TSTP Solution File: ITP004+2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ITP004+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 17:20:11 EDT 2022
% Result : Theorem 1.66s 0.58s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 81 ( 9 unt; 0 def)
% Number of atoms : 309 ( 14 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 360 ( 132 ~; 152 |; 30 &)
% ( 7 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 147 ( 138 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f481,plain,
$false,
inference(subsumption_resolution,[],[f480,f114]) ).
fof(f114,plain,
ne(sK1),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( mem(sK2,arr(sK1,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK2)),sK2))
& ne(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f63,f85,f84]) ).
fof(f84,plain,
( ? [X0] :
( ? [X1] :
( mem(X1,arr(X0,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) )
& ne(X0) )
=> ( ? [X1] :
( mem(X1,arr(sK1,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),X1)),X1)) )
& ne(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
( ? [X1] :
( mem(X1,arr(sK1,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),X1)),X1)) )
=> ( mem(sK2,arr(sK1,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK2)),sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( mem(X1,arr(X0,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) )
& ne(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
~ ! [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(rectify,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X8),ap(c_2Epred__set_2EREST(X8),X9)),X9)) ) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X8),ap(c_2Epred__set_2EREST(X8),X9)),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
fof(f480,plain,
~ ne(sK1),
inference(subsumption_resolution,[],[f479,f162]) ).
fof(f162,plain,
~ mem(sK2,arr(sK1,bool)),
inference(consistent_polarity_flipping,[],[f116]) ).
fof(f116,plain,
mem(sK2,arr(sK1,bool)),
inference(cnf_transformation,[],[f86]) ).
fof(f479,plain,
( mem(sK2,arr(sK1,bool))
| ~ ne(sK1) ),
inference(resolution,[],[f451,f169]) ).
fof(f169,plain,
! [X0] :
( ~ mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0))
| ~ ne(X0) ),
inference(consistent_polarity_flipping,[],[f139]) ).
fof(f139,plain,
! [X0] :
( ~ ne(X0)
| mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ne(X0)
=> mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X8] :
( ne(X8)
=> mem(c_2Epred__set_2ECHOICE(X8),arr(arr(X8,bool),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).
fof(f451,plain,
! [X0] :
( mem(c_2Epred__set_2ECHOICE(sK1),arr(X0,sK1))
| mem(sK2,X0) ),
inference(resolution,[],[f444,f163]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ mem(ap(X1,X3),X0)
| mem(X3,X2)
| mem(X1,arr(X2,X0)) ),
inference(consistent_polarity_flipping,[],[f104]) ).
fof(f104,plain,
! [X2,X3,X0,X1] :
( ~ mem(X3,X2)
| ~ mem(X1,arr(X2,X0))
| mem(ap(X1,X3),X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ mem(X1,arr(X2,X0))
| ! [X3] :
( mem(ap(X1,X3),X0)
| ~ mem(X3,X2) ) ),
inference(rectify,[],[f55]) ).
fof(f55,plain,
! [X2,X1,X0] :
( ~ mem(X1,arr(X0,X2))
| ! [X3] :
( mem(ap(X1,X3),X2)
| ~ mem(X3,X0) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X1,X0,X2] :
( mem(X1,arr(X0,X2))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X1,X3),X2) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0,X2,X1] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
fof(f444,plain,
mem(ap(c_2Epred__set_2ECHOICE(sK1),sK2),sK1),
inference(subsumption_resolution,[],[f443,f262]) ).
fof(f262,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| mem(ap(c_2Epred__set_2ECHOICE(sK1),sK2),sK1) ),
inference(subsumption_resolution,[],[f261,f114]) ).
fof(f261,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| mem(ap(c_2Epred__set_2ECHOICE(sK1),sK2),sK1)
| ~ ne(sK1) ),
inference(subsumption_resolution,[],[f260,f162]) ).
fof(f260,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| mem(sK2,arr(sK1,bool))
| mem(ap(c_2Epred__set_2ECHOICE(sK1),sK2),sK1)
| ~ ne(sK1) ),
inference(resolution,[],[f256,f157]) ).
fof(f157,plain,
! [X0] :
( ~ mem(c_2Epred__set_2EDELETE(X0),arr(arr(X0,bool),arr(X0,arr(X0,bool))))
| ~ ne(X0) ),
inference(consistent_polarity_flipping,[],[f118]) ).
