%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET770+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 : n017.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 12:41:53 PM UTC 2026
% Result : Theorem 3.20s 1.32s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 140 ( 23 unt; 9 def)
% Number of atoms : 471 ( 4 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 574 ( 243 ~; 237 |; 56 &)
% ( 17 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 10 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 194 ( 0 sgn 181 !; 13 ?)
% 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(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
fof(f12,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint) ).
fof(f14,axiom,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X2,X3] :
( ( member(X2,X0)
& member(X3,X0) )
=> ( apply(X1,X2,X3)
=> apply(X1,X3,X2) ) )
& ! [X2,X3,X4] :
( ( member(X2,X0)
& member(X3,X0)
& member(X4,X0) )
=> ( ( apply(X1,X2,X3)
& apply(X1,X3,X4) )
=> apply(X1,X2,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( member(X3,X1)
& apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_class) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( ( equivalence(X1,X0)
& member(X2,X0)
& member(X3,X0) )
=> ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
| disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII06) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( equivalence(X1,X0)
& member(X2,X0)
& member(X3,X0) )
=> ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
| disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X5,X6,X7] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X1,X6,X7) )
=> apply(X1,X5,X7) ) ) ) ),
inference(rectify,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( equivalence(X1,X0)
=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X5,X6,X7] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X1,X6,X7) )
=> apply(X1,X5,X7) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f23,plain,
! [X0,X1] :
( ~ ? [X2] :
( member(X2,X0)
& member(X2,X1) )
=> disjoint(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f26]) ).
fof(f29,plain,
! [X0,X1] :
( disjoint(X0,X1)
| ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X1,X2,X2)
| ~ member(X2,X0) )
& ! [X3,X4] :
( apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X3,X0)
| ~ member(X4,X0) )
& ! [X5,X6,X7] :
( apply(X1,X5,X7)
| ~ apply(X1,X5,X6)
| ~ apply(X1,X6,X7)
| ~ member(X5,X0)
| ~ member(X6,X0)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f31,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X1,X2,X2)
| ~ member(X2,X0) )
& ! [X3,X4] :
( apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X3,X0)
| ~ member(X4,X0) )
& ! [X5,X6,X7] :
( apply(X1,X5,X7)
| ~ apply(X1,X5,X6)
| ~ apply(X1,X6,X7)
| ~ member(X5,X0)
| ~ member(X6,X0)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
? [X0,X1,X2,X3] :
( ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& equivalence(X1,X0)
& member(X2,X0)
& member(X3,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f33,plain,
? [X0,X1,X2,X3] :
( ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
& equivalence(X1,X0)
& member(X2,X0)
& member(X3,X0) ),
inference(flattening,[],[f32]) ).
fof(f34,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,[],[f25]) ).
fof(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f35]) ).
fof(f44,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f53,plain,
! [X0,X1] :
( disjoint(X0,X1)
| ( member(sK3(X0,X1),X0)
& member(sK3(X0,X1),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f29]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) )
& ( ( member(X3,X1)
& apply(X0,X2,X3) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) )
& ( ( member(X3,X1)
& apply(X0,X2,X3) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
& ~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
& equivalence(sK5,sK4)
& member(sK6,sK4)
& member(sK7,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f33]) ).
fof(f58,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f60,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f74,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f84,plain,
! [X0,X1] :
( disjoint(X0,X1)
| member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f85,plain,
! [X0,X1] :
( disjoint(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f86,plain,
! [X0,X1,X6,X7,X5] :
( apply(X1,X5,X7)
| ~ apply(X1,X5,X6)
| ~ apply(X1,X6,X7)
| ~ member(X5,X0)
| ~ member(X6,X0)
| ~ member(X7,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f87,plain,
! [X3,X0,X1,X4] :
( apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X3,X0)
| ~ member(X4,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( apply(X0,X2,X3)
| ~ member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,equivalence_class(X2,X1,X0))
| member(X3,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( member(X3,equivalence_class(X2,X1,X0))
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f55]) ).
