%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP004+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 11:33:55 AM UTC 2026
% Result : Theorem 0.86s 0.60s
% Output : Refutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 10 unt; 1 def)
% Number of atoms : 255 ( 11 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 339 ( 147 ~; 148 |; 19 &)
% ( 6 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 106 ( 0 sgn 102 !; 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/sandbox2/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
fof(f17,axiom,
! [X0] :
( ne(X0)
=> mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),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(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] :
( ~ 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))
| ~ 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(f146,plain,
! [X0,X1] :
( mem(ap(c_2Epred__set_2EREST(X1),X0),arr(X1,bool))
| ~ mem(X0,arr(X1,bool))
| ~ ne(X1) ),
inference(resolution,[],[f74,f96]) ).
fof(f147,plain,
! [X0,X1] :
( mem(ap(c_2Epred__set_2ECHOICE(X1),X0),X1)
| ~ mem(X0,arr(X1,bool))
| ~ ne(X1) ),
inference(resolution,[],[f74,f94]) ).
fof(f253,plain,
( ap(c_2Epred__set_2EREST(sK3),sK4) = ap(ap(c_2Epred__set_2EDELETE(sK3),sK4),ap(c_2Epred__set_2ECHOICE(sK3),sK4))
| ~ ne(sK3) ),
inference(resolution,[],[f111,f113]) ).
fof(f259,plain,
ap(c_2Epred__set_2EREST(sK3),sK4) = ap(ap(c_2Epred__set_2EDELETE(sK3),sK4),ap(c_2Epred__set_2ECHOICE(sK3),sK4)),
inference(forward_subsumption_resolution,[],[f253,f112]) ).
fof(f279,definition,
( spl5_9
<=> mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool)) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
fof(f280,plain,
( mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f281,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| spl5_9 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f304,plain,
! [X2,X3,X0,X1] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),X3)),X1))
| ~ mem(X2,X0)
| ~ mem(sK2(X0,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),X3),X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2)),X3))
| ~ mem(X3,arr(X0,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),arr(X0,bool))
| ~ ne(X0) ),
inference(resolution,[],[f109,f106]) ).
fof(f306,plain,
! [X2,X3,X0,X1] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),X3)),X1))
| ~ mem(X2,X0)
| ~ mem(sK2(X0,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),X3),X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2)),X3))
| ~ mem(X3,arr(X0,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),arr(X0,bool)) ),
inference(duplicate_literal_removal,[],[f304]) ).
fof(f307,plain,
! [X2,X3,X0,X1] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),X3)),X1))
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2)),X3))
| ~ mem(X3,arr(X0,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),arr(X0,bool)) ),
inference(forward_subsumption_resolution,[],[f306,f105]) ).
fof(f595,plain,
( ~ mem(sK4,arr(sK3,bool))
| ~ ne(sK3)
| spl5_9 ),
inference(resolution,[],[f146,f281]) ).
fof(f616,plain,
( ~ ne(sK3)
| spl5_9 ),
inference(forward_subsumption_resolution,[],[f595,f113]) ).
fof(f617,plain,
( $false
| spl5_9 ),
inference(forward_subsumption_resolution,[],[f616,f112]) ).
fof(f618,plain,
spl5_9,
inference(avatar_contradiction_clause,[],[f617]) ).
fof(f1367,plain,
! [X0] :
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),X0)),sK4))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(sK4,arr(sK3,bool))
| ~ ne(sK3)
| 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)) ),
inference(superposition,[],[f307,f259]) ).
fof(f1375,plain,
! [X0] :
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),X0)),sK4))
| ~ mem(sK4,arr(sK3,bool))
| ~ ne(sK3)
| 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)) ),
inference(forward_subsumption_resolution,[],[f1367,f147]) ).
fof(f1380,plain,
! [X0] :
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),X0)),sK4))
| ~ ne(sK3)
| 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)) ),
inference(forward_subsumption_resolution,[],[f1375,f113]) ).
fof(f1390,plain,
! [X0] :
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),X0)),sK4))
| 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)) ),
inference(forward_subsumption_resolution,[],[f1380,f112]) ).
fof(f1399,plain,
( ! [X0] :
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),X0)),sK4))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),X0))
| ~ mem(X0,arr(sK3,bool)) )
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1390,f280]) ).
fof(f1646,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
| ~ mem(sK4,arr(sK3,bool))
| 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_9 ),
inference(resolution,[],[f1399,f107]) ).
fof(f1650,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_9 ),
inference(duplicate_literal_removal,[],[f1646]) ).
fof(f1653,plain,
( ~ mem(sK4,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ ne(sK3)
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1650,f114]) ).
fof(f1656,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ ne(sK3)
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1653,f113]) ).
fof(f1658,plain,
( ~ ne(sK3)
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1656,f280]) ).
fof(f1659,plain,
( $false
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1658,f112]) ).
fof(f1660,plain,
~ spl5_9,
inference(avatar_contradiction_clause,[],[f1659]) ).
cnf(s14,plain,
spl5_9,
inference(sat_conversion,[],[f618]) ).
cnf(s65,plain,
~ spl5_9,
inference(sat_conversion,[],[f1660]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s14,s65]) ).
fof(f1661,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.41 % Computer : n003.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 11:51:40 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.46 Running first-order model finding
% 0.14/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.86/0.60 % (383677)Will run a generic schedule for satisfiability detection.
% 0.86/0.60 % (383682)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2540408676_2999 on theBenchmark for (2999ds/0Mi)
% 0.86/0.60 % (383683)% WARNING: option uhcvi not known.
% 0.86/0.60 % TRYING [1]
% 0.86/0.60 % TRYING [2]
% 0.86/0.60 % TRYING [3]
% 0.86/0.60 % (383683)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3479962344:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.86/0.60 % (383684)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=697259323:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.86/0.60 % (383685)dis+10_1_sil=32000:sp=arity:random_seed=3088263608:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.86/0.60 % (383686)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1826583283:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.86/0.60 % (383687)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3439661015:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.86/0.60 % (383688)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1494958403:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.86/0.60 % TRYING [4]
% 0.86/0.60 % (383685) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-383677-383685"...
% 0.86/0.60 % (383685)...printing done.
% 0.86/0.60 % (383685)Refutation found. Thanks to Tanya!
% 0.86/0.60 % SZS status Theorem for theBenchmark
% 0.86/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.86/0.61 % (383685)------------------------------
% 0.86/0.61 % (383685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.61 % (383685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.61 % (383685)CaDiCaL version: 2.1.3
% 0.86/0.61 % (383685)Termination reason: Refutation
% 0.86/0.61 % (383685)Time elapsed: 0.089 s
% 0.86/0.61 % (383685)Peak memory usage: 13 MB
% 0.86/0.61 % (383685)Instructions burned: 91 (million)
% 0.86/0.61 % (383677)Success in time 0.132 s
% 0.86/0.61 % Vampire exiting
%------------------------------------------------------------------------------