%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET613+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 : n006.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 12:41:22 PM UTC 2026
% Result : Theorem 2.57s 1.27s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 112 ( 14 unt; 9 def)
% Number of atoms : 287 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 296 ( 121 ~; 134 |; 25 &)
% ( 15 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 89 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f3,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(f4,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(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f11,conjecture,
! [X0,X1] : difference(union(X0,X1),intersection(X0,X1)) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_union_intersection) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] : difference(union(X0,X1),intersection(X0,X1)) = union(difference(X0,X1),difference(X1,X0)),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f15,plain,
? [X0,X1] : difference(union(X0,X1),intersection(X0,X1)) != union(difference(X0,X1),difference(X1,X0)),
inference(ennf_transformation,[],[f12]) ).
fof(f18,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,[],[f2]) ).
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(flattening,[],[f18]) ).
fof(f20,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,[],[f3]) ).
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(flattening,[],[f20]) ).
fof(f22,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,[],[f4]) ).
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(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f25,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f24]) ).
fof(f29,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,[],[f14]) ).
fof(f30,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,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f30]) ).
fof(f32,plain,
difference(union(sK3,sK4),intersection(sK3,sK4)) != union(difference(sK3,sK4),difference(sK4,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f15]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f57,plain,
difference(union(sK3,sK4),intersection(sK3,sK4)) != union(difference(sK3,sK4),difference(sK4,sK3)),
inference(cnf_transformation,[],[f32]) ).
fof(f62,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f65,plain,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f46,f62]) ).
fof(f70,plain,
~ sQ5_eqProxy(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),
inference(equality_proxy_replacement,[],[f57,f62]) ).
fof(f78,plain,
( ~ subset(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3)))
| ~ subset(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))) ),
inference(resolution,[],[f65,f70]) ).
fof(f81,definition,
( spl6_1
<=> subset(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f82,plain,
( ~ subset(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3)))
| spl6_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl6_2
<=> subset(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f85,plain,
( ~ subset(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4)))
| spl6_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( ~ spl6_2
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f78,f81,f84]) ).
fof(f89,plain,
( member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),difference(union(sK3,sK4),intersection(sK3,sK4)))
| spl6_1 ),
inference(resolution,[],[f82,f54]) ).
fof(f92,plain,
( member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),union(sK3,sK4))
| spl6_1 ),
inference(resolution,[],[f89,f42]) ).
fof(f96,plain,
( member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK4)
| member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK3)
| spl6_1 ),
inference(resolution,[],[f35,f92]) ).
fof(f98,definition,
( spl6_3
<=> member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK3) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f101,definition,
( spl6_4
<=> member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f103,plain,
( spl6_3
| spl6_4
| spl6_1 ),
inference(avatar_split_clause,[],[f96,f81,f101,f98]) ).
fof(f108,definition,
( spl6_5
<=> member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f109,plain,
( member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK3,sK4))
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl6_6
<=> member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,sK3)) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f112,plain,
( member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,sK3))
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| ~ spl6_5 ),
inference(resolution,[],[f109,f42]) ).
fof(f115,plain,
( ~ member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| ~ spl6_5 ),
inference(resolution,[],[f109,f41]) ).
fof(f122,definition,
( spl6_7
<=> member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f123,plain,
( member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4))
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,definition,
( spl6_8
<=> member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
fof(f126,plain,
( ~ member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(sK3,sK4))
| spl6_8 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( ~ member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| spl6_8 ),
inference(resolution,[],[f126,f37]) ).
fof(f129,plain,
( ~ member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| spl6_8 ),
inference(resolution,[],[f126,f36]) ).
fof(f130,plain,
( $false
| ~ spl6_5
| spl6_8 ),
inference(resolution,[],[f128,f114]) ).
fof(f131,plain,
( ~ spl6_5
| spl6_8 ),
inference(avatar_contradiction_clause,[],[f130]) ).
fof(f132,plain,
( member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| ~ spl6_6 ),
inference(resolution,[],[f112,f42]) ).
fof(f133,plain,
( ~ member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| ~ spl6_6 ),
inference(resolution,[],[f112,f41]) ).
fof(f134,plain,
( $false
| ~ spl6_6
| spl6_8 ),
inference(resolution,[],[f132,f129]) ).
fof(f135,plain,
( ~ spl6_6
| spl6_8 ),
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f136,plain,
( ~ member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),union(difference(sK3,sK4),difference(sK4,sK3)))
| spl6_1 ),
inference(resolution,[],[f82,f55]) ).
fof(f137,plain,
( member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),difference(union(sK3,sK4),intersection(sK3,sK4)))
| spl6_1 ),
inference(resolution,[],[f82,f54]) ).