fof(f92,plain,
member(sK7,sK4),
inference(cnf_transformation,[],[f56]) ).
fof(f93,plain,
member(sK6,sK4),
inference(cnf_transformation,[],[f56]) ).
fof(f94,plain,
equivalence(sK5,sK4),
inference(cnf_transformation,[],[f56]) ).
fof(f95,plain,
~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
inference(cnf_transformation,[],[f56]) ).
fof(f96,plain,
~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
inference(cnf_transformation,[],[f56]) ).
fof(f97,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f74]) ).
fof(f104,plain,
member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK7,sK4,sK5)),
inference(resolution,[],[f84,f95]) ).
fof(f105,plain,
member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5)),
inference(resolution,[],[f85,f95]) ).
fof(f107,plain,
( ~ subset(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
| ~ subset(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)) ),
inference(resolution,[],[f60,f96]) ).
fof(f109,definition,
( spl8_1
<=> subset(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f111,plain,
( ~ subset(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5))
| spl8_1 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl8_2
<=> subset(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f115,plain,
( ~ subset(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
| spl8_2 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f107,f113,f109]) ).
fof(f117,plain,
( member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK7,sK4,sK5))
| spl8_1 ),
inference(resolution,[],[f111,f58]) ).
fof(f119,plain,
member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4),
inference(resolution,[],[f90,f104]) ).
fof(f121,plain,
( member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4)
| spl8_1 ),
inference(resolution,[],[f90,f117]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( subset(X0,equivalence_class(X1,X2,X3))
| ~ apply(X3,X1,sK0(X0,equivalence_class(X1,X2,X3)))
| ~ member(sK0(X0,equivalence_class(X1,X2,X3)),X2) ),
inference(resolution,[],[f91,f59]) ).
fof(f195,plain,
( ~ apply(sK5,sK6,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
| ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4)
| spl8_1 ),
inference(resolution,[],[f138,f111]) ).
fof(f196,plain,
( ~ apply(sK5,sK6,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f195,f121]) ).
fof(f197,plain,
( ! [X0,X1] :
( ~ equivalence(sK5,X1)
| ~ apply(sK5,X0,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
| ~ member(sK6,X1)
| ~ member(X0,X1)
| ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),X1)
| ~ apply(sK5,sK6,X0) )
| spl8_1 ),
inference(resolution,[],[f196,f86]) ).
fof(f223,plain,
( ! [X0] :
( ~ apply(sK5,X0,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
| ~ member(sK6,sK4)
| ~ member(X0,sK4)
| ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4)
| ~ apply(sK5,sK6,X0) )
| spl8_1 ),
inference(resolution,[],[f197,f94]) ).
fof(f224,plain,
( ! [X0] :
( ~ apply(sK5,X0,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
| ~ member(X0,sK4)
| ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4)
| ~ apply(sK5,sK6,X0) )
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f223,f93]) ).
fof(f225,plain,
( ! [X0] :
( ~ apply(sK5,sK6,X0)
| ~ member(X0,sK4)
| ~ apply(sK5,X0,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5))) )
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f224,f121]) ).
fof(f231,plain,
( ! [X0,X1] :
( ~ apply(sK5,X0,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
| ~ member(X0,sK4)
| ~ member(X0,equivalence_class(sK6,X1,sK5)) )
| spl8_1 ),
inference(resolution,[],[f225,f89]) ).
fof(f237,plain,
( ! [X2,X0,X1] :
( ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(X0,X2,sK5))
| ~ member(X0,equivalence_class(sK6,X1,sK5))
| ~ member(X0,sK4) )
| spl8_1 ),
inference(resolution,[],[f231,f89]) ).
fof(f240,plain,
( ! [X0] :
( ~ member(sK7,equivalence_class(sK6,X0,sK5))
| ~ member(sK7,sK4) )
| spl8_1 ),
inference(resolution,[],[f237,f117]) ).
fof(f244,plain,
( ! [X0] : ~ member(sK7,equivalence_class(sK6,X0,sK5))
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f240,f92]) ).
