%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET919+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:42:19 PM UTC 2026
% Result : Theorem 6.63s 1.95s
% Output : Refutation 8.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 114 ( 21 unt; 10 def)
% Number of atoms : 410 ( 123 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 485 ( 189 ~; 220 |; 58 &)
% ( 16 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 115 ( 0 sgn 101 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,conjecture,
! [X0,X1,X2] :
( in(X0,X1)
=> ( ( in(X2,X1)
& X0 != X2 )
| set_intersection2(unordered_pair(X0,X2),X1) = singleton(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
( in(X0,X1)
=> ( ( in(X2,X1)
& X0 != X2 )
| set_intersection2(unordered_pair(X0,X2),X1) = singleton(X0) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f14,plain,
? [X0,X1,X2] :
( ( ~ in(X2,X1)
| X0 = X2 )
& singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
& in(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ( ~ in(X2,X1)
| X0 = X2 )
& singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
& in(X0,X1) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK1(X0,X1,X2) != X0
& sK1(X0,X1,X2) != X1 )
| ~ in(sK1(X0,X1,X2),X2) )
& ( sK1(X0,X1,X2) = X0
| sK1(X0,X1,X2) = X1
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),X0)
& in(sK2(X0,X1,X2),X1) )
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f25]) ).
fof(f29,plain,
( ( ~ in(sK7,sK6)
| sK5 = sK7 )
& singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6)
& in(sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f15]) ).
fof(f32,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f52,plain,
in(sK5,sK6),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
( ~ in(sK7,sK6)
| sK5 = sK7 ),
inference(cnf_transformation,[],[f29]) ).
fof(f55,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f34]) ).
fof(f56,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f55]) ).
fof(f57,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f33]) ).
fof(f58,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f39]) ).
fof(f59,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f58]) ).
fof(f62,plain,
! [X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,unordered_pair(X0,X1)) ),
inference(equality_resolution,[],[f37]) ).
fof(f66,plain,
singleton(sK5) != set_intersection2(sK6,unordered_pair(sK5,sK7)),
inference(forward_demodulation,[],[f53,f32]) ).
fof(f68,definition,
( spl8_1
<=> in(sK5,sK6) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f70,plain,
( in(sK5,sK6)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
spl8_1,
inference(avatar_split_clause,[],[f52,f68]) ).
fof(f77,definition,
( spl8_2
<=> singleton(sK5) = set_intersection2(sK6,unordered_pair(sK5,sK7)) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f79,plain,
( singleton(sK5) != set_intersection2(sK6,unordered_pair(sK5,sK7))
| spl8_2 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
~ spl8_2,
inference(avatar_split_clause,[],[f66,f77]) ).
fof(f85,plain,
( ! [X0] :
( singleton(sK5) != X0
| in(sK2(sK6,unordered_pair(sK5,sK7),X0),sK6)
| in(sK2(sK6,unordered_pair(sK5,sK7),X0),X0) )
| spl8_2 ),
inference(superposition,[],[f79,f47]) ).
fof(f88,definition,
( spl8_3
<=> sK5 = sK7 ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f90,plain,
( sK5 = sK7
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl8_4
<=> in(sK7,sK6) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f94,plain,
( ~ in(sK7,sK6)
| spl8_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl8_3
| ~ spl8_4 ),
inference(avatar_split_clause,[],[f54,f92,f88]) ).
fof(f171,definition,
( spl8_11
<=> ! [X0] :
( singleton(sK5) != X0
| in(sK2(sK6,unordered_pair(sK5,sK7),X0),sK6)
| in(sK2(sK6,unordered_pair(sK5,sK7),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
fof(f172,plain,
( ! [X0] :
( singleton(sK5) != X0
| in(sK2(sK6,unordered_pair(sK5,sK7),X0),sK6)
| in(sK2(sK6,unordered_pair(sK5,sK7),X0),X0) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f173,plain,
( spl8_11
| spl8_2 ),
inference(avatar_split_clause,[],[f85,f77,f171]) ).
fof(f176,plain,
( in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),sK6)
| in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),singleton(sK5))
| ~ spl8_11 ),
inference(equality_resolution,[],[f172]) ).
fof(f178,definition,
( spl8_12
<=> in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),singleton(sK5)) ),
introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition]) ).
fof(f179,plain,
( ~ in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),singleton(sK5))
| spl8_12 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f180,plain,
( in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),singleton(sK5))
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f182,definition,
( spl8_13
<=> in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),sK6) ),
introduced(definition,[new_symbols(definition,[spl8_13])],[avatar_definition]) ).
