%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET372+4 : 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 : n011.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 12:40:52 PM UTC 2026
% Result : Theorem 6.27s 1.85s
% Output : Refutation 7.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 143 ( 17 unt; 19 def)
% Number of atoms : 327 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 319 ( 135 ~; 144 |; 14 &)
% ( 24 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 23 ( 22 usr; 20 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f12,conjecture,
! [X0,X1] : equal_set(power_set(intersection(X0,X1)),intersection(power_set(X0),power_set(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI21) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : equal_set(power_set(intersection(X0,X1)),intersection(power_set(X0),power_set(X1))),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
? [X0,X1] : ~ equal_set(power_set(intersection(X0,X1)),intersection(power_set(X0),power_set(X1))),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f19,plain,
~ equal_set(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f20,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,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(f24,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,[],[f23]) ).
fof(f25,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))],[f24]) ).
fof(f26,plain,
~ equal_set(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f34,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f37,definition,
( spl3_1
<=> equal_set(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f40,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f26,f37]) ).
fof(f43,definition,
( spl3_2
<=> subset(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f44,plain,
( subset(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1)))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( ~ subset(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1)))
| spl3_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl3_3
<=> subset(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f49,plain,
( ~ subset(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1)))
| spl3_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,plain,
( member(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(power_set(sK0),power_set(sK1)))
| spl3_2 ),
inference(resolution,[],[f45,f34]) ).
fof(f52,plain,
( ~ member(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),power_set(intersection(sK0,sK1)))
| spl3_2 ),
inference(resolution,[],[f45,f35]) ).
fof(f55,plain,
( ~ subset(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1))
| spl3_2 ),
inference(forward_literal_rewriting,[],[f52,f28]) ).
fof(f57,definition,
( spl3_4
<=> member(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(power_set(sK0),power_set(sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f59,plain,
( member(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(power_set(sK0),power_set(sK1)))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,plain,
( spl3_4
| spl3_2 ),
inference(avatar_split_clause,[],[f51,f43,f57]) ).
fof(f62,definition,
( spl3_5
<=> subset(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f64,plain,
( ~ subset(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1))
| spl3_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( ~ spl3_5
| spl3_2 ),
inference(avatar_split_clause,[],[f55,f43,f62]) ).
fof(f78,plain,
( member(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),power_set(intersection(sK0,sK1)))
| spl3_3 ),
inference(resolution,[],[f49,f34]) ).
fof(f79,plain,
( ~ member(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),intersection(power_set(sK0),power_set(sK1)))
| spl3_3 ),
inference(resolution,[],[f49,f35]) ).
fof(f83,definition,
( spl3_7
<=> member(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),intersection(power_set(sK0),power_set(sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f85,plain,
( ~ member(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),intersection(power_set(sK0),power_set(sK1)))
| spl3_7 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( ~ spl3_7
| spl3_3 ),
inference(avatar_split_clause,[],[f79,f47,f83]) ).
fof(f87,plain,
( subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),intersection(sK0,sK1))
| spl3_3 ),
inference(forward_literal_rewriting,[],[f78,f27]) ).
fof(f89,definition,
( spl3_8
<=> subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),intersection(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f91,plain,
( subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),intersection(sK0,sK1))
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl3_8
| spl3_3 ),
inference(avatar_split_clause,[],[f87,f47,f89]) ).
fof(f98,plain,
( ! [X0] :
( ~ member(X0,sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))))
| member(X0,intersection(sK0,sK1)) )
| ~ spl3_8 ),
inference(resolution,[],[f91,f33]) ).
fof(f124,definition,
( spl3_12
<=> subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f126,plain,
( ~ subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0)
| spl3_12 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f128,definition,
( spl3_13
<=> subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f130,plain,
( ~ subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1)
| spl3_13 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f133,plain,
( ~ member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0),sK0)
| spl3_12 ),
inference(resolution,[],[f126,f35]) ).
fof(f137,definition,
( spl3_14
<=> member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f140,plain,
( ~ spl3_14
| spl3_12 ),
inference(avatar_split_clause,[],[f133,f124,f137]) ).
fof(f166,plain,
( ~ member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1),sK1)
| spl3_13 ),
inference(resolution,[],[f130,f35]) ).
fof(f170,definition,
( spl3_19
<=> member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_19])],[avatar_definition]) ).
fof(f173,plain,
( ~ spl3_19
| spl3_13 ),
inference(avatar_split_clause,[],[f166,f128,f170]) ).