fof(f249,definition,
( spl8_6
<=> ! [X0] : ~ member(sK7,equivalence_class(sK6,X0,sK5)) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
fof(f250,plain,
( ! [X0] : ~ member(sK7,equivalence_class(sK6,X0,sK5))
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f252,plain,
( spl8_6
| spl8_1 ),
inference(avatar_split_clause,[],[f244,f109,f249]) ).
fof(f255,plain,
( ! [X0] :
( ~ member(sK7,X0)
| ~ apply(sK5,sK6,sK7) )
| ~ spl8_6 ),
inference(resolution,[],[f250,f91]) ).
fof(f257,definition,
( spl8_7
<=> apply(sK5,sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
fof(f259,plain,
( ~ apply(sK5,sK6,sK7)
| spl8_7 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f261,definition,
( spl8_8
<=> ! [X0] : ~ member(sK7,X0) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
fof(f262,plain,
( ! [X0] : ~ member(sK7,X0)
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( ~ spl8_7
| spl8_8
| ~ spl8_6 ),
inference(avatar_split_clause,[],[f255,f249,f261,f257]) ).
fof(f266,plain,
( ! [X0,X1] :
( ~ equivalence(sK5,X1)
| ~ apply(sK5,X0,sK7)
| ~ member(sK6,X1)
| ~ member(X0,X1)
| ~ member(sK7,X1)
| ~ apply(sK5,sK6,X0) )
| spl8_7 ),
inference(resolution,[],[f259,f86]) ).
fof(f270,definition,
( spl8_9
<=> ! [X0] :
( ~ member(sK7,X0)
| ~ equivalence(sK5,X0)
| ~ member(sK6,X0) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
fof(f271,plain,
( ! [X0] :
( ~ equivalence(sK5,X0)
| ~ member(sK7,X0)
| ~ member(sK6,X0) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,definition,
( spl8_10
<=> apply(sK5,sK7,sK6) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
fof(f274,plain,
( apply(sK5,sK7,sK6)
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( ~ apply(sK5,sK7,sK6)
| spl8_10 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f282,plain,
( ! [X0] :
( ~ apply(sK5,sK6,sK7)
| ~ member(sK6,X0)
| ~ member(sK7,X0)
| ~ equivalence(sK5,X0) )
| spl8_10 ),
inference(resolution,[],[f275,f87]) ).
fof(f293,plain,
( ! [X0] :
( ~ apply(sK5,X0,sK7)
| ~ member(sK6,sK4)
| ~ member(X0,sK4)
| ~ member(sK7,sK4)
| ~ apply(sK5,sK6,X0) )
| spl8_7 ),
inference(resolution,[],[f266,f94]) ).
fof(f294,plain,
( ! [X0] :
( ~ apply(sK5,X0,sK7)
| ~ member(X0,sK4)
| ~ member(sK7,sK4)
| ~ apply(sK5,sK6,X0) )
| spl8_7 ),
inference(forward_subsumption_resolution,[],[f293,f93]) ).
fof(f295,plain,
( ! [X0] :
( ~ apply(sK5,sK6,X0)
| ~ member(X0,sK4)
| ~ apply(sK5,X0,sK7) )
| spl8_7 ),
inference(forward_subsumption_resolution,[],[f294,f92]) ).
fof(f303,plain,
( ! [X0,X1] :
( ~ apply(sK5,X0,sK7)
| ~ member(X0,sK4)
| ~ member(X0,equivalence_class(sK6,X1,sK5)) )
| spl8_7 ),
inference(resolution,[],[f295,f89]) ).
fof(f310,plain,
( ! [X2,X0,X1] :
( ~ equivalence(sK5,X2)
| ~ member(X0,equivalence_class(sK6,X1,sK5))
| ~ apply(sK5,sK7,X0)
| ~ member(sK7,X2)
| ~ member(X0,X2)
| ~ member(X0,sK4) )
| spl8_7 ),
inference(resolution,[],[f303,f87]) ).