fof(f184,plain,
( in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),sK6)
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f185,plain,
( spl8_12
| spl8_13
| ~ spl8_11 ),
inference(avatar_split_clause,[],[f176,f171,f182,f178]) ).
fof(f186,plain,
( sK5 = sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5))
| ~ spl8_12 ),
inference(resolution,[],[f180,f57]) ).
fof(f191,plain,
( singleton(sK5) = set_intersection2(sK6,unordered_pair(sK5,sK7))
| ~ in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),sK6)
| ~ in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),unordered_pair(sK5,sK7))
| ~ spl8_12 ),
inference(resolution,[],[f180,f48]) ).
fof(f197,plain,
( ~ in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),sK6)
| ~ in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),unordered_pair(sK5,sK7))
| spl8_2
| ~ spl8_12 ),
inference(forward_subsumption_resolution,[],[f191,f79]) ).
fof(f198,plain,
( ~ in(sK5,sK6)
| ~ in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),unordered_pair(sK5,sK7))
| spl8_2
| ~ spl8_12 ),
inference(forward_demodulation,[],[f197,f186]) ).
fof(f199,plain,
( ~ in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),unordered_pair(sK5,sK7))
| ~ spl8_1
| spl8_2
| ~ spl8_12 ),
inference(forward_subsumption_resolution,[],[f198,f70]) ).
fof(f200,plain,
( ~ in(sK5,unordered_pair(sK5,sK7))
| ~ spl8_1
| spl8_2
| ~ spl8_12 ),
inference(forward_demodulation,[],[f199,f186]) ).
fof(f201,plain,
( $false
| ~ spl8_1
| spl8_2
| ~ spl8_12 ),
inference(forward_subsumption_resolution,[],[f200,f59]) ).
fof(f202,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_12 ),
inference(avatar_contradiction_clause,[],[f201]) ).
fof(f213,plain,
( singleton(sK5) = set_intersection2(sK6,unordered_pair(sK5,sK7))
| in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),unordered_pair(sK5,sK7))
| spl8_12 ),
inference(resolution,[],[f179,f46]) ).
fof(f222,plain,
( in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),unordered_pair(sK5,sK7))
| spl8_2
| spl8_12 ),
inference(forward_subsumption_resolution,[],[f213,f79]) ).
fof(f224,definition,
( spl8_14
<=> in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),unordered_pair(sK5,sK7)) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
fof(f226,plain,
( in(sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)),unordered_pair(sK5,sK7))
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f227,plain,
( spl8_14
| spl8_2
| spl8_12 ),
inference(avatar_split_clause,[],[f222,f178,f77,f224]) ).
fof(f228,plain,
( sK5 = sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5))
| sK7 = sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5))
| ~ spl8_14 ),
inference(resolution,[],[f226,f62]) ).
fof(f240,definition,
( spl8_15
<=> sK7 = sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)) ),
introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition]) ).
fof(f242,plain,
( sK7 = sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5))
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f244,definition,
( spl8_16
<=> sK5 = sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5)) ),
introduced(definition,[new_symbols(definition,[spl8_16])],[avatar_definition]) ).
fof(f246,plain,
( sK5 = sK2(sK6,unordered_pair(sK5,sK7),singleton(sK5))
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f247,plain,
( spl8_15
| spl8_16
| ~ spl8_14 ),
inference(avatar_split_clause,[],[f228,f224,f244,f240]) ).
fof(f255,plain,
( in(sK7,sK6)
| ~ spl8_13
| ~ spl8_15 ),
inference(superposition,[],[f184,f242]) ).
fof(f265,plain,
( $false
| spl8_4
| ~ spl8_13
| ~ spl8_15 ),
inference(forward_subsumption_resolution,[],[f255,f94]) ).
fof(f266,plain,
( spl8_4
| ~ spl8_13
| ~ spl8_15 ),
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f315,plain,
( ~ in(sK2(sK6,unordered_pair(sK5,sK5),singleton(sK5)),singleton(sK5))
| ~ spl8_3
| spl8_12 ),
inference(superposition,[],[f179,f90]) ).
fof(f318,plain,
( sK5 = sK2(sK6,unordered_pair(sK5,sK5),singleton(sK5))
| ~ spl8_3
| ~ spl8_15 ),
inference(superposition,[],[f242,f90]) ).