fof(f446,plain,
( member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))))
| spl3_5 ),
inference(resolution,[],[f64,f34]) ).
fof(f447,plain,
( ~ member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),intersection(sK0,sK1))
| spl3_5 ),
inference(resolution,[],[f64,f35]) ).
fof(f451,definition,
( spl3_40
<=> member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),intersection(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_40])],[avatar_definition]) ).
fof(f453,plain,
( ~ member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),intersection(sK0,sK1))
| spl3_40 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f454,plain,
( ~ spl3_40
| spl3_5 ),
inference(avatar_split_clause,[],[f447,f62,f451]) ).
fof(f456,definition,
( spl3_41
<=> member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1)))) ),
introduced(definition,[new_symbols(definition,[spl3_41])],[avatar_definition]) ).
fof(f459,plain,
( spl3_41
| spl3_5 ),
inference(avatar_split_clause,[],[f446,f62,f456]) ).
fof(f460,plain,
( member(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),power_set(sK1))
| ~ spl3_4 ),
inference(resolution,[],[f59,f29]) ).
fof(f461,plain,
( member(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),power_set(sK0))
| ~ spl3_4 ),
inference(resolution,[],[f59,f30]) ).
fof(f465,plain,
( subset(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),sK0)
| ~ spl3_4 ),
inference(forward_literal_rewriting,[],[f461,f27]) ).
fof(f466,plain,
( subset(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),sK1)
| ~ spl3_4 ),
inference(forward_literal_rewriting,[],[f460,f27]) ).
fof(f468,definition,
( spl3_42
<=> subset(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_42])],[avatar_definition]) ).
fof(f470,plain,
( subset(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),sK0)
| ~ spl3_42 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f471,plain,
( spl3_42
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f465,f57,f468]) ).
fof(f473,definition,
( spl3_43
<=> subset(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_43])],[avatar_definition]) ).
fof(f475,plain,
( subset(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),sK1)
| ~ spl3_43 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f476,plain,
( spl3_43
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f466,f57,f473]) ).
fof(f511,plain,
( ! [X0] :
( member(X0,sK0)
| ~ member(X0,sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1)))) )
| ~ spl3_42 ),
inference(resolution,[],[f470,f33]) ).
fof(f530,plain,
( ! [X0] :
( member(X0,sK1)
| ~ member(X0,sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1)))) )
| ~ spl3_43 ),
inference(resolution,[],[f475,f33]) ).
fof(f579,plain,
( ~ member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK0)
| ~ member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK1)
| spl3_40 ),
inference(resolution,[],[f453,f31]) ).
fof(f584,definition,
( spl3_54
<=> member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_54])],[avatar_definition]) ).
fof(f586,plain,
( ~ member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK1)
| spl3_54 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f588,definition,
( spl3_55
<=> member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_55])],[avatar_definition]) ).
fof(f590,plain,
( ~ member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK0)
| spl3_55 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f591,plain,
( ~ spl3_54
| ~ spl3_55
| spl3_40 ),
inference(avatar_split_clause,[],[f579,f451,f588,f584]) ).
fof(f793,plain,
( ~ member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))))
| ~ spl3_43
| spl3_54 ),
inference(resolution,[],[f586,f530]) ).
fof(f797,plain,
( ~ spl3_41
| ~ spl3_43
| spl3_54 ),
inference(avatar_split_clause,[],[f793,f584,f473,f456]) ).
fof(f801,plain,
( ~ member(sK2(sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))),intersection(sK0,sK1)),sK2(intersection(power_set(sK0),power_set(sK1)),power_set(intersection(sK0,sK1))))
| ~ spl3_42
| spl3_55 ),
inference(resolution,[],[f590,f511]) ).
fof(f805,plain,
( ~ spl3_41
| ~ spl3_42
| spl3_55 ),
inference(avatar_split_clause,[],[f801,f588,f468,f456]) ).
fof(f808,plain,
( equal_set(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1)))
| ~ subset(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1)))
| ~ spl3_2 ),
inference(resolution,[],[f44,f32]) ).
fof(f813,plain,
( ~ spl3_3
| spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f808,f43,f37,f47]) ).
fof(f847,plain,
( ~ member(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),power_set(sK0))
| ~ member(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),power_set(sK1))
| spl3_7 ),
inference(resolution,[],[f85,f31]) ).
