%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP004+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 11:27:44 AM UTC 2026
% Result : Theorem 2.68s 1.28s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of formulae : 93 ( 11 unt; 4 def)
% Number of atoms : 359 ( 9 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 490 ( 224 ~; 219 |; 19 &)
% ( 9 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 117 ( 0 sgn 113 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
fof(f17,axiom,
! [X0] :
( ne(X0)
=> mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).
fof(f19,axiom,
! [X0] :
( ne(X0)
=> mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).
fof(f24,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3] :
( mem(X3,X0)
=> ( p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
=> p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).
fof(f25,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ! [X2] :
( mem(X2,X0)
=> ! [X3] :
( mem(X3,X0)
=> ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
<=> ( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
& X2 != X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).
fof(f26,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
fof(f27,conjecture,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0] :
( mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f44,plain,
! [X0] :
( mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool)))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
<=> ( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
& X2 != X3 ) )
| ~ mem(X3,X0) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1))
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f53,plain,
? [X0] :
( ? [X1] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1))
& mem(X1,arr(X0,bool)) )
& ne(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ? [X3] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0) ) )
& ( ! [X3] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ? [X3] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0) ) )
& ( ! [X4] :
( p(ap(ap(c_2Ebool_2EIN(X0),X4),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| ~ mem(X4,X0) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
& mem(sK2(X0,X1,X2),X0) ) )
& ( ! [X4] :
( p(ap(ap(c_2Ebool_2EIN(X0),X4),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| ~ mem(X4,X0) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| X2 = X3 )
& ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
& X2 != X3 )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) )
| ~ mem(X3,X0) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| X2 = X3 )
& ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
& X2 != X3 )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) )
| ~ mem(X3,X0) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
& mem(sK4,arr(sK3,bool))
& ne(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f53]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f94,plain,
! [X0] :
( mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f96,plain,
! [X0] :
( mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool)))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f104,plain,
! [X2,X0,X1,X4] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| p(ap(ap(c_2Ebool_2EIN(X0),X4),X2))
| ~ mem(X4,X0)
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f105,plain,
! [X2,X0,X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| mem(sK2(X0,X1,X2),X0)
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f106,plain,
! [X2,X0,X1] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ~ mem(X3,X0)
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f111,plain,
! [X0,X1] :
( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f112,plain,
ne(sK3),
inference(cnf_transformation,[],[f70]) ).
fof(f113,plain,
mem(sK4,arr(sK3,bool)),
inference(cnf_transformation,[],[f70]) ).
fof(f114,plain,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4)),
inference(cnf_transformation,[],[f70]) ).
fof(f166,plain,
( mem(sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4),sK3)
| ~ mem(sK4,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ ne(sK3) ),
inference(resolution,[],[f105,f114]) ).
fof(f168,plain,
( mem(sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4),sK3)
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ ne(sK3) ),
inference(forward_subsumption_resolution,[],[f166,f113]) ).
fof(f169,plain,
( mem(sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4),sK3)
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool)) ),
inference(forward_subsumption_resolution,[],[f168,f112]) ).
fof(f171,definition,
( spl5_1
<=> mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f172,plain,
( mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f173,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| spl5_1 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f175,definition,
( spl5_2
<=> mem(sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f177,plain,
( mem(sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4),sK3)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f169,f175,f171]) ).
fof(f179,plain,
( ! [X0] :
( ~ mem(c_2Epred__set_2EREST(sK3),arr(X0,arr(sK3,bool)))
| ~ mem(sK4,X0) )
| spl5_1 ),
inference(resolution,[],[f173,f74]) ).
fof(f186,plain,
( ~ mem(sK4,arr(sK3,bool))
| ~ ne(sK3)
| spl5_1 ),
inference(resolution,[],[f179,f96]) ).
fof(f187,plain,
( ~ ne(sK3)
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f186,f113]) ).
fof(f188,plain,
( $false
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f187,f112]) ).
fof(f189,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f188]) ).
fof(f191,plain,
! [X0,X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X1))
| ~ mem(X1,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X1))
| ~ mem(X1,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(resolution,[],[f107,f106]) ).
fof(f192,plain,
! [X0,X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X1))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(duplicate_literal_removal,[],[f191]) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(c_2Epred__set_2EREST(X0),X1)))
| p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ~ mem(ap(c_2Epred__set_2ECHOICE(X0),X1),X0)
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(superposition,[],[f109,f111]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(c_2Epred__set_2EREST(X0),X1)))
| p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ~ mem(ap(c_2Epred__set_2ECHOICE(X0),X1),X0)
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(duplicate_literal_removal,[],[f194]) ).