fof(f321,plain,
( ~ in(sK5,singleton(sK5))
| ~ spl8_3
| spl8_12
| ~ spl8_15 ),
inference(forward_demodulation,[],[f315,f318]) ).
fof(f322,plain,
( $false
| ~ spl8_3
| spl8_12
| ~ spl8_15 ),
inference(forward_subsumption_resolution,[],[f321,f56]) ).
fof(f323,plain,
( ~ spl8_3
| spl8_12
| ~ spl8_15 ),
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f366,plain,
( ~ in(sK5,sK6)
| singleton(sK5) = set_intersection2(sK6,unordered_pair(sK5,sK7))
| ~ in(sK5,unordered_pair(sK5,sK7))
| ~ in(sK5,singleton(sK5))
| ~ spl8_16 ),
inference(superposition,[],[f48,f246]) ).
fof(f371,plain,
( singleton(sK5) = set_intersection2(sK6,unordered_pair(sK5,sK7))
| ~ in(sK5,unordered_pair(sK5,sK7))
| ~ in(sK5,singleton(sK5))
| ~ spl8_1
| ~ spl8_16 ),
inference(forward_subsumption_resolution,[],[f366,f70]) ).
fof(f376,plain,
( ~ in(sK5,unordered_pair(sK5,sK7))
| ~ in(sK5,singleton(sK5))
| ~ spl8_1
| spl8_2
| ~ spl8_16 ),
inference(forward_subsumption_resolution,[],[f371,f79]) ).
fof(f379,plain,
( ~ in(sK5,singleton(sK5))
| ~ spl8_1
| spl8_2
| ~ spl8_16 ),
inference(forward_subsumption_resolution,[],[f376,f59]) ).
fof(f384,plain,
( $false
| ~ spl8_1
| spl8_2
| ~ spl8_16 ),
inference(forward_subsumption_resolution,[],[f379,f56]) ).
fof(f385,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_16 ),
inference(avatar_contradiction_clause,[],[f384]) ).
cnf(s1,plain,
spl8_1,
inference(sat_conversion,[],[f71]) ).
cnf(s2,plain,
~ spl8_2,
inference(sat_conversion,[],[f80]) ).
cnf(s3,plain,
( spl8_3
| ~ spl8_4 ),
inference(sat_conversion,[],[f95]) ).
cnf(s10,plain,
( spl8_2
| spl8_11 ),
inference(sat_conversion,[],[f173]) ).
cnf(s11,plain,
( ~ spl8_11
| spl8_12
| spl8_13 ),
inference(sat_conversion,[],[f185]) ).
cnf(s12,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_12 ),
inference(sat_conversion,[],[f202]) ).
cnf(s13,plain,
( spl8_2
| spl8_12
| spl8_14 ),
inference(sat_conversion,[],[f227]) ).
cnf(s14,plain,
( ~ spl8_14
| spl8_15
| spl8_16 ),
inference(sat_conversion,[],[f247]) ).
cnf(s15,plain,
( spl8_4
| ~ spl8_13
| ~ spl8_15 ),
inference(sat_conversion,[],[f266]) ).
cnf(s22,plain,
( ~ spl8_3
| spl8_12
| ~ spl8_15 ),
inference(sat_conversion,[],[f323]) ).
cnf(s27,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_16 ),
inference(sat_conversion,[],[f385]) ).
cnf(s28,plain,
spl8_11,
inference(rat,[],[s10,s2]) ).
cnf(s31,plain,
~ spl8_16,
inference(rat,[],[s27,s2,s1]) ).
cnf(s32,plain,
~ spl8_12,
inference(rat,[],[s12,s2,s1]) ).
cnf(s35,plain,
spl8_14,
inference(rat,[],[s13,s2,s32]) ).
cnf(s36,plain,
spl8_13,
inference(rat,[],[s11,s28,s32]) ).
cnf(s37,plain,
spl8_15,
inference(rat,[],[s14,s31,s35]) ).
cnf(s38,plain,
spl8_4,
inference(rat,[],[s15,s37,s36]) ).
cnf(s39,plain,
~ spl8_3,
inference(rat,[],[s22,s32,s37]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s3,s38,s39]) ).
fof(f386,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET919+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.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 03:12:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 6.63/1.95 % (2959799)Detected formulas, will run a generic FOF schedule.
