%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET765+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:41:52 PM UTC 2026
% Result : Theorem 2.50s 1.31s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 5
% Syntax : Number of formulae : 102 ( 6 unt; 2 def)
% Number of atoms : 634 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 954 ( 422 ~; 436 |; 73 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 357 ( 336 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
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/sandbox2/benchmark/theBenchmark.p',equivalence) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( equivalence(X1,X0)
& subset(X2,X0) )
=> equivalence(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII01) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( equivalence(X1,X0)
& subset(X2,X0) )
=> equivalence(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,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(f20,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f21,plain,
? [X0,X1,X2] :
( ~ equivalence(X1,X2)
& equivalence(X1,X0)
& subset(X2,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ~ equivalence(X1,X2)
& equivalence(X1,X0)
& subset(X2,X0) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f24,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [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) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f25,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [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) ) ) ),
inference(flattening,[],[f24]) ).
fof(f26,definition,
! [X1,X0] :
( sP0(X1,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) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f27,definition,
! [X1,X0] :
( sP1(X1,X0)
<=> ( ! [X2] :
( apply(X1,X2,X2)
| ~ member(X2,X0) )
& ! [X3,X4] :
( apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X3,X0)
| ~ member(X4,X0) )
& sP0(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f28,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> sP1(X1,X0) ),
inference(definition_folding,[],[f25,f27,f26]) ).
fof(f29,plain,
( ~ equivalence(sK3,sK4)
& equivalence(sK3,sK2)
& subset(sK4,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f22]) ).
fof(f30,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ? [X2] :
( ~ apply(X1,X2,X2)
& member(X2,X0) )
| ? [X3,X4] :
( ~ apply(X1,X4,X3)
& apply(X1,X3,X4)
& member(X3,X0)
& member(X4,X0) )
| ~ sP0(X1,X0) )
& ( ( ! [X2] :
( apply(X1,X2,X2)
| ~ member(X2,X0) )
& ! [X3,X4] :
( apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X3,X0)
| ~ member(X4,X0) )
& sP0(X1,X0) )
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f31,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ? [X2] :
( ~ apply(X1,X2,X2)
& member(X2,X0) )
| ? [X3,X4] :
( ~ apply(X1,X4,X3)
& apply(X1,X3,X4)
& member(X3,X0)
& member(X4,X0) )
| ~ sP0(X1,X0) )
& ( ( ! [X2] :
( apply(X1,X2,X2)
| ~ member(X2,X0) )
& ! [X3,X4] :
( apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X3,X0)
| ~ member(X4,X0) )
& sP0(X1,X0) )
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ~ apply(X0,X2,X2)
& member(X2,X1) )
| ? [X3,X4] :
( ~ apply(X0,X4,X3)
& apply(X0,X3,X4)
& member(X3,X1)
& member(X4,X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X5] :
( apply(X0,X5,X5)
| ~ member(X5,X1) )
& ! [X6,X7] :
( apply(X0,X7,X6)
| ~ apply(X0,X6,X7)
| ~ member(X6,X1)
| ~ member(X7,X1) )
& sP0(X0,X1) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
& member(sK5(X0,X1),X1) )
| ( ~ apply(X0,sK7(X0,X1),sK6(X0,X1))
& apply(X0,sK6(X0,X1),sK7(X0,X1))
& member(sK6(X0,X1),X1)
& member(sK7(X0,X1),X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X5] :
( apply(X0,X5,X5)
| ~ member(X5,X1) )
& ! [X6,X7] :
( apply(X0,X7,X6)
| ~ apply(X0,X6,X7)
| ~ member(X6,X1)
| ~ member(X7,X1) )
& sP0(X0,X1) )
| ~ sP1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1)),skolemize(X4,sK7(X0,X1))],[f32]) ).