fof(f138,plain,
( ~ member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),difference(sK3,sK4))
| spl6_1 ),
inference(resolution,[],[f136,f37]) ).
fof(f141,plain,
( ~ member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),intersection(sK3,sK4))
| spl6_1 ),
inference(resolution,[],[f137,f41]) ).
fof(f142,plain,
( ~ member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK3)
| member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK4)
| spl6_1 ),
inference(resolution,[],[f138,f43]) ).
fof(f144,plain,
( spl6_4
| ~ spl6_3
| spl6_1 ),
inference(avatar_split_clause,[],[f142,f81,f98,f101]) ).
fof(f147,plain,
( ~ member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK3)
| ~ member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK4)
| spl6_1 ),
inference(resolution,[],[f141,f40]) ).
fof(f149,plain,
( ~ spl6_4
| ~ spl6_3
| spl6_1 ),
inference(avatar_split_clause,[],[f147,f81,f98,f101]) ).
fof(f150,plain,
( ~ member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(union(sK3,sK4),intersection(sK3,sK4)))
| spl6_2 ),
inference(resolution,[],[f85,f55]) ).
fof(f151,plain,
( member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3)))
| spl6_2 ),
inference(resolution,[],[f85,f54]) ).
fof(f157,plain,
( ~ member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(sK3,sK4))
| member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4))
| spl6_2 ),
inference(resolution,[],[f150,f43]) ).
fof(f159,plain,
( spl6_7
| ~ spl6_8
| spl6_2 ),
inference(avatar_split_clause,[],[f157,f84,f125,f122]) ).
fof(f161,plain,
( member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,sK3))
| member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK3,sK4))
| spl6_2 ),
inference(resolution,[],[f151,f35]) ).
fof(f162,plain,
( spl6_5
| spl6_6
| spl6_2 ),
inference(avatar_split_clause,[],[f161,f84,f111,f108]) ).
fof(f165,plain,
( member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| ~ spl6_7 ),
inference(resolution,[],[f123,f39]) ).
fof(f166,plain,
( member(sK2(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| ~ spl6_7 ),
inference(resolution,[],[f123,f38]) ).
fof(f167,plain,
( $false
| ~ spl6_5
| ~ spl6_7 ),
inference(resolution,[],[f166,f115]) ).
fof(f168,plain,
( ~ spl6_5
| ~ spl6_7 ),
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f182,plain,
( $false
| ~ spl6_6
| ~ spl6_7 ),
inference(resolution,[],[f165,f133]) ).
fof(f184,plain,
( ~ spl6_6
| ~ spl6_7 ),
inference(avatar_contradiction_clause,[],[f182]) ).
fof(f185,plain,
( ~ member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),union(difference(sK3,sK4),difference(sK4,sK3)))
| spl6_1 ),
inference(resolution,[],[f82,f55]) ).
fof(f189,plain,
( ~ member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),difference(sK4,sK3))
| spl6_1 ),
inference(resolution,[],[f185,f36]) ).
fof(f195,plain,
( ~ member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK4)
| member(sK2(difference(union(sK3,sK4),intersection(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))),sK3)
| spl6_1 ),
inference(resolution,[],[f189,f43]) ).
fof(f197,plain,
( spl6_3
| ~ spl6_4
| spl6_1 ),
inference(avatar_split_clause,[],[f195,f81,f101,f98]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f87]) ).
cnf(s3,plain,
( spl6_1
| spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f103]) ).
cnf(s6,plain,
( ~ spl6_5
| spl6_8 ),
inference(sat_conversion,[],[f131]) ).
cnf(s7,plain,
( ~ spl6_6
| spl6_8 ),
inference(sat_conversion,[],[f135]) ).
cnf(s8,plain,
( spl6_1
| ~ spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f144]) ).
cnf(s9,plain,
( spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f149]) ).
cnf(s10,plain,
( spl6_2
| spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f159]) ).
cnf(s11,plain,
( spl6_2
| spl6_5
| spl6_6 ),
inference(sat_conversion,[],[f162]) ).
cnf(s12,plain,
( ~ spl6_5
| ~ spl6_7 ),
inference(sat_conversion,[],[f168]) ).
cnf(s13,plain,
( ~ spl6_6
| ~ spl6_7 ),
inference(sat_conversion,[],[f184]) ).
cnf(s14,plain,
( spl6_1
| spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f197]) ).
cnf(s15,plain,
( spl6_3
| spl6_1 ),
inference(rat,[],[s3,s14]) ).
cnf(s16,plain,
( ~ spl6_3
| spl6_1 ),
inference(rat,[],[s9,s8]) ).
cnf(s17,plain,
spl6_1,
inference(rat,[],[s16,s15]) ).