% 6.63/1.95 % (2959807)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=448907615:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.63/1.95 % (2959807)Refutation not found, incomplete strategy
% 6.63/1.95 % (2959807)------------------------------
% 6.63/1.95 % (2959807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959807)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959807)Termination reason: Refutation not found, incomplete strategy
% 6.63/1.95 % (2959807)Time elapsed: 0.001 s
% 6.63/1.95 % (2959807)Peak memory usage: 88 MB
% 6.63/1.95 % (2959807)Instructions burned: 1 (million)
% 6.63/1.95 % (2959805)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=3692255228:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.63/1.95 % (2959806)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=2452778435:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.63/1.95 % (2959804)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=3207662877:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.63/1.95 % (2959810)dis-21_1_sil=8000:lcm=predicate:random_seed=1780794989: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)
% 6.63/1.95 % (2959808)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2474884197:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.63/1.95 % (2959809)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3485447330:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.63/1.95 % (2959808)Instruction limit reached!
% 6.63/1.95 % (2959808)------------------------------
% 6.63/1.95 % (2959808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959808)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959808)Termination reason: Instruction limit
% 6.63/1.95 % (2959808)Termination phase: Saturation
% 6.63/1.95 % (2959808)Time elapsed: 0.070 s
% 6.63/1.95 % (2959808)Peak memory usage: 88 MB
% 6.63/1.95 % (2959808)Instructions burned: 120 (million)
% 6.63/1.95 % (2959810)Instruction limit reached!
% 6.63/1.95 % (2959810)------------------------------
% 6.63/1.95 % (2959810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959810)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959810)Termination reason: Instruction limit
% 6.63/1.95 % (2959810)Termination phase: Saturation
% 6.63/1.95 % (2959810)Time elapsed: 0.077 s
% 6.63/1.95 % (2959810)Peak memory usage: 89 MB
% 6.63/1.95 % (2959810)Instructions burned: 130 (million)
% 6.63/1.95 % (2959809)Instruction limit reached!
% 6.63/1.95 % (2959809)------------------------------
% 6.63/1.95 % (2959809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959809)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959809)Termination reason: Instruction limit
% 6.63/1.95 % (2959809)Termination phase: Saturation
% 6.63/1.95 % (2959809)Time elapsed: 0.091 s
% 6.63/1.95 % (2959809)Peak memory usage: 89 MB
% 6.63/1.95 % (2959809)Instructions burned: 139 (million)
% 6.63/1.95 % (2959807)------------------------------
% 6.63/1.95 % (2959807)------------------------------
% 6.63/1.95 % (2959819)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3355044378:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.63/1.95 % (2959818)lrs+10_1_sil=8000:sp=occurrence:random_seed=2049103460:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.63/1.95 % (2959821)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3600030280:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.63/1.95 % (2959820)lrs+1011_1_sil=32000:sp=occurrence:random_seed=152949815:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.63/1.95 % (2959821)Instruction limit reached!
% 6.63/1.95 % (2959821)------------------------------
% 6.63/1.95 % (2959821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959821)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959821)Termination reason: Instruction limit
% 6.63/1.95 % (2959821)Termination phase: Saturation
% 6.63/1.95 % (2959821)Time elapsed: 0.072 s
% 6.63/1.95 % (2959821)Peak memory usage: 91 MB
% 6.63/1.95 % (2959821)Instructions burned: 250 (million)
% 6.63/1.95 % (2959819)Instruction limit reached!
% 6.63/1.95 % (2959819)------------------------------
% 6.63/1.95 % (2959819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959819)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959819)Termination reason: Instruction limit
% 6.63/1.95 % (2959819)Termination phase: Saturation
% 6.63/1.95 % (2959819)Time elapsed: 0.084 s
% 6.63/1.95 % (2959819)Peak memory usage: 90 MB
% 6.63/1.95 % (2959819)Instructions burned: 159 (million)
% 6.63/1.95 % (2959826)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3056196816:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.63/1.95 % (2959826)Refutation not found, incomplete strategy
% 6.63/1.95 % (2959826)------------------------------
% 6.63/1.95 % (2959826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959826)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959826)Termination reason: Refutation not found, incomplete strategy
% 6.63/1.95 % (2959826)Time elapsed: 0.001 s
% 6.63/1.95 % (2959826)Peak memory usage: 89 MB
% 6.63/1.95 % (2959826)Instructions burned: 1 (million)
% 6.63/1.95 % (2959818)Instruction limit reached!