fof(f378,plain,
( ! [X0,X1] :
( ~ member(X0,equivalence_class(sK6,X1,sK5))
| ~ apply(sK5,sK7,X0)
| ~ member(sK7,sK4)
| ~ member(X0,sK4)
| ~ member(X0,sK4) )
| spl8_7 ),
inference(resolution,[],[f310,f94]) ).
fof(f379,plain,
( ! [X0,X1] :
( ~ member(X0,equivalence_class(sK6,X1,sK5))
| ~ apply(sK5,sK7,X0)
| ~ member(sK7,sK4)
| ~ member(X0,sK4) )
| spl8_7 ),
inference(duplicate_literal_removal,[],[f378]) ).
fof(f380,plain,
( ! [X0,X1] :
( ~ apply(sK5,sK7,X0)
| ~ member(X0,equivalence_class(sK6,X1,sK5))
| ~ member(X0,sK4) )
| spl8_7 ),
inference(forward_subsumption_resolution,[],[f379,f92]) ).
fof(f386,plain,
( ! [X2,X0,X1] :
( ~ member(X0,equivalence_class(sK6,X1,sK5))
| ~ member(X0,sK4)
| ~ member(X0,equivalence_class(sK7,X2,sK5)) )
| spl8_7 ),
inference(resolution,[],[f380,f89]) ).
fof(f389,plain,
( ! [X0] :
( ~ member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| ~ member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK7,X0,sK5)) )
| spl8_7 ),
inference(resolution,[],[f386,f105]) ).
fof(f394,plain,
( ! [X0] : ~ member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK7,X0,sK5))
| spl8_7 ),
inference(forward_subsumption_resolution,[],[f389,f119]) ).
fof(f397,plain,
( $false
| spl8_7 ),
inference(resolution,[],[f394,f104]) ).
fof(f399,plain,
spl8_7,
inference(avatar_contradiction_clause,[],[f397]) ).
fof(f408,plain,
( spl8_9
| ~ spl8_7
| spl8_10 ),
inference(avatar_split_clause,[],[f282,f273,f257,f270]) ).
fof(f425,plain,
( $false
| ~ spl8_8 ),
inference(resolution,[],[f262,f97]) ).
fof(f437,plain,
~ spl8_8,
inference(avatar_contradiction_clause,[],[f425]) ).
fof(f446,plain,
( ~ apply(sK5,sK7,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| spl8_2 ),
inference(resolution,[],[f115,f138]) ).
fof(f447,plain,
( member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5))
| spl8_2 ),
inference(resolution,[],[f115,f58]) ).
fof(f449,definition,
( spl8_14
<=> member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
fof(f450,plain,
( member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f453,definition,
( spl8_15
<=> apply(sK5,sK7,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))) ),
introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition]) ).
fof(f455,plain,
( ~ apply(sK5,sK7,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| spl8_15 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f456,plain,
( ~ spl8_14
| ~ spl8_15
| spl8_2 ),
inference(avatar_split_clause,[],[f446,f113,f453,f449]) ).
fof(f457,plain,
( ~ member(sK7,sK4)
| ~ member(sK6,sK4)
| ~ spl8_9 ),
inference(resolution,[],[f271,f94]) ).
fof(f458,plain,
( ~ member(sK6,sK4)
| ~ spl8_9 ),
inference(forward_subsumption_resolution,[],[f457,f92]) ).
fof(f459,plain,
( $false
| ~ spl8_9 ),
inference(forward_subsumption_resolution,[],[f458,f93]) ).
fof(f460,plain,
~ spl8_9,
inference(avatar_contradiction_clause,[],[f459]) ).
fof(f465,plain,
( member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| spl8_2 ),
inference(resolution,[],[f447,f90]) ).
fof(f468,plain,
( spl8_14
| spl8_2 ),
inference(avatar_split_clause,[],[f465,f113,f449]) ).