fof(f202,plain,
! [X2,X3,X0,X1] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X3))
| ~ mem(sK2(X0,X1,X2),X0)
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X3))
| ~ mem(X3,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(resolution,[],[f104,f106]) ).
fof(f203,plain,
! [X2,X3,X0,X1] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X3))
| ~ mem(sK2(X0,X1,X2),X0)
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X3))
| ~ mem(X3,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool)) ),
inference(duplicate_literal_removal,[],[f202]) ).
fof(f204,plain,
! [X2,X3,X0,X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X3))
| ~ mem(X3,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0)
| p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X3))
| ~ mem(X2,arr(X0,bool)) ),
inference(forward_subsumption_resolution,[],[f203,f105]) ).
fof(f377,plain,
! [X0] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),X0))
| ~ mem(X0,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ ne(sK3)
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),X0))
| ~ mem(sK4,arr(sK3,bool)) ),
inference(resolution,[],[f204,f114]) ).
fof(f379,plain,
( ! [X0] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),X0))
| ~ mem(X0,arr(sK3,bool))
| ~ ne(sK3)
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),X0))
| ~ mem(sK4,arr(sK3,bool)) )
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f377,f172]) ).
fof(f380,plain,
( ! [X0] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),X0))
| ~ mem(X0,arr(sK3,bool))
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),X0))
| ~ mem(sK4,arr(sK3,bool)) )
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f379,f112]) ).
fof(f381,plain,
( ! [X0] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),X0))
| ~ mem(X0,arr(sK3,bool))
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),X0)) )
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f380,f113]) ).
fof(f425,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),ap(c_2Epred__set_2EREST(sK3),sK4)))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ ne(sK3)
| ~ spl5_1 ),
inference(resolution,[],[f381,f192]) ).
fof(f432,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),ap(c_2Epred__set_2EREST(sK3),sK4)))
| ~ ne(sK3)
| ~ spl5_1 ),
inference(duplicate_literal_removal,[],[f425]) ).
fof(f436,plain,
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),ap(c_2Epred__set_2EREST(sK3),sK4)))
| ~ ne(sK3)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f432,f172]) ).
fof(f440,plain,
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),ap(c_2Epred__set_2EREST(sK3),sK4)))
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f436,f112]) ).
fof(f441,plain,
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),sK4))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4),sK3)
| ~ mem(sK4,arr(sK3,bool))
| ~ ne(sK3)
| ~ spl5_1 ),
inference(resolution,[],[f440,f195]) ).
fof(f454,plain,
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),sK4))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(sK4,arr(sK3,bool))
| ~ ne(sK3)
| ~ spl5_1
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f441,f177]) ).
fof(f456,plain,
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),sK4))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ ne(sK3)
| ~ spl5_1
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f454,f113]) ).
fof(f458,plain,
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),sK4))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ spl5_1
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f456,f112]) ).
fof(f460,definition,
( spl5_20
<=> mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_20])],[avatar_definition]) ).
fof(f462,plain,
( ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| spl5_20 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f464,definition,
( spl5_21
<=> p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_21])],[avatar_definition]) ).
fof(f466,plain,
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),sK4)),sK4))
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f467,plain,
( ~ spl5_20
| spl5_21
| ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f458,f175,f171,f464,f460]) ).
fof(f482,plain,
( ! [X0] :
( ~ mem(c_2Epred__set_2ECHOICE(sK3),arr(X0,sK3))
| ~ mem(sK4,X0) )
| spl5_20 ),
inference(resolution,[],[f462,f74]) ).
fof(f485,plain,
( ~ mem(sK4,arr(sK3,bool))
| ~ ne(sK3)
| spl5_20 ),
inference(resolution,[],[f482,f94]) ).
fof(f486,plain,
( ~ ne(sK3)
| spl5_20 ),
inference(forward_subsumption_resolution,[],[f485,f113]) ).
fof(f487,plain,
( $false
| spl5_20 ),
inference(forward_subsumption_resolution,[],[f486,f112]) ).
fof(f488,plain,
spl5_20,
inference(avatar_contradiction_clause,[],[f487]) ).
fof(f504,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
| ~ mem(sK4,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ ne(sK3)
| ~ spl5_21 ),
inference(resolution,[],[f466,f107]) ).
fof(f518,plain,
( ~ mem(sK4,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ ne(sK3)
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f504,f114]) ).
fof(f521,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ ne(sK3)
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f518,f113]) ).
fof(f524,plain,
( ~ ne(sK3)
| ~ spl5_1
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f521,f172]) ).
fof(f525,plain,
( $false
| ~ spl5_1
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f524,f112]) ).
