TSTP Solution File: ITP010+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP010+2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.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 : Mon May 20 22:42:28 EDT 2024
% Result : Theorem 0.12s 0.36s
% Output : Refutation 0.12s
% 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(f405,plain,
$false,
inference(subsumption_resolution,[],[f403,f404]) ).
fof(f404,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35)),
inference(duplicate_literal_removal,[],[f254]) ).
fof(f254,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35)) ),
inference(cnf_transformation,[],[f169]) ).
fof(f169,plain,
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35)) )
& mem(sK35,arr(sK33,bool))
& mem(sK34,arr(sK32,bool))
& ne(sK33)
& ne(sK32) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35])],[f164,f168,f167,f166,f165]) ).
fof(f165,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(sK32,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(sK32,bool)) )
& ne(X1) )
& ne(sK32) ) ),
introduced(choice_axiom,[]) ).
fof(f166,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(sK32,bool)) )
& ne(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),X2),X3)) )
& mem(X3,arr(sK33,bool)) )
& mem(X2,arr(sK32,bool)) )
& ne(sK33) ) ),
introduced(choice_axiom,[]) ).
fof(f167,plain,
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),X2),X3)) )
& mem(X3,arr(sK33,bool)) )
& mem(X2,arr(sK32,bool)) )
=> ( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),X3)) )
& mem(X3,arr(sK33,bool)) )
& mem(sK34,arr(sK32,bool)) ) ),
introduced(choice_axiom,[]) ).
fof(f168,plain,
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),X3)) )
& mem(X3,arr(sK33,bool)) )
=> ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35)) )
& mem(sK35,arr(sK33,bool)) ) ),
introduced(choice_axiom,[]) ).
fof(f164,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,[],[f163]) ).
fof(f163,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,[],[f86]) ).
fof(f86,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,[],[f43]) ).
fof(f43,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,[],[f42]) ).
fof(f42,negated_conjecture,
~ ! [X8] :
( ne(X8)
=> ! [X9] :
( ne(X9)
=> ! [X13] :
( mem(X13,arr(X8,bool))
=> ! [X14] :
( mem(X14,arr(X9,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X13),X14))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X13),X14)) ) ) ) ) ),
inference(negated_conjecture,[],[f41]) ).
fof(f41,conjecture,
! [X8] :
( ne(X8)
=> ! [X9] :
( ne(X9)
=> ! [X13] :
( mem(X13,arr(X8,bool))
=> ! [X14] :
( mem(X14,arr(X9,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X13),X14))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X13),X14)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f403,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35)),
inference(duplicate_literal_removal,[],[f253]) ).
fof(f253,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK32,sK33),sK34),sK35)) ),
inference(cnf_transformation,[],[f169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : ITP010+2 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.09/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat May 18 16:48:38 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (26115)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (26118)WARNING: value z3 for option sas not known
% 0.12/0.36 % (26117)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.36 % (26118)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)
% 0.12/0.36 % (26119)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.36 % (26122)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)
% 0.12/0.36 % (26121)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)
% 0.12/0.36 % (26120)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)
% 0.12/0.36 % (26116)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.36 % (26122)First to succeed.
% 0.12/0.36 % (26118)Also succeeded, but the first one will report.
% 0.12/0.36 % (26121)Also succeeded, but the first one will report.
% 0.12/0.36 % (26122)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26115"
% 0.12/0.36 % (26120)Also succeeded, but the first one will report.
% 0.12/0.36 % (26122)Refutation found. Thanks to Tanya!
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36 % (26122)------------------------------
% 0.12/0.36 % (26122)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.36 % (26122)Termination reason: Refutation
% 0.12/0.36
% 0.12/0.36 % (26122)Memory used [KB]: 1018
% 0.12/0.36 % (26122)Time elapsed: 0.006 s
% 0.12/0.36 % (26122)Instructions burned: 10 (million)
% 0.12/0.36 % (26115)Success in time 0.021 s
%------------------------------------------------------------------------------