fof(f851,plain,
( ~ subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0)
| ~ member(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),power_set(sK1))
| spl3_7 ),
inference(forward_literal_rewriting,[],[f847,f28]) ).
fof(f852,plain,
( ~ subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1)
| ~ subset(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0)
| spl3_7 ),
inference(forward_literal_rewriting,[],[f851,f28]) ).
fof(f853,plain,
( ~ spl3_12
| ~ spl3_13
| spl3_7 ),
inference(avatar_split_clause,[],[f852,f83,f128,f124]) ).
fof(f854,plain,
( member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0),sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))))
| spl3_12 ),
inference(resolution,[],[f126,f34]) ).
fof(f858,plain,
( member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0),intersection(sK0,sK1))
| ~ spl3_8
| spl3_12 ),
inference(forward_literal_rewriting,[],[f854,f98]) ).
fof(f860,definition,
( spl3_76
<=> member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0),intersection(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_76])],[avatar_definition]) ).
fof(f862,plain,
( member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0),intersection(sK0,sK1))
| ~ spl3_76 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f863,plain,
( spl3_76
| ~ spl3_8
| spl3_12 ),
inference(avatar_split_clause,[],[f858,f124,f89,f860]) ).
fof(f942,plain,
( member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK0),sK0)
| ~ spl3_76 ),
inference(resolution,[],[f862,f30]) ).
fof(f946,plain,
( spl3_14
| ~ spl3_76 ),
inference(avatar_split_clause,[],[f942,f860,f137]) ).
fof(f958,plain,
( member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1),sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))))
| spl3_13 ),
inference(resolution,[],[f130,f34]) ).
fof(f962,plain,
( member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1),intersection(sK0,sK1))
| ~ spl3_8
| spl3_13 ),
inference(forward_literal_rewriting,[],[f958,f98]) ).
fof(f964,definition,
( spl3_83
<=> member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1),intersection(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_83])],[avatar_definition]) ).
fof(f966,plain,
( member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1),intersection(sK0,sK1))
| ~ spl3_83 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f967,plain,
( spl3_83
| ~ spl3_8
| spl3_13 ),
inference(avatar_split_clause,[],[f962,f128,f89,f964]) ).
fof(f972,plain,
( member(sK2(sK2(power_set(intersection(sK0,sK1)),intersection(power_set(sK0),power_set(sK1))),sK1),sK1)
| ~ spl3_83 ),
inference(resolution,[],[f966,f29]) ).
fof(f982,plain,
( spl3_19
| ~ spl3_83 ),
inference(avatar_split_clause,[],[f972,f964,f170]) ).
cnf(s1,plain,
~ spl3_1,
inference(sat_conversion,[],[f40]) ).
cnf(s3,plain,
( spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
( spl3_2
| ~ spl3_5 ),
inference(sat_conversion,[],[f65]) ).
cnf(s7,plain,
( spl3_3
| ~ spl3_7 ),
inference(sat_conversion,[],[f86]) ).
cnf(s8,plain,
( spl3_3
| spl3_8 ),
inference(sat_conversion,[],[f92]) ).
cnf(s12,plain,
( spl3_12
| ~ spl3_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s16,plain,
( spl3_13
| ~ spl3_19 ),
inference(sat_conversion,[],[f173]) ).
cnf(s41,plain,
( spl3_5
| ~ spl3_40 ),
inference(sat_conversion,[],[f454]) ).
cnf(s42,plain,
( spl3_5
| spl3_41 ),
inference(sat_conversion,[],[f459]) ).
cnf(s43,plain,
( ~ spl3_4
| spl3_42 ),
inference(sat_conversion,[],[f471]) ).
cnf(s44,plain,
( ~ spl3_4
| spl3_43 ),
inference(sat_conversion,[],[f476]) ).
cnf(s60,plain,
( spl3_40
| ~ spl3_54
| ~ spl3_55 ),
inference(sat_conversion,[],[f591]) ).
cnf(s96,plain,
( ~ spl3_41
| ~ spl3_43
| spl3_54 ),
inference(sat_conversion,[],[f797]) ).
cnf(s97,plain,
( ~ spl3_41
| ~ spl3_42
| spl3_55 ),
inference(sat_conversion,[],[f805]) ).
cnf(s99,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f813]) ).
cnf(s104,plain,
( spl3_7
| ~ spl3_12
| ~ spl3_13 ),
inference(sat_conversion,[],[f853]) ).