fof(f118,plain,
! [X0] :
( mem(c_2Epred__set_2EDELETE(X0),arr(arr(X0,bool),arr(X0,arr(X0,bool))))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ~ ne(X0)
| mem(c_2Epred__set_2EDELETE(X0),arr(arr(X0,bool),arr(X0,arr(X0,bool)))) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ne(X0)
=> mem(c_2Epred__set_2EDELETE(X0),arr(arr(X0,bool),arr(X0,arr(X0,bool)))) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X8] :
( ne(X8)
=> mem(c_2Epred__set_2EDELETE(X8),arr(arr(X8,bool),arr(X8,arr(X8,bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EDELETE) ).
fof(f256,plain,
! [X2,X0,X1] :
( mem(c_2Epred__set_2EDELETE(sK1),arr(X2,arr(X0,X1)))
| mem(ap(c_2Epred__set_2ECHOICE(sK1),sK2),X0)
| mem(sK2,X2)
| ~ mem(ap(c_2Epred__set_2EREST(sK1),sK2),X1) ),
inference(resolution,[],[f228,f163]) ).
fof(f228,plain,
! [X0,X1] :
( mem(ap(c_2Epred__set_2EDELETE(sK1),sK2),arr(X1,X0))
| mem(ap(c_2Epred__set_2ECHOICE(sK1),sK2),X1)
| ~ mem(ap(c_2Epred__set_2EREST(sK1),sK2),X0) ),
inference(superposition,[],[f163,f225]) ).
fof(f225,plain,
ap(ap(c_2Epred__set_2EDELETE(sK1),sK2),ap(c_2Epred__set_2ECHOICE(sK1),sK2)) = ap(c_2Epred__set_2EREST(sK1),sK2),
inference(resolution,[],[f217,f162]) ).
fof(f217,plain,
! [X5] :
( mem(X5,arr(sK1,bool))
| ap(ap(c_2Epred__set_2EDELETE(sK1),X5),ap(c_2Epred__set_2ECHOICE(sK1),X5)) = ap(c_2Epred__set_2EREST(sK1),X5) ),
inference(resolution,[],[f173,f114]) ).
fof(f173,plain,
! [X0,X1] :
( ~ ne(X0)
| mem(X1,arr(X0,bool))
| ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) = ap(c_2Epred__set_2EREST(X0),X1) ),
inference(consistent_polarity_flipping,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( ~ ne(X0)
| ~ mem(X1,arr(X0,bool))
| ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) = ap(c_2Epred__set_2EREST(X0),X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ~ ne(X0)
| ! [X1] :
( ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) = ap(c_2Epred__set_2EREST(X0),X1)
| ~ mem(X1,arr(X0,bool)) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) = ap(c_2Epred__set_2EREST(X0),X1) ) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> ap(c_2Epred__set_2EREST(X8),X9) = ap(ap(c_2Epred__set_2EDELETE(X8),X9),ap(c_2Epred__set_2ECHOICE(X8),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
fof(f443,plain,
( mem(ap(c_2Epred__set_2ECHOICE(sK1),sK2),sK1)
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool)) ),
inference(subsumption_resolution,[],[f439,f248]) ).
fof(f248,plain,
( ~ p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),ap(c_2Epred__set_2EREST(sK1),sK2)))
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool)) ),
inference(subsumption_resolution,[],[f247,f114]) ).
fof(f247,plain,
( ~ p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),ap(c_2Epred__set_2EREST(sK1),sK2)))
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| ~ ne(sK1) ),
inference(subsumption_resolution,[],[f246,f162]) ).
fof(f246,plain,
( ~ p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),ap(c_2Epred__set_2EREST(sK1),sK2)))
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| mem(sK2,arr(sK1,bool))
| ~ ne(sK1) ),
inference(resolution,[],[f185,f180]) ).
fof(f180,plain,
p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK2)),sK2)),
inference(consistent_polarity_flipping,[],[f115]) ).
fof(f115,plain,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK2)),sK2)),
inference(cnf_transformation,[],[f86]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ ne(X0)
| ~ p(ap(ap(c_2Ebool_2EIN(X0),sK0(X0,X1,X2)),X1))
| mem(X2,arr(X0,bool))
| mem(X1,arr(X0,bool)) ),
inference(consistent_polarity_flipping,[],[f109]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ mem(X1,arr(X0,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ ne(X0)
| ~ mem(X2,arr(X0,bool))
| p(ap(ap(c_2Ebool_2EIN(X0),sK0(X0,X1,X2)),X1)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [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))
| ( p(ap(ap(c_2Ebool_2EIN(X0),sK0(X0,X1,X2)),X1))
& mem(sK0(X0,X1,X2),X0)
& ~ p(ap(ap(c_2Ebool_2EIN(X0),sK0(X0,X1,X2)),X2)) ) )
& ( ! [X4] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| ~ mem(X4,X0)
| p(ap(ap(c_2Ebool_2EIN(X0),X4),X2)) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f79,f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ? [X3] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0)
& ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) )
=> ( p(ap(ap(c_2Ebool_2EIN(X0),sK0(X0,X1,X2)),X1))
& mem(sK0(X0,X1,X2),X0)
& ~ p(ap(ap(c_2Ebool_2EIN(X0),sK0(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [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] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0)
& ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) )
& ( ! [X4] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| ~ mem(X4,X0)
| p(ap(ap(c_2Ebool_2EIN(X0),X4),X2)) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) ) ) ) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [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] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0)
& ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) )
& ( ! [X3] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0)
| p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) ) ) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [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] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0)
| p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ) ),
inference(flattening,[],[f69]) ).
