(sK2,symmetric_difference(sK3,sK4)) != union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f18]) ).
fof(f36,plain,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f58,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f59,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f61,plain,
difference(sK2,symmetric_difference(sK3,sK4)) != union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),
inference(cnf_transformation,[],[f33]) ).
fof(f64,plain,
union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)) != difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),
inference(definition_unfolding,[],[f61,f36]) ).
fof(f69,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f73,plain,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f49,f69]) ).
fof(f79,plain,
~ sQ5_eqProxy(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),
inference(equality_proxy_replacement,[],[f64,f69]) ).
fof(f81,plain,
! [X0,X1] :
( sQ5_eqProxy(X1,X0)
| ~ sQ5_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f69]) ).
fof(f82,plain,
~ sQ5_eqProxy(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),
inference(resolution,[],[f81,f79]) ).
fof(f88,plain,
( ~ subset(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)))
| ~ subset(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))) ),
inference(resolution,[],[f73,f82]) ).
fof(f90,definition,
( spl6_1
<=> subset(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f91,plain,
( ~ subset(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))))
| spl6_1 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl6_2
<=> subset(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f94,plain,
( ~ subset(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)))
| spl6_2 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f95,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f88,f93,f90]) ).
fof(f103,definition,
( spl6_3
<=> member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),difference(sK2,union(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f104,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),difference(sK2,union(sK3,sK4)))
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,definition,
( spl6_4
<=> member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),intersection(intersection(sK2,sK3),sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f107,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),intersection(intersection(sK2,sK3),sK4))
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)))
| spl6_2 ),
inference(resolution,[],[f94,f59]) ).
fof(f110,plain,
( member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))))
| spl6_2 ),
inference(resolution,[],[f94,f58]) ).
fof(f111,plain,
( member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK2)
| spl6_2 ),
inference(resolution,[],[f110,f44]) ).
fof(f112,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),difference(union(sK3,sK4),intersection(sK3,sK4)))
| spl6_2 ),
inference(resolution,[],[f110,f43]) ).
fof(f113,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),difference(sK2,union(sK3,sK4)))
| spl6_2 ),
inference(resolution,[],[f109,f39]) ).
fof(f114,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),intersection(intersection(sK2,sK3),sK4))
| spl6_2 ),
inference(resolution,[],[f109,f38]) ).
fof(f117,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),intersection(sK2,sK3))
| ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK4)
| spl6_2 ),
inference(resolution,[],[f42,f114]) ).
fof(f119,definition,
( spl6_5
<=> member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f122,definition,
( spl6_6
<=> member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),intersection(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f123,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),intersection(sK2,sK3))
| spl6_6 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( ~ spl6_5
| ~ spl6_6
| spl6_2 ),
inference(avatar_split_clause,[],[f117,f93,f122,f119]) ).
fof(f127,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK2)
| member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),union(sK3,sK4))
| spl6_2 ),
inference(resolution,[],[f45,f113]) ).
fof(f128,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),union(sK3,sK4))
| member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),intersection(sK3,sK4))
| spl6_2 ),
inference(resolution,[],[f45,f112]) ).
fof(f130,definition,
( spl6_7
<=> member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),intersection(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f131,plain,
( member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),intersection(sK3,sK4))
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,definition,
( spl6_8
<=> member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),union(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
fof(f135,plain,
( spl6_7
| ~ spl6_8
| spl6_2 ),
inference(avatar_split_clause,[],[f128,f93,f133,f130]) ).
fof(f138,definition,
( spl6_9
<=> member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
fof(f139,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK2)
| spl6_9 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f140,plain,
( spl6_8
| ~ spl6_9
| spl6_2 ),
inference(avatar_split_clause,[],[f127,f93,f138,f133]) ).
fof(f141,plain,
( $false
| spl6_2
| spl6_9 ),
inference(resolution,[],[f139,f111]) ).
fof(f142,plain,
( spl6_2
| spl6_9 ),
inference(avatar_contradiction_clause,[],[f141]) ).
fof(f143,plain,
( member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK3)
| ~ spl6_7 ),
inference(resolution,[],[f131,f41]) ).
fof(f144,plain,
( member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK4)
| ~ spl6_7 ),
inference(resolution,[],[f131,f40]) ).
fof(f147,definition,
( spl6_10
<=> member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK3) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
fof(f155,definition,
( spl6_11
<=> member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),difference(union(sK3,sK4),intersection(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
fof(f156,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),difference(union(sK3,sK4),intersection(sK3,sK4)))
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,definition,
( spl6_12
<=> member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition]) ).
fof(f159,plain,
( ~ member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK2)
| spl6_12 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f163,plain,
( spl6_10
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f143,f130,f147]) ).