% 6.63/1.95 % (2959818)------------------------------
% 6.63/1.95 % (2959818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959818)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959818)Termination reason: Instruction limit
% 6.63/1.95 % (2959818)Termination phase: Saturation
% 6.63/1.95 % (2959818)Time elapsed: 0.191 s
% 6.63/1.95 % (2959818)Peak memory usage: 91 MB
% 6.63/1.95 % (2959818)Instructions burned: 286 (million)
% 6.63/1.95 % (2959827)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3777178077:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.63/1.95 % (2959820)Instruction limit reached!
% 6.63/1.95 % (2959820)------------------------------
% 6.63/1.95 % (2959820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959820)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959820)Termination reason: Instruction limit
% 6.63/1.95 % (2959820)Termination phase: Saturation
% 6.63/1.95 % (2959820)Time elapsed: 0.210 s
% 6.63/1.95 % (2959820)Peak memory usage: 91 MB
% 6.63/1.95 % (2959820)Instructions burned: 326 (million)
% 6.63/1.95 % (2959826)------------------------------
% 6.63/1.95 % (2959826)------------------------------
% 6.63/1.95 % (2959829)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=568871346:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.63/1.95 % (2959831)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1769829977:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.63/1.95 % (2959829)Instruction limit reached!
% 6.63/1.95 % (2959829)------------------------------
% 6.63/1.95 % (2959829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959829)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959829)Termination reason: Instruction limit
% 6.63/1.95 % (2959829)Termination phase: Saturation
% 6.63/1.95 % (2959829)Time elapsed: 0.069 s
% 6.63/1.95 % (2959829)Peak memory usage: 88 MB
% 6.63/1.95 % (2959829)Instructions burned: 114 (million)
% 6.63/1.95 % (2959806)First to succeed.
% 6.63/1.95 % (2959806)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2959799"
% 6.63/1.95 % (2959832)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3489804993:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.63/1.95 % (2959805)Also succeeded, but the first one will report.
% 6.63/1.95 % (2959831)Instruction limit reached!
% 6.63/1.95 % (2959831)------------------------------
% 6.63/1.95 % (2959831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959831)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959831)Termination reason: Instruction limit
% 6.63/1.95 % (2959831)Termination phase: Saturation
% 6.63/1.95 % (2959831)Time elapsed: 0.060 s
% 6.63/1.95 % (2959831)Peak memory usage: 88 MB
% 6.63/1.95 % (2959831)Instructions burned: 129 (million)
% 6.63/1.95 % (2959832)Instruction limit reached!
% 6.63/1.95 % (2959832)------------------------------
% 6.63/1.95 % (2959832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959832)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959832)Termination reason: Instruction limit
% 6.63/1.95 % (2959832)Termination phase: Saturation
% 6.63/1.95 % (2959832)Time elapsed: 0.035 s
% 6.63/1.95 % (2959832)Peak memory usage: 89 MB
% 6.63/1.95 % (2959832)Instructions burned: 116 (million)
% 6.63/1.95 % (2959804)Also succeeded, but the first one will report.
% 6.63/1.95 % (2959835)lrs+10_1_sil=8000:sp=occurrence:random_seed=1826025828:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.63/1.95 % (2959837)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=378868156:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.63/1.95 % (2959837)Refutation not found, incomplete strategy
% 6.63/1.95 % (2959837)------------------------------
% 6.63/1.95 % (2959837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (2959837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (2959837)CaDiCaL version: 2.1.3
% 6.63/1.95 % (2959837)Termination reason: Refutation not found, incomplete strategy
% 6.63/1.95 % (2959837)Time elapsed: 0.002 s
% 6.63/1.95 % (2959837)Peak memory usage: 88 MB
% 6.63/1.95 % (2959837)Instructions burned: 1 (million)
% 6.63/1.95 % (2959838)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3750400709:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.63/1.95 % (2959806)Refutation found. Thanks to Tanya!
% 6.63/1.95 % SZS status Theorem for theBenchmark
% 6.63/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 8.28/2.14 % (2959806)------------------------------
% 8.28/2.14 % (2959806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.28/2.14 % (2959806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.28/2.14 % (2959806)CaDiCaL version: 2.1.3
% 8.28/2.14 % (2959806)Termination reason: Refutation
% 8.28/2.14 % (2959806)Time elapsed: 0.642 s
% 8.28/2.14 % (2959806)Peak memory usage: 127 MB
% 8.28/2.14 % (2959806)Instructions burned: 941 (million)
% 8.28/2.14 % (2959806)------------------------------
% 8.28/2.14 % (2959806)------------------------------
% 8.28/2.14 % (2959799)Success in time 1.088 s
% 8.28/2.14 % Vampire exiting
%------------------------------------------------------------------------------