fof(f69,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,[],[f30]) ).
fof(f30,plain,
! [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)) ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> ! [X10] :
( mem(X10,arr(X8,bool))
=> ( ! [X11] :
( mem(X11,X8)
=> ( p(ap(ap(c_2Ebool_2EIN(X8),X11),X9))
=> p(ap(ap(c_2Ebool_2EIN(X8),X11),X10)) ) )
<=> p(ap(ap(c_2Epred__set_2ESUBSET(X8),X9),X10)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).
fof(f439,plain,
( mem(ap(c_2Epred__set_2ECHOICE(sK1),sK2),sK1)
| p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),ap(c_2Epred__set_2EREST(sK1),sK2)))
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool)) ),
inference(superposition,[],[f401,f225]) ).
fof(f401,plain,
! [X0] :
( p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),ap(ap(c_2Epred__set_2EDELETE(sK1),sK2),X0)))
| mem(X0,sK1)
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool)) ),
inference(subsumption_resolution,[],[f400,f220]) ).
fof(f220,plain,
( ~ mem(sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2),sK1)
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool)) ),
inference(subsumption_resolution,[],[f219,f114]) ).
fof(f219,plain,
( ~ ne(sK1)
| ~ mem(sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2),sK1)
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool)) ),
inference(subsumption_resolution,[],[f218,f162]) ).
fof(f218,plain,
( mem(sK2,arr(sK1,bool))
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| ~ mem(sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2),sK1)
| ~ ne(sK1) ),
inference(resolution,[],[f165,f180]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| mem(X2,arr(X0,bool))
| mem(X1,arr(X0,bool))
| ~ ne(X0)
| ~ mem(sK0(X0,X1,X2),X0) ),
inference(consistent_polarity_flipping,[],[f108]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| mem(sK0(X0,X1,X2),X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f400,plain,
! [X0] :
( p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),ap(ap(c_2Epred__set_2EDELETE(sK1),sK2),X0)))
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| mem(sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2),sK1)
| mem(X0,sK1) ),
inference(subsumption_resolution,[],[f399,f114]) ).
fof(f399,plain,
! [X0] :
( mem(sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2),sK1)
| ~ ne(sK1)
| p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),ap(ap(c_2Epred__set_2EDELETE(sK1),sK2),X0)))
| mem(X0,sK1)
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool)) ),
inference(subsumption_resolution,[],[f395,f162]) ).
fof(f395,plain,
! [X0] :
( mem(sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2),sK1)
| mem(X0,sK1)
| p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),ap(ap(c_2Epred__set_2EDELETE(sK1),sK2),X0)))
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| mem(sK2,arr(sK1,bool))
| ~ ne(sK1) ),
inference(resolution,[],[f151,f243]) ).
fof(f243,plain,
( p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),sK2))
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool)) ),
inference(subsumption_resolution,[],[f242,f114]) ).
fof(f242,plain,
( mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| ~ ne(sK1)
| p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),sK2)) ),
inference(subsumption_resolution,[],[f241,f162]) ).