cnf(s18,plain,
~ spl6_2,
inference(rat,[],[s2,s17]) ).
cnf(s19,plain,
~ spl6_6,
inference(rat,[],[s10,s7,s13,s18]) ).
cnf(s20,plain,
spl6_5,
inference(rat,[],[s11,s18,s19]) ).
cnf(s21,plain,
~ spl6_7,
inference(rat,[],[s12,s20]) ).
cnf(s22,plain,
spl6_8,
inference(rat,[],[s6,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s10,s18,s22,s21]) ).
fof(f198,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET613+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n006.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 02:19:41 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.57/1.27 % (3526890)Detected formulas, will run a generic FOF schedule.
% 2.57/1.27 % (3526898)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3909579223:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.27 % (3526898)Refutation not found, incomplete strategy
% 2.57/1.27 % (3526898)------------------------------
% 2.57/1.27 % (3526898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.27 % (3526898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.27 % (3526898)CaDiCaL version: 2.1.3
% 2.57/1.27 % (3526898)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.27 % (3526898)Time elapsed: 0.001 s
% 2.57/1.27 % (3526898)Peak memory usage: 88 MB
% 2.57/1.27 % (3526898)Instructions burned: 1 (million)
% 2.57/1.27 % (3526901)dis-21_1_sil=8000:lcm=predicate:random_seed=1828819569: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)
% 2.57/1.27 % (3526901)First to succeed.
% 2.57/1.27 % (3526899)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=836680102:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.27 % (3526895)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=498221358:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.27 % (3526896)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=2230626684:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.27 % (3526897)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=2567131851:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.27 % (3526901)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3526890"
% 2.57/1.27 % (3526900)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3588565707:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.27 % (3526899)Instruction limit reached!
% 2.57/1.27 % (3526899)------------------------------
% 2.57/1.27 % (3526899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.27 % (3526899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.27 % (3526899)CaDiCaL version: 2.1.3
% 2.57/1.27 % (3526899)Termination reason: Instruction limit
% 2.57/1.27 % (3526899)Termination phase: Saturation
% 2.57/1.27 % (3526899)Time elapsed: 0.070 s
% 2.57/1.27 % (3526899)Peak memory usage: 89 MB
% 2.57/1.27 % (3526899)Instructions burned: 119 (million)
% 2.57/1.27 % (3526900)Instruction limit reached!
% 2.57/1.27 % (3526900)------------------------------
% 2.57/1.27 % (3526900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.27 % (3526900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.27 % (3526900)CaDiCaL version: 2.1.3
% 2.57/1.27 % (3526900)Termination reason: Instruction limit
% 2.57/1.27 % (3526900)Termination phase: Saturation
% 2.57/1.27 % (3526900)Time elapsed: 0.080 s
% 2.57/1.27 % (3526900)Peak memory usage: 89 MB
% 2.57/1.27 % (3526900)Instructions burned: 139 (million)
% 2.57/1.27 % (3526898)------------------------------
% 2.57/1.27 % (3526898)------------------------------
% 2.57/1.27 % (3526911)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3283396560:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.57/1.27 % (3526909)lrs+10_1_sil=8000:sp=occurrence:random_seed=3204285666:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.57/1.27 % (3526910)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2425495529:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.57/1.27 % (3526910)Refutation not found, incomplete strategy
% 2.57/1.27 % (3526910)------------------------------
% 2.57/1.27 % (3526910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.27 % (3526910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.27 % (3526910)CaDiCaL version: 2.1.3
% 2.57/1.27 % (3526910)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.27 % (3526910)Time elapsed: 0.002 s
% 2.57/1.27 % (3526910)Peak memory usage: 89 MB
% 2.57/1.27 % (3526910)Instructions burned: 2 (million)
% 2.57/1.27 % (3526901)Refutation found. Thanks to Tanya!
% 2.57/1.27 % SZS status Theorem for theBenchmark
% 2.57/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.36/1.36 % (3526901)------------------------------
% 3.36/1.36 % (3526901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.36 % (3526901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.36 % (3526901)CaDiCaL version: 2.1.3
% 3.36/1.36 % (3526901)Termination reason: Refutation
% 3.36/1.36 % (3526901)Time elapsed: 0.006 s
% 3.36/1.36 % (3526901)Peak memory usage: 89 MB
% 3.36/1.36 % (3526901)Instructions burned: 7 (million)
% 3.36/1.36 % (3526901)------------------------------
% 3.36/1.36 % (3526901)------------------------------
% 3.36/1.36 % (3526890)Success in time 0.401 s
% 3.36/1.36 % Vampire exiting
%------------------------------------------------------------------------------