%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:41:29 PM UTC 2026
% Result : Theorem 2.69s 1.25s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 106 ( 14 unt; 11 def)
% Number of atoms : 263 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 254 ( 97 ~; 119 |; 21 &)
% ( 16 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 73 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f12,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f16,conjecture,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th117) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),intersection(X0,X2)),
inference(ennf_transformation,[],[f17]) ).
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,[],[f6]) ).
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,[],[f7]) ).
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(f27,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,[],[f18]) ).
fof(f28,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,[],[f27]) ).
fof(f29,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))],[f28]) ).
fof(f33,plain,
intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f19]) ).
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(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f60,plain,
intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
inference(cnf_transformation,[],[f33]) ).
fof(f65,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f71,plain,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f48,f65]) ).
fof(f76,plain,
~ sQ5_eqProxy(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),
inference(equality_proxy_replacement,[],[f60,f65]) ).
fof(f88,plain,
( ~ subset(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4)))
| ~ subset(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))) ),
inference(resolution,[],[f71,f76]) ).
fof(f93,definition,
( spl6_1
<=> subset(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f94,plain,
( ~ subset(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4)))
| spl6_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl6_2
<=> subset(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f97,plain,
( ~ subset(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4)))
| spl6_2 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( ~ spl6_2
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f88,f93,f96]) ).
fof(f101,plain,
( member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),intersection(sK2,difference(sK3,sK4)))
| spl6_1 ),
inference(resolution,[],[f94,f53]) ).
fof(f102,plain,
( member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK2)
| spl6_1 ),
inference(resolution,[],[f101,f41]) ).
fof(f103,plain,
( member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),difference(sK3,sK4))
| spl6_1 ),
inference(resolution,[],[f101,f40]) ).
fof(f104,plain,
( member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK3)
| spl6_1 ),
inference(resolution,[],[f103,f44]) ).
fof(f112,definition,
( spl6_3
<=> member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),intersection(sK2,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f113,plain,
( member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),intersection(sK2,sK4))
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,definition,
( spl6_4
<=> member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),intersection(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f116,plain,
( ~ member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),intersection(sK2,sK3))
| spl6_4 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( ~ member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK2)
| ~ member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK3)
| spl6_4 ),
inference(resolution,[],[f116,f42]) ).
fof(f120,definition,
( spl6_5
<=> member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK3) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f121,plain,
( ~ member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK3)
| spl6_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,definition,
( spl6_6
<=> member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f124,plain,
( ~ member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK2)
| spl6_6 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( ~ spl6_5
| ~ spl6_6
| spl6_4 ),
inference(avatar_split_clause,[],[f118,f115,f123,f120]) ).
fof(f126,plain,
( $false
| spl6_1
| spl6_5 ),
inference(resolution,[],[f121,f104]) ).
fof(f127,plain,
( spl6_1
| spl6_5 ),
inference(avatar_contradiction_clause,[],[f126]) ).
fof(f128,plain,
( $false
| spl6_1
| spl6_6 ),
inference(resolution,[],[f124,f102]) ).
fof(f129,plain,
( spl6_1
| spl6_6 ),
inference(avatar_contradiction_clause,[],[f128]) ).
fof(f130,plain,
( ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),intersection(sK2,difference(sK3,sK4)))
| spl6_2 ),
inference(resolution,[],[f97,f54]) ).
fof(f131,plain,
( member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),difference(intersection(sK2,sK3),intersection(sK2,sK4)))
| spl6_2 ),
inference(resolution,[],[f97,f53]) ).
fof(f132,plain,
( ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK2)
| ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),difference(sK3,sK4))
| spl6_2 ),
inference(resolution,[],[f130,f42]) ).
fof(f134,definition,
( spl6_7
<=> member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),difference(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f135,plain,
( ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),difference(sK3,sK4))
| spl6_7 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl6_8
<=> member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
fof(f138,plain,
( ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK2)
| spl6_8 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( ~ spl6_7
| ~ spl6_8
| spl6_2 ),
inference(avatar_split_clause,[],[f132,f96,f137,f134]) ).