fof(f34,plain,
! [X1,X0] :
( ( sP0(X1,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) ) )
& ( ! [X5,X6,X7] :
( apply(X1,X5,X7)
| ~ apply(X1,X5,X6)
| ~ apply(X1,X6,X7)
| ~ member(X5,X0)
| ~ member(X6,X0)
| ~ member(X7,X0) )
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f35,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X2,X3)
& apply(X0,X3,X4)
& member(X2,X1)
& member(X3,X1)
& member(X4,X1) ) )
& ( ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ apply(X0,sK8(X0,X1),sK10(X0,X1))
& apply(X0,sK8(X0,X1),sK9(X0,X1))
& apply(X0,sK9(X0,X1),sK10(X0,X1))
& member(sK8(X0,X1),X1)
& member(sK9(X0,X1),X1)
& member(sK10(X0,X1),X1) ) )
& ( ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1))],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ( equivalence(X1,X0)
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| ~ equivalence(X1,X0) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f38,plain,
subset(sK4,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f39,plain,
equivalence(sK3,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
~ equivalence(sK3,sK4),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f43,plain,
! [X0,X1,X6,X7] :
( apply(X0,X7,X6)
| ~ apply(X0,X6,X7)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f44,plain,
! [X0,X1,X5] :
( apply(X0,X5,X5)
| ~ member(X5,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f45,plain,
! [X0,X1] :
( member(sK7(X0,X1),X1)
| member(sK5(X0,X1),X1)
| sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f46,plain,
! [X0,X1] :
( member(sK6(X0,X1),X1)
| member(sK5(X0,X1),X1)
| sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f47,plain,
! [X0,X1] :
( apply(X0,sK6(X0,X1),sK7(X0,X1))
| member(sK5(X0,X1),X1)
| sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f48,plain,
! [X0,X1] :
( ~ apply(X0,sK7(X0,X1),sK6(X0,X1))
| member(sK5(X0,X1),X1)
| sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0,X1] :
( ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1)
| member(sK7(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
! [X0,X1] :
( ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1)
| member(sK6(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X0,X1] :
( apply(X0,sK6(X0,X1),sK7(X0,X1))
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
! [X0,X1] :
( ~ apply(X0,sK7(X0,X1),sK6(X0,X1))
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1,X6,X7,X5] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X0,X1] :
( member(sK10(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0,X1] :
( member(sK9(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0,X1] :
( member(sK8(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0,X1] :
( apply(X0,sK9(X0,X1),sK10(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f58,plain,
! [X0,X1] :
( apply(X0,sK8(X0,X1),sK9(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X0,X1] :
( ~ apply(X0,sK8(X0,X1),sK10(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f60,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f61,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ~ sP1(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f62,plain,
~ sP1(sK3,sK4),
inference(resolution,[],[f61,f40]) ).
fof(f65,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1),X1)
| sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK6(X0,X1),sK7(X0,X1))
| ~ member(sK6(X0,X1),X2)
| ~ member(sK7(X0,X1),X2)
| ~ sP1(X0,X2) ),
inference(resolution,[],[f48,f43]) ).
fof(f66,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1),X1)
| sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ member(sK6(X0,X1),X2)
| ~ member(sK7(X0,X1),X2)
| ~ sP1(X0,X2) ),
inference(forward_subsumption_resolution,[],[f65,f47]) ).
fof(f67,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1),X1)
| sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ member(sK5(X0,X1),X2)
| ~ sP1(X0,X2) ),
inference(resolution,[],[f49,f44]) ).
fof(f70,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1),X1)
| sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ member(sK5(X0,X1),X2)
| ~ sP1(X0,X2) ),
inference(resolution,[],[f50,f44]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK6(X0,X1),sK7(X0,X1))
| ~ member(sK6(X0,X1),X2)
| ~ member(sK7(X0,X1),X2)
| ~ sP1(X0,X2) ),
inference(resolution,[],[f52,f43]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ member(sK6(X0,X1),X2)
| ~ member(sK7(X0,X1),X2)
| ~ sP1(X0,X2) ),
inference(forward_subsumption_resolution,[],[f73,f51]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,sK8(X0,X1),X2)
| ~ apply(X0,X2,sK10(X0,X1))
| ~ member(sK8(X0,X1),X3)
| ~ member(X2,X3)
| ~ member(sK10(X0,X1),X3)
| ~ sP0(X0,X3)
| sP0(X0,X1) ),
inference(resolution,[],[f53,f59]) ).