fof(f526,plain,
( ~ spl5_1
| ~ spl5_21 ),
inference(avatar_contradiction_clause,[],[f525]) ).
cnf(s1,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f178]) ).
cnf(s2,plain,
spl5_1,
inference(sat_conversion,[],[f189]) ).
cnf(s19,plain,
( ~ spl5_1
| ~ spl5_2
| ~ spl5_20
| spl5_21 ),
inference(sat_conversion,[],[f467]) ).
cnf(s21,plain,
spl5_20,
inference(sat_conversion,[],[f488]) ).
cnf(s24,plain,
( ~ spl5_1
| ~ spl5_21 ),
inference(sat_conversion,[],[f526]) ).
cnf(s25,plain,
( ~ spl5_1
| ~ spl5_2
| spl5_21 ),
inference(rat,[],[s19,s21]) ).
cnf(s27,plain,
~ spl5_21,
inference(rat,[],[s24,s2]) ).
cnf(s28,plain,
~ spl5_2,
inference(rat,[],[s25,s27,s2]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s1,s28,s2]) ).
fof(f527,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP004+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 11:50:00 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 2.68/1.28 % (2259278)Detected formulas, will run a generic FOF schedule.
% 2.68/1.28 % (2259283)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=4043786862:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.28 % (2259284)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=3882425686:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.28 % (2259289)dis-21_1_sil=8000:lcm=predicate:random_seed=2853955185: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)
% 2.68/1.28 % (2259286)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1300008941:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.28 % (2259287)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2493459356:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.28 % (2259285)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=963853154:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.28 % (2259288)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=46822915:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.28 % (2259286)Refutation not found, incomplete strategy
% 2.68/1.28 % (2259286)------------------------------
% 2.68/1.28 % (2259286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (2259286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (2259286)CaDiCaL version: 2.1.3
% 2.68/1.28 % (2259286)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.28 % (2259286)Time elapsed: 0.002 s
% 2.68/1.28 % (2259286)Peak memory usage: 88 MB
% 2.68/1.28 % (2259286)Instructions burned: 1 (million)
% 2.68/1.28 % (2259288)First to succeed.
% 2.68/1.28 % (2259288)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2259278"
% 2.68/1.28 % (2259287)Instruction limit reached!
% 2.68/1.28 % (2259287)------------------------------
% 2.68/1.28 % (2259287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (2259287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (2259287)CaDiCaL version: 2.1.3
% 2.68/1.28 % (2259287)Termination reason: Instruction limit
% 2.68/1.28 % (2259287)Termination phase: Saturation
% 2.68/1.28 % (2259287)Time elapsed: 0.068 s
% 2.68/1.28 % (2259287)Peak memory usage: 88 MB
% 2.68/1.28 % (2259287)Instructions burned: 120 (million)
% 2.68/1.28 % (2259289)Instruction limit reached!
% 2.68/1.28 % (2259289)------------------------------
% 2.68/1.28 % (2259289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (2259289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (2259289)CaDiCaL version: 2.1.3
% 2.68/1.28 % (2259289)Termination reason: Instruction limit
% 2.68/1.28 % (2259289)Termination phase: Saturation
% 2.68/1.28 % (2259289)Time elapsed: 0.077 s
% 2.68/1.28 % (2259289)Peak memory usage: 89 MB
% 2.68/1.28 % (2259289)Instructions burned: 130 (million)
% 2.68/1.28 % (2259298)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3655222204:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.68/1.28 % (2259297)lrs+10_1_sil=8000:sp=occurrence:random_seed=665067601:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.68/1.28 % (2259286)------------------------------
% 2.68/1.28 % (2259286)------------------------------
% 2.68/1.28 % (2259297)Also succeeded, but the first one will report.
% 2.68/1.28 % (2259288)Refutation found. Thanks to Tanya!
% 2.68/1.28 % SZS status Theorem for theBenchmark
% 2.68/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.38 % (2259288)------------------------------
% 3.57/1.38 % (2259288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.38 % (2259288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.38 % (2259288)CaDiCaL version: 2.1.3
% 3.57/1.38 % (2259288)Termination reason: Refutation
% 3.57/1.38 % (2259288)Time elapsed: 0.026 s
% 3.57/1.38 % (2259288)Peak memory usage: 90 MB
% 3.57/1.38 % (2259288)Instructions burned: 34 (million)
% 3.57/1.38 % (2259288)------------------------------
% 3.57/1.38 % (2259288)------------------------------
% 3.57/1.38 % (2259278)Success in time 0.439 s
% 3.57/1.38 % Vampire exiting
%------------------------------------------------------------------------------