fof(f241,plain,
( mem(sK2,arr(sK1,bool))
| ~ ne(sK1)
| mem(ap(c_2Epred__set_2EREST(sK1),sK2),arr(sK1,bool))
| p(ap(ap(c_2Ebool_2EIN(sK1),sK0(sK1,ap(c_2Epred__set_2EREST(sK1),sK2),sK2)),sK2)) ),
inference(resolution,[],[f172,f180]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| mem(X2,arr(X0,bool))
| ~ ne(X0)
| mem(X1,arr(X0,bool))
| p(ap(ap(c_2Ebool_2EIN(X0),sK0(X0,X1,X2)),X2)) ),
inference(consistent_polarity_flipping,[],[f107]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),sK0(X0,X1,X2)),X2))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f151,plain,
! [X2,X3,X0,X1] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ~ ne(X0)
| mem(X3,X0)
| mem(X1,arr(X0,bool))
| p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| mem(X2,X0) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool))
| ~ mem(X3,X0)
| ~ ne(X0)
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ mem(X3,X0)
| ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| X2 = X3
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
& ( ( X2 != X3
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) ) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ mem(X3,X0)
| ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| X2 = X3
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
& ( ( X2 != X3
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) ) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ mem(X3,X0)
| ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
<=> ( X2 != X3
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) ) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
! [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)))
<=> ( X2 != X3
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) ) ) ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> ! [X12] :
( mem(X12,X8)
=> ! [X13] :
( mem(X13,X8)
=> ( p(ap(ap(c_2Ebool_2EIN(X8),X12),ap(ap(c_2Epred__set_2EDELETE(X8),X9),X13)))
<=> ( X12 != X13
& p(ap(ap(c_2Ebool_2EIN(X8),X12),X9)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP004+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 23:30:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48 % (23303)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.49 % (23309)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (23325)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.51 % (23317)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.51 % (23323)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.51 % (23301)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51 % (23307)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52 % (23305)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.52 % (23324)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.52 TRYING [1]
% 0.19/0.52 % (23319)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.52 % (23307)Instruction limit reached!
% 0.19/0.52 % (23307)------------------------------
% 0.19/0.52 % (23307)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (23307)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (23307)Termination reason: Unknown
% 0.19/0.53 % (23307)Termination phase: Saturation
% 0.19/0.53
% 0.19/0.53 % (23307)Memory used [KB]: 5500
% 0.19/0.53 % (23307)Time elapsed: 0.077 s
% 0.19/0.53 % (23307)Instructions burned: 7 (million)
% 0.19/0.53 % (23307)------------------------------
% 0.19/0.53 % (23307)------------------------------
% 0.19/0.53 % (23322)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.53 % (23327)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.53 % (23306)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53 % (23316)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.53 % (23302)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.53 % (23313)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.53 % (23315)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.53 % (23301)Refutation not found, incomplete strategy% (23301)------------------------------
% 0.19/0.53 % (23301)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (23326)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.53 % (23308)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.53 % (23329)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.19/0.53 % (23300)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.54 % (23304)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.54 % (23301)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (23301)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.54
% 0.19/0.54 % (23301)Memory used [KB]: 5500
% 0.19/0.54 % (23301)Time elapsed: 0.122 s
% 0.19/0.54 % (23301)Instructions burned: 5 (million)
% 0.19/0.54 % (23301)------------------------------
% 0.19/0.54 % (23301)------------------------------
% 0.19/0.54 % (23312)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.54 % (23318)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.54 % (23314)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.54 % (23308)Instruction limit reached!
% 0.19/0.54 % (23308)------------------------------
% 0.19/0.54 % (23308)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55 % (23321)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.55 % (23311)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.55 TRYING [2]
% 0.19/0.55 TRYING [1]
% 1.53/0.55 % (23320)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.53/0.55 % (23328)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.53/0.55 % (23310)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.53/0.55 % (23308)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.55 % (23308)Termination reason: Unknown
% 1.53/0.55 % (23308)Termination phase: Blocked clause elimination
% 1.53/0.55
% 1.53/0.55 % (23308)Memory used [KB]: 1023
% 1.53/0.55 % (23308)Time elapsed: 0.004 s
% 1.53/0.55 % (23308)Instructions burned: 4 (million)
% 1.53/0.55 % (23308)------------------------------
% 1.53/0.55 % (23308)------------------------------
% 1.53/0.56 TRYING [1]
% 1.66/0.57 % (23319)First to succeed.
% 1.66/0.57 TRYING [2]
% 1.66/0.57 TRYING [2]
% 1.66/0.57 TRYING [3]
% 1.66/0.58 % (23319)Refutation found. Thanks to Tanya!
% 1.66/0.58 % SZS status Theorem for theBenchmark
% 1.66/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.66/0.58 % (23319)------------------------------
% 1.66/0.58 % (23319)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.66/0.58 % (23319)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.66/0.58 % (23319)Termination reason: Refutation
% 1.66/0.58
% 1.66/0.58 % (23319)Memory used [KB]: 1407
% 1.66/0.58 % (23319)Time elapsed: 0.145 s
% 1.66/0.58 % (23319)Instructions burned: 32 (million)
% 1.66/0.58 % (23319)------------------------------
% 1.66/0.58 % (23319)------------------------------
% 1.66/0.58 % (23299)Success in time 0.224 s
%------------------------------------------------------------------------------