fof(f84,plain,
! [X2,X3,X0,X1] :
( ~ member(sK7(X0,X1),X2)
| ~ sP0(X0,X1)
| ~ member(sK6(X0,X1),X2)
| sP1(X0,X1)
| ~ sP1(X0,X2)
| ~ member(sK5(X0,X1),X3)
| ~ sP1(X0,X3) ),
inference(resolution,[],[f74,f44]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK7(X0,X1),X4)
| ~ member(sK6(X0,X1),X2)
| sP1(X0,X1)
| ~ sP1(X0,X2)
| ~ member(sK5(X0,X1),X3)
| ~ sP1(X0,X3)
| ~ sP0(X0,X1)
| ~ subset(X4,X2) ),
inference(resolution,[],[f84,f41]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ apply(X0,sK9(X0,X1),sK10(X0,X1))
| ~ member(sK8(X0,X1),X2)
| ~ member(sK9(X0,X1),X2)
| ~ member(sK10(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1)
| sP0(X0,X1) ),
inference(resolution,[],[f75,f58]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ apply(X0,sK9(X0,X1),sK10(X0,X1))
| ~ member(sK8(X0,X1),X2)
| ~ member(sK9(X0,X1),X2)
| ~ member(sK10(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) ),
inference(duplicate_literal_removal,[],[f95]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ member(sK10(X0,X1),X2)
| ~ member(sK9(X0,X1),X2)
| ~ member(sK8(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f100,f57]) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( ~ member(sK10(X0,X1),X3)
| ~ member(sK8(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1)
| ~ member(sK9(X0,X1),X2)
| ~ subset(X3,X2) ),
inference(resolution,[],[f101,f41]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(sK8(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1)
| ~ member(sK9(X0,X1),X2)
| ~ subset(X1,X2)
| sP0(X0,X1) ),
inference(resolution,[],[f103,f54]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ member(sK9(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1)
| ~ member(sK8(X0,X1),X2)
| ~ subset(X1,X2) ),
inference(duplicate_literal_removal,[],[f112]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( ~ member(sK9(X0,X2),X3)
| sP0(X0,X2)
| ~ member(sK8(X0,X2),X1)
| ~ subset(X2,X1)
| ~ sP0(X0,X1)
| ~ subset(X3,X1) ),
inference(resolution,[],[f114,f41]) ).
fof(f125,plain,
! [X2,X0,X1] :
( sP0(X0,X1)
| ~ member(sK8(X0,X1),X2)
| ~ subset(X1,X2)
| ~ sP0(X0,X2)
| ~ subset(X1,X2)
| sP0(X0,X1) ),
inference(resolution,[],[f116,f55]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ member(sK8(X0,X1),X2)
| sP0(X0,X1)
| ~ subset(X1,X2)
| ~ sP0(X0,X2) ),
inference(duplicate_literal_removal,[],[f125]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( ~ member(sK8(X0,X1),X3)
| ~ subset(X1,X2)
| ~ sP0(X0,X2)
| sP0(X0,X1)
| ~ subset(X3,X2) ),
inference(resolution,[],[f127,f41]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ sP0(X2,X1)
| sP0(X2,X0)
| ~ subset(X0,X1)
| sP0(X2,X0) ),
inference(resolution,[],[f133,f56]) ).
fof(f137,plain,
! [X2,X0,X1] :
( sP0(X2,X0)
| ~ sP0(X2,X1)
| ~ subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f135]) ).
fof(f204,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK6(X0,X1),X2)
| sP1(X0,X1)
| ~ sP1(X0,X2)
| ~ member(sK5(X0,X1),X3)
| ~ sP1(X0,X3)
| ~ sP0(X0,X1)
| ~ subset(X1,X2)
| sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ member(sK5(X0,X1),X4)
| ~ sP1(X0,X4) ),
inference(resolution,[],[f92,f67]) ).