fof(f469,plain,
( ! [X0,X1] :
( ~ equivalence(sK5,X1)
| ~ apply(sK5,X0,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| ~ member(sK7,X1)
| ~ member(X0,X1)
| ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),X1)
| ~ apply(sK5,sK7,X0) )
| spl8_15 ),
inference(resolution,[],[f455,f86]) ).
fof(f636,plain,
( ! [X0] :
( ~ apply(sK5,X0,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| ~ member(sK7,sK4)
| ~ member(X0,sK4)
| ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| ~ apply(sK5,sK7,X0) )
| spl8_15 ),
inference(resolution,[],[f469,f94]) ).
fof(f637,plain,
( ! [X0] :
( ~ apply(sK5,X0,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| ~ member(X0,sK4)
| ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
| ~ apply(sK5,sK7,X0) )
| spl8_15 ),
inference(forward_subsumption_resolution,[],[f636,f92]) ).
fof(f638,plain,
( ! [X0] :
( ~ apply(sK5,X0,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
| ~ member(X0,sK4)
| ~ apply(sK5,sK7,X0) )
| ~ spl8_14
| spl8_15 ),
inference(forward_subsumption_resolution,[],[f637,f450]) ).
fof(f642,plain,
( ! [X0,X1] :
( ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(X0,X1,sK5))
| ~ apply(sK5,sK7,X0)
| ~ member(X0,sK4) )
| ~ spl8_14
| spl8_15 ),
inference(resolution,[],[f638,f89]) ).
fof(f648,plain,
( ~ apply(sK5,sK7,sK6)
| ~ member(sK6,sK4)
| spl8_2
| ~ spl8_14
| spl8_15 ),
inference(resolution,[],[f642,f447]) ).
fof(f653,plain,
( ~ member(sK6,sK4)
| spl8_2
| ~ spl8_10
| ~ spl8_14
| spl8_15 ),
inference(forward_subsumption_resolution,[],[f648,f274]) ).
fof(f655,plain,
( $false
| spl8_2
| ~ spl8_10
| ~ spl8_14
| spl8_15 ),
inference(forward_subsumption_resolution,[],[f653,f93]) ).
fof(f656,plain,
( spl8_2
| ~ spl8_10
| ~ spl8_14
| spl8_15 ),
inference(avatar_contradiction_clause,[],[f655]) ).
cnf(s1,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f116]) ).
cnf(s4,plain,
( spl8_1
| spl8_6 ),
inference(sat_conversion,[],[f252]) ).
cnf(s5,plain,
( ~ spl8_6
| ~ spl8_7
| spl8_8 ),
inference(sat_conversion,[],[f263]) ).
cnf(s7,plain,
spl8_7,
inference(sat_conversion,[],[f399]) ).
cnf(s9,plain,
( ~ spl8_7
| spl8_9
| spl8_10 ),
inference(sat_conversion,[],[f408]) ).
cnf(s13,plain,
~ spl8_8,
inference(sat_conversion,[],[f437]) ).
cnf(s16,plain,
( spl8_2
| ~ spl8_14
| ~ spl8_15 ),
inference(sat_conversion,[],[f456]) ).
cnf(s17,plain,
~ spl8_9,
inference(sat_conversion,[],[f460]) ).
cnf(s19,plain,
( spl8_2
| spl8_14 ),
inference(sat_conversion,[],[f468]) ).
cnf(s23,plain,
( spl8_2
| ~ spl8_10
| ~ spl8_14
| spl8_15 ),
inference(sat_conversion,[],[f656]) ).
cnf(s24,plain,
( ~ spl8_7
| spl8_10 ),
inference(rat,[],[s9,s17]) ).
cnf(s25,plain,
spl8_10,
inference(rat,[],[s24,s7]) ).
cnf(s26,plain,
~ spl8_6,
inference(rat,[],[s5,s13,s7]) ).
cnf(s27,plain,
spl8_1,
inference(rat,[],[s4,s26]) ).
cnf(s29,plain,
~ spl8_2,
inference(rat,[],[s1,s27]) ).
cnf(s30,plain,
spl8_14,
inference(rat,[],[s19,s29]) ).
cnf(s31,plain,
~ spl8_15,
inference(rat,[],[s16,s29,s30]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s23,s29,s25,s31,s30]) ).
fof(f657,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET770+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 02:41:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 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
% 3.20/1.32 % (3162066)Detected formulas, will run a generic FOF schedule.