cnf(s105,plain,
( ~ spl3_8
| spl3_12
| spl3_76 ),
inference(sat_conversion,[],[f863]) ).
cnf(s112,plain,
( spl3_14
| ~ spl3_76 ),
inference(sat_conversion,[],[f946]) ).
cnf(s114,plain,
( ~ spl3_8
| spl3_13
| spl3_83 ),
inference(sat_conversion,[],[f967]) ).
cnf(s116,plain,
( spl3_19
| ~ spl3_83 ),
inference(sat_conversion,[],[f982]) ).
cnf(s117,plain,
spl3_2,
inference(rat,[],[s60,s97,s96,s43,s44,s41,s42,s3,s4]) ).
cnf(s118,plain,
~ spl3_3,
inference(rat,[],[s99,s1,s117]) ).
cnf(s119,plain,
spl3_8,
inference(rat,[],[s8,s118]) ).
cnf(s120,plain,
~ spl3_7,
inference(rat,[],[s7,s118]) ).
cnf(s121,plain,
spl3_12,
inference(rat,[],[s112,s12,s105,s119]) ).
cnf(s122,plain,
~ spl3_13,
inference(rat,[],[s104,s120,s121]) ).
cnf(s123,plain,
spl3_83,
inference(rat,[],[s114,s119,s122]) ).
cnf(s125,plain,
~ spl3_19,
inference(rat,[],[s16,s122]) ).
cnf(s127,plain,
$false,
inference(rat,[],[s116,s123,s125]) ).
fof(f983,plain,
$false,
inference(avatar_sat_refutation,[],[s127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET372+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 01:36:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.27/1.85 % (2939656)Detected formulas, will run a generic FOF schedule.
% 6.27/1.85 % (2939662)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=509338827:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.27/1.85 % (2939664)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1536929597:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.27/1.85 % (2939664)Refutation not found, incomplete strategy
% 6.27/1.85 % (2939664)------------------------------
% 6.27/1.85 % (2939664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939664)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939664)Termination reason: Refutation not found, incomplete strategy
% 6.27/1.85 % (2939664)Time elapsed: 0.001 s
% 6.27/1.85 % (2939664)Peak memory usage: 88 MB
% 6.27/1.85 % (2939663)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=2676293683:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.27/1.85 % (2939661)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=1695475966:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.27/1.85 % (2939666)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=103776392:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.27/1.85 % (2939665)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=524977910:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.27/1.85 % (2939667)dis-21_1_sil=8000:lcm=predicate:random_seed=3815136308: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)
% 6.27/1.85 % (2939665)Instruction limit reached!
% 6.27/1.85 % (2939665)------------------------------
% 6.27/1.85 % (2939665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939665)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939665)Termination reason: Instruction limit
% 6.27/1.85 % (2939665)Termination phase: Saturation
% 6.27/1.85 % (2939665)Time elapsed: 0.067 s
% 6.27/1.85 % (2939665)Peak memory usage: 88 MB
% 6.27/1.85 % (2939665)Instructions burned: 120 (million)
% 6.27/1.85 % (2939667)Instruction limit reached!
% 6.27/1.85 % (2939667)------------------------------
% 6.27/1.85 % (2939667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939667)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939667)Termination reason: Instruction limit
% 6.27/1.85 % (2939667)Termination phase: Saturation
% 6.27/1.85 % (2939667)Time elapsed: 0.078 s
% 6.27/1.85 % (2939667)Peak memory usage: 89 MB
% 6.27/1.85 % (2939667)Instructions burned: 131 (million)
% 6.27/1.85 % (2939666)Instruction limit reached!
% 6.27/1.85 % (2939666)------------------------------
% 6.27/1.85 % (2939666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939666)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939666)Termination reason: Instruction limit
% 6.27/1.85 % (2939666)Termination phase: Saturation
% 6.27/1.85 % (2939666)Time elapsed: 0.098 s
% 6.27/1.85 % (2939666)Peak memory usage: 89 MB
% 6.27/1.85 % (2939666)Instructions burned: 140 (million)
% 6.27/1.85 % (2939675)lrs+10_1_sil=8000:sp=occurrence:random_seed=577280127:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.27/1.85 % (2939676)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3221372865:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.27/1.85 % (2939676)Refutation not found, incomplete strategy
% 6.27/1.85 % (2939676)------------------------------
% 6.27/1.85 % (2939676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939676)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939676)Termination reason: Refutation not found, incomplete strategy
% 6.27/1.85 % (2939676)Time elapsed: 0.001 s
% 6.27/1.85 % (2939676)Peak memory usage: 88 MB
% 6.27/1.85 % (2939677)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3907727359:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.27/1.85 % (2939677)Refutation not found, incomplete strategy
% 6.27/1.85 % (2939677)------------------------------
% 6.27/1.85 % (2939677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939677)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939677)Termination reason: Refutation not found, incomplete strategy
% 6.27/1.85 % (2939677)Time elapsed: 0.001 s
% 6.27/1.85 % (2939677)Peak memory usage: 88 MB
% 6.27/1.85 % (2939664)------------------------------
% 6.27/1.85 % (2939664)------------------------------
% 6.27/1.85 % (2939681)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=2661368310:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.27/1.85 % (2939675)Instruction limit reached!