fof(f164,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),intersection(sK2,sK3))
| ~ spl6_4 ),
inference(resolution,[],[f107,f41]) ).
fof(f165,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK4)
| ~ spl6_4 ),
inference(resolution,[],[f107,f40]) ).
fof(f168,plain,
( spl6_5
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f144,f130,f119]) ).
fof(f169,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK2)
| ~ spl6_4 ),
inference(resolution,[],[f164,f41]) ).
fof(f170,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK3)
| ~ spl6_4 ),
inference(resolution,[],[f164,f40]) ).
fof(f173,plain,
( $false
| ~ spl6_4
| spl6_12 ),
inference(resolution,[],[f169,f159]) ).
fof(f174,plain,
( ~ spl6_4
| spl6_12 ),
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f175,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK2)
| ~ spl6_3 ),
inference(resolution,[],[f104,f44]) ).
fof(f176,plain,
( ~ member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),union(sK3,sK4))
| ~ spl6_3 ),
inference(resolution,[],[f104,f43]) ).
fof(f177,plain,
( $false
| ~ spl6_3
| spl6_12 ),
inference(resolution,[],[f175,f159]) ).
fof(f178,plain,
( ~ spl6_3
| spl6_12 ),
inference(avatar_contradiction_clause,[],[f177]) ).
fof(f181,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),union(sK3,sK4))
| ~ spl6_11 ),
inference(resolution,[],[f156,f44]) ).
fof(f182,plain,
( ~ member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),intersection(sK3,sK4))
| ~ spl6_11 ),
inference(resolution,[],[f156,f43]) ).
fof(f186,plain,
( ~ member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK3)
| ~ member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK4)
| ~ spl6_11 ),
inference(resolution,[],[f182,f42]) ).
fof(f188,definition,
( spl6_13
<=> member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition]) ).
fof(f189,plain,
( ~ member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK4)
| spl6_13 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,definition,
( spl6_14
<=> member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK3) ),
introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition]) ).
fof(f192,plain,
( ~ member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK3)
| spl6_14 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f193,plain,
( ~ spl6_13
| ~ spl6_14
| ~ spl6_11 ),
inference(avatar_split_clause,[],[f186,f155,f191,f188]) ).
fof(f194,plain,
( $false
| ~ spl6_4
| spl6_13 ),
inference(resolution,[],[f189,f165]) ).
fof(f195,plain,
( ~ spl6_4
| spl6_13 ),
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f196,plain,
( $false
| ~ spl6_4
| spl6_14 ),
inference(resolution,[],[f192,f170]) ).
fof(f197,plain,
( ~ spl6_4
| spl6_14 ),
inference(avatar_contradiction_clause,[],[f196]) ).
fof(f213,plain,
( ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK2)
| ~ member(sK1(difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4))),sK3)
| spl6_6 ),
inference(resolution,[],[f123,f42]) ).
fof(f216,plain,
( ~ spl6_10
| ~ spl6_9
| spl6_6 ),
inference(avatar_split_clause,[],[f213,f122,f138,f147]) ).
fof(f217,plain,
( ~ member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))))
| spl6_1 ),
inference(resolution,[],[f91,f59]) ).
fof(f218,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)))
| spl6_1 ),
inference(resolution,[],[f91,f58]) ).
fof(f219,plain,
( ~ member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),sK2)
| member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),difference(union(sK3,sK4),intersection(sK3,sK4)))
| spl6_1 ),
inference(resolution,[],[f217,f45]) ).
fof(f221,plain,
( spl6_11
| ~ spl6_12
| spl6_1 ),
inference(avatar_split_clause,[],[f219,f90,f158,f155]) ).
fof(f223,plain,
( member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),intersection(intersection(sK2,sK3),sK4))
| member(sK1(union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4)))),difference(sK2,union(sK3,sK4)))
| spl6_1 ),
inference(resolution,[],[f218,f37]) ).
fof(f224,plain,
( spl6_3
| spl6_4
| spl6_1 ),
inference(avatar_split_clause,[],[f223,f90,f106,f103]) ).
fof(f283,plain,
( $false
| ~ spl6_3
| ~ spl6_11 ),
inference(resolution,[],[f181,f176]) ).
fof(f285,plain,
( ~ spl6_3
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[],[f283]) ).
cnf(s1,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f95]) ).
cnf(s4,plain,
( spl6_2
| ~ spl6_5
| ~ spl6_6 ),
inference(sat_conversion,[],[f124]) ).
cnf(s5,plain,
( spl6_2
| spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f135]) ).
cnf(s6,plain,
( spl6_2
| spl6_8
| ~ spl6_9 ),
inference(sat_conversion,[],[f140]) ).