fof(f140,plain,
( member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),intersection(sK2,sK3))
| spl6_2 ),
inference(resolution,[],[f131,f44]) ).
fof(f141,plain,
( ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),intersection(sK2,sK4))
| spl6_2 ),
inference(resolution,[],[f131,f43]) ).
fof(f142,plain,
( ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK3)
| member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK4)
| spl6_7 ),
inference(resolution,[],[f135,f45]) ).
fof(f144,definition,
( spl6_9
<=> member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
fof(f147,definition,
( spl6_10
<=> member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK3) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
fof(f148,plain,
( ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK3)
| spl6_10 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f149,plain,
( spl6_9
| ~ spl6_10
| spl6_7 ),
inference(avatar_split_clause,[],[f142,f134,f147,f144]) ).
fof(f150,plain,
( member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK2)
| spl6_2 ),
inference(resolution,[],[f140,f41]) ).
fof(f151,plain,
( member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK3)
| spl6_2 ),
inference(resolution,[],[f140,f40]) ).
fof(f152,plain,
( ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK2)
| ~ member(sK0(difference(intersection(sK2,sK3),intersection(sK2,sK4)),intersection(sK2,difference(sK3,sK4))),sK4)
| spl6_2 ),
inference(resolution,[],[f141,f42]) ).
fof(f154,plain,
( ~ spl6_9
| ~ spl6_8
| spl6_2 ),
inference(avatar_split_clause,[],[f152,f96,f137,f144]) ).
fof(f155,plain,
( $false
| spl6_2
| spl6_8 ),
inference(resolution,[],[f150,f138]) ).
fof(f156,plain,
( spl6_2
| spl6_8 ),
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f157,plain,
( $false
| spl6_2
| spl6_10 ),
inference(resolution,[],[f151,f148]) ).
fof(f158,plain,
( spl6_2
| spl6_10 ),
inference(avatar_contradiction_clause,[],[f157]) ).
fof(f159,plain,
( ~ member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),difference(intersection(sK2,sK3),intersection(sK2,sK4)))
| spl6_1 ),
inference(resolution,[],[f94,f54]) ).
fof(f160,plain,
( member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),intersection(sK2,difference(sK3,sK4)))
| spl6_1 ),
inference(resolution,[],[f94,f53]) ).
fof(f162,plain,
( member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),difference(sK3,sK4))
| spl6_1 ),
inference(resolution,[],[f160,f40]) ).
fof(f169,plain,
( ~ member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),intersection(sK2,sK3))
| member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),intersection(sK2,sK4))
| spl6_1 ),
inference(resolution,[],[f159,f45]) ).
fof(f171,plain,
( spl6_3
| ~ spl6_4
| spl6_1 ),
inference(avatar_split_clause,[],[f169,f93,f115,f112]) ).
fof(f173,plain,
( member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK4)
| ~ spl6_3 ),
inference(resolution,[],[f113,f40]) ).
fof(f175,plain,
( ~ member(sK0(intersection(sK2,difference(sK3,sK4)),difference(intersection(sK2,sK3),intersection(sK2,sK4))),sK4)
| spl6_1 ),
inference(resolution,[],[f162,f43]) ).
fof(f178,plain,
( $false
| spl6_1
| ~ spl6_3 ),
inference(resolution,[],[f175,f173]) ).
fof(f180,plain,
( spl6_1
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f178]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f99]) ).
cnf(s4,plain,
( spl6_4
| ~ spl6_5
| ~ spl6_6 ),
inference(sat_conversion,[],[f125]) ).
cnf(s5,plain,
( spl6_1
| spl6_5 ),
inference(sat_conversion,[],[f127]) ).
cnf(s6,plain,
( spl6_1
| spl6_6 ),
inference(sat_conversion,[],[f129]) ).
cnf(s7,plain,
( spl6_2
| ~ spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f139]) ).
cnf(s8,plain,
( spl6_7
| spl6_9
| ~ spl6_10 ),
inference(sat_conversion,[],[f149]) ).