fof(f208,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK6(X0,X1),X2)
| sP1(X0,X1)
| ~ sP1(X0,X2)
| ~ member(sK5(X0,X1),X3)
| ~ sP1(X0,X3)
| ~ sP0(X0,X1)
| ~ subset(X1,X2)
| ~ member(sK5(X0,X1),X4)
| ~ sP1(X0,X4) ),
inference(duplicate_literal_removal,[],[f204]) ).
fof(f301,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(sK6(X0,X1),X5)
| ~ sP1(X0,X2)
| ~ member(sK5(X0,X1),X3)
| ~ sP1(X0,X3)
| ~ sP0(X0,X1)
| ~ subset(X1,X2)
| ~ member(sK5(X0,X1),X4)
| ~ sP1(X0,X4)
| sP1(X0,X1)
| ~ subset(X5,X2) ),
inference(resolution,[],[f208,f41]) ).
fof(f463,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP1(X0,X1)
| ~ member(sK5(X0,X2),X3)
| ~ sP1(X0,X3)
| ~ sP0(X0,X2)
| ~ subset(X2,X1)
| ~ member(sK5(X0,X2),X4)
| ~ sP1(X0,X4)
| sP1(X0,X2)
| ~ subset(X2,X1)
| sP1(X0,X2)
| ~ sP0(X0,X2)
| ~ member(sK5(X0,X2),X5)
| ~ sP1(X0,X5) ),
inference(resolution,[],[f301,f70]) ).
fof(f467,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(sK5(X0,X2),X5)
| ~ member(sK5(X0,X2),X3)
| ~ sP1(X0,X3)
| ~ sP0(X0,X2)
| ~ subset(X2,X1)
| ~ member(sK5(X0,X2),X4)
| ~ sP1(X0,X4)
| sP1(X0,X2)
| ~ sP1(X0,X1)
| ~ sP1(X0,X5) ),
inference(duplicate_literal_removal,[],[f463]) ).
fof(f494,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK5(X0,X1),X2)
| ~ member(sK5(X0,X1),X3)
| ~ sP1(X0,X3)
| ~ sP0(X0,X1)
| ~ subset(X1,X4)
| ~ sP1(X0,X2)
| sP1(X0,X1)
| ~ sP1(X0,X4)
| ~ sP1(X0,X2) ),
inference(factoring,[],[f467]) ).
fof(f495,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK5(X0,X1),X3)
| ~ member(sK5(X0,X1),X2)
| ~ sP1(X0,X3)
| ~ sP0(X0,X1)
| ~ subset(X1,X4)
| ~ sP1(X0,X2)
| sP1(X0,X1)
| ~ sP1(X0,X4) ),
inference(duplicate_literal_removal,[],[f494]) ).
fof(f514,plain,
! [X2,X3,X0,X1] :
( ~ member(sK5(X0,X1),X2)
| ~ sP1(X0,X2)
| ~ sP0(X0,X1)
| ~ subset(X1,X3)
| ~ sP1(X0,X2)
| sP1(X0,X1)
| ~ sP1(X0,X3) ),
inference(factoring,[],[f495]) ).
fof(f515,plain,
! [X2,X3,X0,X1] :
( ~ member(sK5(X0,X1),X2)
| ~ sP1(X0,X2)
| ~ sP0(X0,X1)
| ~ subset(X1,X3)
| sP1(X0,X1)
| ~ sP1(X0,X3) ),
inference(duplicate_literal_removal,[],[f514]) ).
fof(f529,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK5(X0,X2),X4)
| ~ sP0(X0,X2)
| ~ subset(X2,X3)
| sP1(X0,X2)
| ~ sP1(X0,X3)
| ~ sP1(X0,X1)
| ~ subset(X4,X1) ),
inference(resolution,[],[f515,f41]) ).
fof(f539,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(X0,X1)
| ~ subset(X1,X2)
| sP1(X0,X1)
| ~ sP1(X0,X2)
| ~ sP1(X0,X3)
| ~ subset(X1,X3)
| sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ member(sK6(X0,X1),X4)
| ~ member(sK7(X0,X1),X4)
| ~ sP1(X0,X4) ),
inference(resolution,[],[f529,f66]) ).