cnf(s7,plain,
( spl6_2
| spl6_9 ),
inference(sat_conversion,[],[f142]) ).
cnf(s11,plain,
( ~ spl6_7
| spl6_10 ),
inference(sat_conversion,[],[f163]) ).
cnf(s12,plain,
( spl6_5
| ~ spl6_7 ),
inference(sat_conversion,[],[f168]) ).
cnf(s14,plain,
( ~ spl6_4
| spl6_12 ),
inference(sat_conversion,[],[f174]) ).
cnf(s15,plain,
( ~ spl6_3
| spl6_12 ),
inference(sat_conversion,[],[f178]) ).
cnf(s16,plain,
( ~ spl6_11
| ~ spl6_13
| ~ spl6_14 ),
inference(sat_conversion,[],[f193]) ).
cnf(s17,plain,
( ~ spl6_4
| spl6_13 ),
inference(sat_conversion,[],[f195]) ).
cnf(s18,plain,
( ~ spl6_4
| spl6_14 ),
inference(sat_conversion,[],[f197]) ).
cnf(s22,plain,
( spl6_6
| ~ spl6_9
| ~ spl6_10 ),
inference(sat_conversion,[],[f216]) ).
cnf(s23,plain,
( spl6_1
| spl6_11
| ~ spl6_12 ),
inference(sat_conversion,[],[f221]) ).
cnf(s24,plain,
( spl6_1
| spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f224]) ).
cnf(s30,plain,
( ~ spl6_3
| ~ spl6_11 ),
inference(sat_conversion,[],[f285]) ).
cnf(s32,plain,
( spl6_2
| ~ spl6_9 ),
inference(rat,[],[s22,s4,s11,s12,s5,s6]) ).
cnf(s33,plain,
spl6_2,
inference(rat,[],[s32,s7]) ).
cnf(s34,plain,
( ~ spl6_4
| spl6_1 ),
inference(rat,[],[s23,s16,s14,s17,s18]) ).
cnf(s35,plain,
( spl6_4
| spl6_1 ),
inference(rat,[],[s23,s15,s30,s24]) ).
cnf(s36,plain,
spl6_1,
inference(rat,[],[s35,s34]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s1,s33,s36]) ).
fof(f289,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:19:45 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.16/1.32 % (1967612)Detected formulas, will run a generic FOF schedule.
% 2.16/1.32 % (1967620)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3085621255:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.16/1.32 % (1967620)Refutation not found, incomplete strategy
% 2.16/1.32 % (1967620)------------------------------
% 2.16/1.32 % (1967620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.16/1.32 % (1967620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/1.32 % (1967620)CaDiCaL version: 2.1.3
% 2.16/1.32 % (1967620)Termination reason: Refutation not found, incomplete strategy
% 2.16/1.32 % (1967620)Time elapsed: 0.001 s
% 2.16/1.32 % (1967620)Peak memory usage: 88 MB
% 2.16/1.32 % (1967620)Instructions burned: 1 (million)
% 2.16/1.32 % (1967621)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2866980555:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.16/1.32 % (1967618)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=850116616:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.16/1.32 % (1967619)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=1729975512:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.16/1.32 % (1967623)dis-21_1_sil=8000:lcm=predicate:random_seed=4119639695: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)
% 2.16/1.32 % (1967617)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=1337992625:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.16/1.32 % (1967622)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1312572169:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.16/1.32 % (1967623)First to succeed.
% 2.16/1.32 % (1967623)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1967612"
% 2.16/1.32 % (1967621)Also succeeded, but the first one will report.
% 2.16/1.32 % (1967622)Also succeeded, but the first one will report.
% 2.16/1.32 % (1967620)------------------------------
% 2.16/1.32 % (1967620)------------------------------
% 2.16/1.32 % (1967631)lrs+10_1_sil=8000:sp=occurrence:random_seed=2479624084:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.16/1.32 % (1967623)Refutation found. Thanks to Tanya!
% 2.16/1.32 % SZS status Theorem for theBenchmark
% 2.16/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.86/1.52 % (1967623)------------------------------
% 3.86/1.52 % (1967623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.52 % (1967623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.52 % (1967623)CaDiCaL version: 2.1.3
% 3.86/1.52 % (1967623)Termination reason: Refutation
% 3.86/1.52 % (1967623)Time elapsed: 0.008 s
% 3.86/1.52 % (1967623)Peak memory usage: 89 MB
% 3.86/1.52 % (1967623)Instructions burned: 10 (million)
% 3.86/1.52 % (1967623)------------------------------
% 3.86/1.52 % (1967623)------------------------------
% 3.86/1.52 % (1967612)Success in time 0.449 s
% 3.86/1.52 % Vampire exiting
%------------------------------------------------------------------------------