% 3.20/1.32 % (3162074)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3220771884:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.20/1.32 % (3162074)Refutation not found, incomplete strategy
% 3.20/1.32 % (3162074)------------------------------
% 3.20/1.32 % (3162074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.32 % (3162074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.32 % (3162074)CaDiCaL version: 2.1.3
% 3.20/1.32 % (3162074)Termination reason: Refutation not found, incomplete strategy
% 3.20/1.32 % (3162074)Time elapsed: 0.001 s
% 3.20/1.32 % (3162074)Peak memory usage: 88 MB
% 3.20/1.32 % (3162074)Instructions burned: 1 (million)
% 3.20/1.32 % (3162077)dis-21_1_sil=8000:lcm=predicate:random_seed=2792552484: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)
% 3.20/1.32 % (3162073)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=3391828138:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.20/1.32 % (3162071)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=621752058:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.20/1.32 % (3162072)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=825157131:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.20/1.32 % (3162075)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3319793981:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.20/1.32 % (3162076)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1115890723:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.20/1.32 % (3162076)First to succeed.
% 3.20/1.32 % (3162076)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3162066"
% 3.20/1.32 % (3162075)Also succeeded, but the first one will report.
% 3.20/1.32 % (3162077)Instruction limit reached!
% 3.20/1.32 % (3162077)------------------------------
% 3.20/1.32 % (3162077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.32 % (3162077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.32 % (3162077)CaDiCaL version: 2.1.3
% 3.20/1.32 % (3162077)Termination reason: Instruction limit
% 3.20/1.32 % (3162077)Termination phase: Saturation
% 3.20/1.32 % (3162077)Time elapsed: 0.082 s
% 3.20/1.32 % (3162077)Peak memory usage: 89 MB
% 3.20/1.32 % (3162077)Instructions burned: 129 (million)
% 3.20/1.32 % (3162074)------------------------------
% 3.20/1.32 % (3162074)------------------------------
% 3.20/1.32 % (3162085)lrs+10_1_sil=8000:sp=occurrence:random_seed=2399125871:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.20/1.32 % (3162086)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1740577828:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.20/1.32 % (3162086)Instruction limit reached!
% 3.20/1.32 % (3162086)------------------------------
% 3.20/1.32 % (3162086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.32 % (3162086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.32 % (3162086)CaDiCaL version: 2.1.3
% 3.20/1.32 % (3162086)Termination reason: Instruction limit
% 3.20/1.32 % (3162086)Termination phase: Saturation
% 3.20/1.32 % (3162086)Time elapsed: 0.039 s
% 3.20/1.32 % (3162086)Peak memory usage: 88 MB
% 3.20/1.32 % (3162086)Instructions burned: 157 (million)
% 3.20/1.32 % (3162076)Refutation found. Thanks to Tanya!
% 3.20/1.32 % SZS status Theorem for theBenchmark
% 3.20/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.42 % (3162076)------------------------------
% 3.80/1.42 % (3162076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.42 % (3162076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.42 % (3162076)CaDiCaL version: 2.1.3
% 3.80/1.42 % (3162076)Termination reason: Refutation
% 3.80/1.42 % (3162076)Time elapsed: 0.031 s
% 3.80/1.42 % (3162076)Peak memory usage: 90 MB
% 3.80/1.42 % (3162076)Instructions burned: 40 (million)
% 3.80/1.42 % (3162076)------------------------------
% 3.80/1.42 % (3162076)------------------------------
% 3.80/1.42 % (3162066)Success in time 0.465 s
% 3.80/1.42 % Vampire exiting
%------------------------------------------------------------------------------