fof(f541,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK7(X0,X1),X4)
| ~ subset(X1,X2)
| sP1(X0,X1)
| ~ sP1(X0,X2)
| ~ sP1(X0,X3)
| ~ subset(X1,X3)
| ~ member(sK6(X0,X1),X4)
| ~ sP0(X0,X1)
| ~ sP1(X0,X4) ),
inference(duplicate_literal_removal,[],[f539]) ).
fof(f592,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(sK7(X2,X0),X5)
| sP1(X2,X0)
| ~ sP1(X2,X1)
| ~ sP1(X2,X3)
| ~ subset(X0,X3)
| ~ member(sK6(X2,X0),X4)
| ~ sP0(X2,X0)
| ~ sP1(X2,X4)
| ~ subset(X0,X1)
| ~ subset(X5,X4) ),
inference(resolution,[],[f541,f41]) ).
fof(f631,plain,
! [X2,X3,X0,X1,X4] :
( sP1(X0,X1)
| ~ sP1(X0,X2)
| ~ sP1(X0,X3)
| ~ subset(X1,X3)
| ~ member(sK6(X0,X1),X4)
| ~ sP0(X0,X1)
| ~ sP1(X0,X4)
| ~ subset(X1,X2)
| ~ subset(X1,X4)
| member(sK5(X0,X1),X1)
| sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(resolution,[],[f592,f45]) ).
fof(f633,plain,
! [X2,X3,X0,X1,X4] :
( sP1(X0,X1)
| ~ sP1(X0,X2)
| ~ sP1(X0,X3)
| ~ subset(X1,X3)
| ~ member(sK6(X0,X1),X4)
| ~ sP0(X0,X1)
| ~ sP1(X0,X4)
| ~ subset(X1,X2)
| ~ subset(X1,X4)
| member(sK5(X0,X1),X1) ),
inference(duplicate_literal_removal,[],[f631]) ).
fof(f635,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK6(X0,X1),X4)
| ~ sP1(X0,X2)
| ~ sP1(X0,X3)
| ~ subset(X1,X3)
| sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ sP1(X0,X4)
| ~ subset(X1,X2)
| ~ subset(X1,X4) ),
inference(forward_subsumption_resolution,[],[f633,f529]) ).
fof(f638,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(sK6(X0,X3),X5)
| ~ sP1(X0,X2)
| ~ subset(X3,X2)
| sP1(X0,X3)
| ~ sP0(X0,X3)
| ~ sP1(X0,X4)
| ~ subset(X3,X1)
| ~ subset(X3,X4)
| ~ sP1(X0,X1)
| ~ subset(X5,X4) ),
inference(resolution,[],[f635,f41]) ).
fof(f644,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1)
| ~ subset(X2,X1)
| sP1(X0,X2)
| ~ sP0(X0,X2)
| ~ sP1(X0,X3)
| ~ subset(X2,X4)
| ~ subset(X2,X3)
| ~ sP1(X0,X4)
| ~ subset(X2,X3)
| member(sK5(X0,X2),X2)
| sP1(X0,X2)
| ~ sP0(X0,X2) ),
inference(resolution,[],[f638,f46]) ).
fof(f646,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1)
| ~ subset(X2,X1)
| sP1(X0,X2)
| ~ sP0(X0,X2)
| ~ sP1(X0,X3)
| ~ subset(X2,X4)
| ~ subset(X2,X3)
| ~ sP1(X0,X4)
| member(sK5(X0,X2),X2) ),
inference(duplicate_literal_removal,[],[f644]) ).
fof(f648,plain,
! [X2,X3,X0,X1,X4] :
( sP1(X0,X2)
| ~ subset(X2,X1)
| ~ sP1(X0,X1)
| ~ sP0(X0,X2)
| ~ sP1(X0,X3)
| ~ subset(X2,X4)
| ~ subset(X2,X3)
| ~ sP1(X0,X4) ),
inference(forward_subsumption_resolution,[],[f646,f529]) ).
