TSTP Solution File: SET762+4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 09:18:52 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 42 ~; 28 |; 24 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 84 ( 70 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f575,plain,
$false,
inference(resolution,[],[f570,f200]) ).
fof(f200,plain,
~ subset(image2(sK0,empty_set),empty_set),
inference(subsumption_resolution,[],[f199,f177]) ).
fof(f177,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f124,f122]) ).
fof(f122,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f124,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f74,f75]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f199,plain,
( ~ subset(empty_set,image2(sK0,empty_set))
| ~ subset(image2(sK0,empty_set),empty_set) ),
inference(resolution,[],[f126,f121]) ).
fof(f121,plain,
~ equal_set(image2(sK0,empty_set),empty_set),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ~ equal_set(image2(sK0,empty_set),empty_set)
& maps(sK0,sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f60,f71]) ).
fof(f71,plain,
( ? [X0,X1,X2] :
( ~ equal_set(image2(X0,empty_set),empty_set)
& maps(X0,X1,X2) )
=> ( ~ equal_set(image2(sK0,empty_set),empty_set)
& maps(sK0,sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
? [X0,X1,X2] :
( ~ equal_set(image2(X0,empty_set),empty_set)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X0,X1,X2] :
( maps(X0,X1,X2)
=> equal_set(image2(X0,empty_set),empty_set) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X5,X0,X1] :
( maps(X5,X0,X1)
=> equal_set(image2(X5,empty_set),empty_set) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X5,X0,X1] :
( maps(X5,X0,X1)
=> equal_set(image2(X5,empty_set),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa12) ).
fof(f126,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f570,plain,
! [X0,X1] : subset(image2(X0,empty_set),X1),
inference(resolution,[],[f551,f124]) ).
fof(f551,plain,
! [X0,X1] : ~ member(X0,image2(X1,empty_set)),
inference(resolution,[],[f155,f122]) ).
fof(f155,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X1)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ( apply(X0,sK8(X0,X1,X2),X2)
& member(sK8(X0,X1,X2),X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f102,f103]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
=> ( apply(X0,sK8(X0,X1,X2),X2)
& member(sK8(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X5,X0,X4] :
( member(X4,image2(X5,X0))
<=> ? [X2] :
( apply(X5,X2,X4)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 16:33:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (11359)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (11362)WARNING: value z3 for option sas not known
% 0.15/0.38 % (11360)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (11363)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (11362)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)
% 0.15/0.38 % (11361)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (11364)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)
% 0.15/0.38 % (11365)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)
% 0.15/0.38 % (11366)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)
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.40 TRYING [1]
% 0.22/0.40 TRYING [2]
% 0.22/0.40 % (11362)First to succeed.
% 0.22/0.40 % (11362)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11359"
% 0.22/0.40 % (11362)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (11362)------------------------------
% 0.22/0.40 % (11362)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.40 % (11362)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (11362)Memory used [KB]: 1092
% 0.22/0.40 % (11362)Time elapsed: 0.016 s
% 0.22/0.40 % (11362)Instructions burned: 21 (million)
% 0.22/0.40 % (11359)Success in time 0.033 s
%------------------------------------------------------------------------------