TSTP Solution File: ITP010+5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP010+5 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.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 : Sun May 5 06:57:42 EDT 2024
% Result : Theorem 31.46s 5.73s
% Output : Refutation 31.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 3 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 126 ( 35 ~; 24 |; 47 &)
% ( 3 <=>; 16 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 12 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f116641,plain,
$false,
inference(subsumption_resolution,[],[f116621,f116622]) ).
fof(f116622,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)),
inference(duplicate_literal_removal,[],[f68636]) ).
fof(f68636,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) ),
inference(cnf_transformation,[],[f36122]) ).
fof(f36122,plain,
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) )
& mem(sK6913,arr(sK6911,bool))
& mem(sK6912,arr(sK6910,bool))
& ne(sK6911)
& ne(sK6910) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6910,sK6911,sK6912,sK6913])],[f36117,f36121,f36120,f36119,f36118]) ).
fof(f36118,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(sK6910,bool)) )
& ne(X1) )
& ne(sK6910) ) ),
introduced(choice_axiom,[]) ).
fof(f36119,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(sK6910,bool)) )
& ne(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3)) )
& mem(X3,arr(sK6911,bool)) )
& mem(X2,arr(sK6910,bool)) )
& ne(sK6911) ) ),
introduced(choice_axiom,[]) ).
fof(f36120,plain,
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),X2),X3)) )
& mem(X3,arr(sK6911,bool)) )
& mem(X2,arr(sK6910,bool)) )
=> ( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3)) )
& mem(X3,arr(sK6911,bool)) )
& mem(sK6912,arr(sK6910,bool)) ) ),
introduced(choice_axiom,[]) ).
fof(f36121,plain,
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),X3)) )
& mem(X3,arr(sK6911,bool)) )
=> ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) )
& mem(sK6913,arr(sK6911,bool)) ) ),
introduced(choice_axiom,[]) ).
fof(f36117,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(flattening,[],[f36116]) ).
fof(f36116,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(nnf_transformation,[],[f17046]) ).
fof(f17046,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<~> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(ennf_transformation,[],[f8600]) ).
fof(f8600,plain,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) ) ) ) ) ),
inference(rectify,[],[f8599]) ).
fof(f8599,negated_conjecture,
~ ! [X8] :
( ne(X8)
=> ! [X10] :
( ne(X10)
=> ! [X167] :
( mem(X167,arr(X8,bool))
=> ! [X41] :
( mem(X41,arr(X10,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X10),X167),X41))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X10),X167),X41)) ) ) ) ) ),
inference(negated_conjecture,[],[f8598]) ).
fof(f8598,conjecture,
! [X8] :
( ne(X8)
=> ! [X10] :
( ne(X10)
=> ! [X167] :
( mem(X167,arr(X8,bool))
=> ! [X41] :
( mem(X41,arr(X10,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X10),X167),X41))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X10),X167),X41)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f116621,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)),
inference(duplicate_literal_removal,[],[f68635]) ).
fof(f68635,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK6910,sK6911),sK6912),sK6913)) ),
inference(cnf_transformation,[],[f36122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP010+5 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 19:03:39 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (19053)Running in auto input_syntax mode. Trying TPTP
% 1.09/1.29 % (19054)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.09/1.29 % (19056)WARNING: value z3 for option sas not known
% 1.09/1.29 % (19055)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 1.09/1.29 % (19056)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 1.09/1.29 % (19057)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 1.09/1.29 % (19059)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 1.09/1.29 % (19060)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 1.09/1.29 % (19058)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 31.46/5.70 % (19060)First to succeed.
% 31.46/5.71 % (19060)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19053"
% 31.46/5.73 % (19060)Refutation found. Thanks to Tanya!
% 31.46/5.73 % SZS status Theorem for theBenchmark
% 31.46/5.73 % SZS output start Proof for theBenchmark
% See solution above
% 31.46/5.74 % (19060)------------------------------
% 31.46/5.74 % (19060)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 31.46/5.74 % (19060)Termination reason: Refutation
% 31.46/5.74
% 31.46/5.74 % (19060)Memory used [KB]: 160654
% 31.46/5.74 % (19060)Time elapsed: 4.412 s
% 31.46/5.74 % (19060)Instructions burned: 10121 (million)
% 31.46/5.74 % (19053)Success in time 5.372 s
%------------------------------------------------------------------------------