fof(f654,plain,
! [X2,X0,X1] :
( ~ sP1(sK3,X2)
| ~ sP1(sK3,X0)
| ~ sP0(sK3,sK4)
| ~ sP1(sK3,X1)
| ~ subset(sK4,X2)
| ~ subset(sK4,X1)
| ~ subset(sK4,X0) ),
inference(resolution,[],[f648,f62]) ).
fof(f658,plain,
! [X0,X1] :
( ~ sP1(sK3,X0)
| ~ sP1(sK3,X1)
| ~ sP0(sK3,sK4)
| ~ subset(sK4,X0)
| ~ subset(sK4,X0)
| ~ subset(sK4,X1) ),
inference(factoring,[],[f654]) ).
fof(f659,plain,
! [X0,X1] :
( ~ sP1(sK3,X1)
| ~ sP1(sK3,X0)
| ~ sP0(sK3,sK4)
| ~ subset(sK4,X0)
| ~ subset(sK4,X1) ),
inference(duplicate_literal_removal,[],[f658]) ).
fof(f664,plain,
! [X0] :
( ~ sP1(sK3,X0)
| ~ sP0(sK3,sK4)
| ~ subset(sK4,X0)
| ~ subset(sK4,X0) ),
inference(factoring,[],[f659]) ).
fof(f665,plain,
! [X0] :
( ~ sP1(sK3,X0)
| ~ sP0(sK3,sK4)
| ~ subset(sK4,X0) ),
inference(duplicate_literal_removal,[],[f664]) ).
fof(f676,plain,
! [X0] :
( ~ sP0(sK3,sK4)
| ~ subset(sK4,X0)
| ~ equivalence(sK3,X0) ),
inference(resolution,[],[f665,f60]) ).
fof(f682,plain,
! [X0,X1] :
( ~ sP0(sK3,X1)
| ~ equivalence(sK3,X0)
| ~ subset(sK4,X0)
| ~ subset(sK4,X1) ),
inference(resolution,[],[f676,f137]) ).
fof(f701,plain,
! [X0,X1] :
( ~ sP1(sK3,X1)
| ~ subset(sK4,X0)
| ~ subset(sK4,X1)
| ~ equivalence(sK3,X0) ),
inference(resolution,[],[f682,f42]) ).
fof(f711,plain,
! [X0,X1] :
( ~ equivalence(sK3,X1)
| ~ subset(sK4,X1)
| ~ equivalence(sK3,X0)
| ~ subset(sK4,X0) ),
inference(resolution,[],[f701,f60]) ).
fof(f714,plain,
! [X0] :
( ~ equivalence(sK3,X0)
| ~ subset(sK4,X0)
| ~ subset(sK4,X0) ),
inference(factoring,[],[f711]) ).
fof(f715,plain,
! [X0] :
( ~ equivalence(sK3,X0)
| ~ subset(sK4,X0) ),
inference(duplicate_literal_removal,[],[f714]) ).
fof(f728,plain,
~ subset(sK4,sK2),
inference(resolution,[],[f715,f39]) ).
fof(f730,plain,
$false,
inference(forward_subsumption_resolution,[],[f728,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET765+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 02:50:04 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.50/1.31 % (3210446)Detected formulas, will run a generic FOF schedule.
% 2.50/1.31 % (3210457)dis-21_1_sil=8000:lcm=predicate:random_seed=1116845424:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.50/1.31 % (3210453)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=1587080515:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.31 % (3210454)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4229454527:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.31 % (3210452)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=2705829277:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.31 % (3210451)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=1857352154:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.31 % (3210454)Refutation not found, incomplete strategy
% 2.50/1.31 % (3210454)------------------------------
% 2.50/1.31 % (3210454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.31 % (3210454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.31 % (3210454)CaDiCaL version: 2.1.3
% 2.50/1.31 % (3210454)Termination reason: Refutation not found, incomplete strategy
% 2.50/1.31 % (3210454)Time elapsed: 0.002 s
% 2.50/1.31 % (3210454)Peak memory usage: 88 MB
% 2.50/1.31 % (3210454)Instructions burned: 2 (million)
% 2.50/1.31 % (3210455)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1929499961:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.31 % (3210457)Instruction limit reached!