% 6.27/1.85 % (2939675)------------------------------
% 6.27/1.85 % (2939675)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939675)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939675)Termination reason: Instruction limit
% 6.27/1.85 % (2939675)Termination phase: Saturation
% 6.27/1.85 % (2939675)Time elapsed: 0.167 s
% 6.27/1.85 % (2939675)Peak memory usage: 91 MB
% 6.27/1.85 % (2939675)Instructions burned: 286 (million)
% 6.27/1.85 % (2939676)------------------------------
% 6.27/1.85 % (2939676)------------------------------
% 6.27/1.85 % (2939677)------------------------------
% 6.27/1.85 % (2939677)------------------------------
% 6.27/1.85 % (2939683)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1278236371:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 6.27/1.85 % (2939683)Refutation not found, incomplete strategy
% 6.27/1.85 % (2939683)------------------------------
% 6.27/1.85 % (2939683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939683)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939683)Termination reason: Refutation not found, incomplete strategy
% 6.27/1.85 % (2939683)Time elapsed: 0.001 s
% 6.27/1.85 % (2939683)Peak memory usage: 88 MB
% 6.27/1.85 % (2939681)Instruction limit reached!
% 6.27/1.85 % (2939681)------------------------------
% 6.27/1.85 % (2939681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939681)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939681)Termination reason: Instruction limit
% 6.27/1.85 % (2939681)Termination phase: Saturation
% 6.27/1.85 % (2939681)Time elapsed: 0.130 s
% 6.27/1.85 % (2939681)Peak memory usage: 92 MB
% 6.27/1.85 % (2939681)Instructions burned: 248 (million)
% 6.27/1.85 % (2939684)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1401557226:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.27/1.85 % (2939685)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1230482164:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.27/1.85 % (2939685)First to succeed.
% 6.27/1.85 % (2939685)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2939656"
% 6.27/1.85 % (2939687)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1614536448:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.27/1.85 % (2939687)Instruction limit reached!
% 6.27/1.85 % (2939687)------------------------------
% 6.27/1.85 % (2939687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/1.85 % (2939687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.85 % (2939687)CaDiCaL version: 2.1.3
% 6.27/1.85 % (2939687)Termination reason: Instruction limit
% 6.27/1.85 % (2939687)Termination phase: Saturation
% 6.27/1.85 % (2939687)Time elapsed: 0.059 s
% 6.27/1.85 % (2939687)Peak memory usage: 88 MB
% 6.27/1.85 % (2939687)Instructions burned: 127 (million)
% 6.27/1.85 % (2939683)------------------------------
% 6.27/1.85 % (2939683)------------------------------
% 6.27/1.85 % (2939661)Also succeeded, but the first one will report.
% 6.27/1.85 % (2939691)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4203521176:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 6.27/1.85 % (2939685)Refutation found. Thanks to Tanya!
% 6.27/1.85 % SZS status Theorem for theBenchmark
% 6.27/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 7.73/2.05 % (2939685)------------------------------
% 7.73/2.05 % (2939685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/2.05 % (2939685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/2.05 % (2939685)CaDiCaL version: 2.1.3
% 7.73/2.05 % (2939685)Termination reason: Refutation
% 7.73/2.05 % (2939685)Time elapsed: 0.017 s
% 7.73/2.05 % (2939685)Peak memory usage: 90 MB
% 7.73/2.05 % (2939685)Instructions burned: 22 (million)
% 7.73/2.05 % (2939685)------------------------------
% 7.73/2.05 % (2939685)------------------------------
% 7.73/2.05 % (2939656)Success in time 1.009 s
% 7.73/2.05 % Vampire exiting
%------------------------------------------------------------------------------