cnf(s9,plain,
( spl6_2
| ~ spl6_8
| ~ spl6_9 ),
inference(sat_conversion,[],[f154]) ).
cnf(s10,plain,
( spl6_2
| spl6_8 ),
inference(sat_conversion,[],[f156]) ).
cnf(s11,plain,
( spl6_2
| spl6_10 ),
inference(sat_conversion,[],[f158]) ).
cnf(s12,plain,
( spl6_1
| spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f171]) ).
cnf(s13,plain,
( spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f180]) ).
cnf(s14,plain,
spl6_1,
inference(rat,[],[s4,s12,s5,s6,s13]) ).
cnf(s15,plain,
~ spl6_2,
inference(rat,[],[s2,s14]) ).
cnf(s16,plain,
spl6_10,
inference(rat,[],[s11,s15]) ).
cnf(s17,plain,
spl6_8,
inference(rat,[],[s10,s15]) ).
cnf(s18,plain,
~ spl6_7,
inference(rat,[],[s7,s17,s15]) ).
cnf(s19,plain,
~ spl6_9,
inference(rat,[],[s9,s15,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s8,s16,s19,s18]) ).
fof(f181,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:23:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.69/1.25 % (1376677)Detected formulas, will run a generic FOF schedule.
% 2.69/1.25 % (1376685)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1105550478:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.25 % (1376685)Refutation not found, incomplete strategy
% 2.69/1.25 % (1376685)------------------------------
% 2.69/1.25 % (1376685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.25 % (1376685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.25 % (1376685)CaDiCaL version: 2.1.3
% 2.69/1.25 % (1376685)Termination reason: Refutation not found, incomplete strategy
% 2.69/1.25 % (1376685)Time elapsed: 0.001 s
% 2.69/1.25 % (1376685)Peak memory usage: 88 MB
% 2.69/1.25 % (1376686)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2701068413:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.25 % (1376687)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3164489802:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.25 % (1376682)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=4092667704:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.25 % (1376688)dis-21_1_sil=8000:lcm=predicate:random_seed=3159582759: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)
% 2.69/1.25 % (1376684)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=4278341369:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.25 % (1376683)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=3050022711:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.25 % (1376688)First to succeed.
% 2.69/1.25 % (1376688)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1376677"
% 2.69/1.25 % (1376687)Also succeeded, but the first one will report.
% 2.69/1.25 % (1376686)Instruction limit reached!
% 2.69/1.25 % (1376686)------------------------------
% 2.69/1.25 % (1376686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.25 % (1376686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.25 % (1376686)CaDiCaL version: 2.1.3
% 2.69/1.25 % (1376686)Termination reason: Instruction limit
% 2.69/1.25 % (1376686)Termination phase: Saturation
% 2.69/1.25 % (1376686)Time elapsed: 0.061 s
% 2.69/1.25 % (1376686)Peak memory usage: 88 MB
% 2.69/1.25 % (1376686)Instructions burned: 119 (million)
% 2.69/1.25 % (1376685)------------------------------
% 2.69/1.25 % (1376685)------------------------------
% 2.69/1.25 % (1376696)lrs+10_1_sil=8000:sp=occurrence:random_seed=495826235:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.69/1.25 % (1376697)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3680677702:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.69/1.25 % (1376688)Refutation found. Thanks to Tanya!
% 2.69/1.25 % SZS status Theorem for theBenchmark
% 2.69/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.36/1.35 % (1376688)------------------------------
% 3.36/1.35 % (1376688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.35 % (1376688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.35 % (1376688)CaDiCaL version: 2.1.3
% 3.36/1.35 % (1376688)Termination reason: Refutation
% 3.36/1.35 % (1376688)Time elapsed: 0.005 s
% 3.36/1.35 % (1376688)Peak memory usage: 89 MB
% 3.36/1.35 % (1376688)Instructions burned: 6 (million)
% 3.36/1.35 % (1376688)------------------------------
% 3.36/1.35 % (1376688)------------------------------
% 3.36/1.35 % (1376677)Success in time 0.407 s
% 3.36/1.35 % Vampire exiting
%------------------------------------------------------------------------------