% 2.50/1.31 % (3210457)------------------------------
% 2.50/1.31 % (3210457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.31 % (3210457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.31 % (3210457)CaDiCaL version: 2.1.3
% 2.50/1.31 % (3210457)Termination reason: Instruction limit
% 2.50/1.31 % (3210457)Termination phase: Saturation
% 2.50/1.31 % (3210457)Time elapsed: 0.049 s
% 2.50/1.31 % (3210457)Peak memory usage: 90 MB
% 2.50/1.31 % (3210457)Instructions burned: 140 (million)
% 2.50/1.31 % (3210456)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3518119313:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.31 % (3210455)First to succeed.
% 2.50/1.31 % (3210455)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3210446"
% 2.50/1.31 % (3210456)Instruction limit reached!
% 2.50/1.31 % (3210456)------------------------------
% 2.50/1.31 % (3210456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.31 % (3210456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.31 % (3210456)CaDiCaL version: 2.1.3
% 2.50/1.31 % (3210456)Termination reason: Instruction limit
% 2.50/1.31 % (3210456)Termination phase: Saturation
% 2.50/1.31 % (3210456)Time elapsed: 0.073 s
% 2.50/1.31 % (3210456)Peak memory usage: 89 MB
% 2.50/1.31 % (3210456)Instructions burned: 140 (million)
% 2.50/1.31 % (3210465)lrs+10_1_sil=8000:sp=occurrence:random_seed=2203289254:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.50/1.31 % (3210465)Instruction limit reached!
% 2.50/1.31 % (3210465)------------------------------
% 2.50/1.31 % (3210465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.31 % (3210465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.31 % (3210465)CaDiCaL version: 2.1.3
% 2.50/1.31 % (3210465)Termination reason: Instruction limit
% 2.50/1.31 % (3210465)Termination phase: Saturation
% 2.50/1.31 % (3210465)Time elapsed: 0.091 s
% 2.50/1.31 % (3210465)Peak memory usage: 92 MB
% 2.50/1.31 % (3210465)Instructions burned: 287 (million)
% 2.50/1.31 % (3210466)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3180816373:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.50/1.31 % (3210466)Refutation not found, incomplete strategy
% 2.50/1.31 % (3210466)------------------------------
% 2.50/1.31 % (3210466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.31 % (3210466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.31 % (3210466)CaDiCaL version: 2.1.3
% 2.50/1.31 % (3210466)Termination reason: Refutation not found, incomplete strategy
% 2.50/1.31 % (3210466)Time elapsed: 0.002 s
% 2.50/1.31 % (3210466)Peak memory usage: 88 MB
% 2.50/1.31 % (3210466)Instructions burned: 2 (million)
% 2.50/1.31 % (3210454)------------------------------
% 2.50/1.31 % (3210454)------------------------------
% 2.50/1.31 % (3210468)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4107062271:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 2.50/1.31 % (3210455)Refutation found. Thanks to Tanya!
% 2.50/1.31 % SZS status Theorem for theBenchmark
% 2.50/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.40 % (3210455)------------------------------
% 2.50/1.40 % (3210455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.40 % (3210455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.40 % (3210455)CaDiCaL version: 2.1.3
% 2.50/1.40 % (3210455)Termination reason: Refutation
% 2.50/1.40 % (3210455)Time elapsed: 0.040 s
% 2.50/1.40 % (3210455)Peak memory usage: 88 MB
% 2.50/1.40 % (3210455)Instructions burned: 75 (million)
% 2.50/1.40 % (3210455)------------------------------
% 2.50/1.40 % (3210455)------------------------------
% 2.50/1.40 % (3210446)Success in time 0.451 s
% 2.50/1.40 % Vampire exiting
%------------------------------------------------------------------------------