TSTP Solution File: SET754+4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET754+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n010.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 May 1 03:48:51 EDT 2024
% Result : Theorem 0.61s 0.81s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 8 unt; 0 def)
% Number of atoms : 215 ( 6 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 246 ( 84 ~; 71 |; 64 &)
% ( 8 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 176 ( 145 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f92,plain,
$false,
inference(subsumption_resolution,[],[f91,f78]) ).
fof(f78,plain,
member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK3),
inference(resolution,[],[f59,f61]) ).
fof(f61,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f44,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f44,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,[],[f43]) ).
fof(f43,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,[],[f38]) ).
fof(f38,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/tmp/tmp.SG18GfasnK/Vampire---4.8_7491',subset) ).
fof(f59,plain,
~ subset(sK3,inverse_image2(sK0,image2(sK0,sK3))),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
( ~ subset(sK3,inverse_image2(sK0,image2(sK0,sK3)))
& subset(sK3,sK1)
& maps(sK0,sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f37,f41]) ).
fof(f41,plain,
( ? [X0,X1,X2,X3] :
( ~ subset(X3,inverse_image2(X0,image2(X0,X3)))
& subset(X3,X1)
& maps(X0,X1,X2) )
=> ( ~ subset(sK3,inverse_image2(sK0,image2(sK0,sK3)))
& subset(sK3,sK1)
& maps(sK0,sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
? [X0,X1,X2,X3] :
( ~ subset(X3,inverse_image2(X0,image2(X0,X3)))
& subset(X3,X1)
& maps(X0,X1,X2) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( ~ subset(X3,inverse_image2(X0,image2(X0,X3)))
& subset(X3,X1)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X0,X1,X2,X3] :
( ( subset(X3,X1)
& maps(X0,X1,X2) )
=> subset(X3,inverse_image2(X0,image2(X0,X3))) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X5,X0,X1,X10] :
( ( subset(X10,X0)
& maps(X5,X0,X1) )
=> subset(X10,inverse_image2(X5,image2(X5,X10))) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X5,X0,X1,X10] :
( ( subset(X10,X0)
& maps(X5,X0,X1) )
=> subset(X10,inverse_image2(X5,image2(X5,X10))) ),
file('/export/starexec/sandbox/tmp/tmp.SG18GfasnK/Vampire---4.8_7491',thIIa04) ).
fof(f91,plain,
~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK3),
inference(resolution,[],[f90,f75]) ).
fof(f75,plain,
! [X0] :
( member(X0,sK1)
| ~ member(X0,sK3) ),
inference(resolution,[],[f58,f60]) ).
fof(f60,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f58,plain,
subset(sK3,sK1),
inference(cnf_transformation,[],[f42]) ).
fof(f90,plain,
~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK1),
inference(subsumption_resolution,[],[f88,f78]) ).
fof(f88,plain,
( ~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK3)
| ~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),sK1) ),
inference(resolution,[],[f86,f79]) ).
fof(f79,plain,
~ member(sK4(sK3,inverse_image2(sK0,image2(sK0,sK3))),inverse_image2(sK0,image2(sK0,sK3))),
inference(resolution,[],[f59,f62]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f86,plain,
! [X0,X1] :
( member(X0,inverse_image2(sK0,image2(sK0,X1)))
| ~ member(X0,X1)
| ~ member(X0,sK1) ),
inference(duplicate_literal_removal,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ~ member(X0,sK1)
| ~ member(X0,X1)
| member(X0,inverse_image2(sK0,image2(sK0,X1)))
| ~ member(X0,sK1) ),
inference(resolution,[],[f81,f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ member(sK5(sK0,sK2,X0),X1)
| member(X0,inverse_image2(sK0,X1))
| ~ member(X0,sK1) ),
inference(resolution,[],[f77,f71]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| member(X2,inverse_image2(X0,X1))
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ( apply(X0,X2,sK7(X0,X1,X2))
& member(sK7(X0,X1,X2),X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f54,f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) )
=> ( apply(X0,X2,sK7(X0,X1,X2))
& member(sK7(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X5,X1,X2] :
( member(X2,inverse_image2(X5,X1))
<=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.SG18GfasnK/Vampire---4.8_7491',inverse_image2) ).
fof(f77,plain,
! [X0] :
( apply(sK0,X0,sK5(sK0,sK2,X0))
| ~ member(X0,sK1) ),
inference(resolution,[],[f57,f64]) ).
fof(f64,plain,
! [X2,X0,X1,X6] :
( ~ maps(X0,X1,X2)
| ~ member(X6,X1)
| apply(X0,X6,sK5(X0,X2,X6)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ( apply(X0,X6,sK5(X0,X2,X6))
& member(sK5(X0,X2,X6),X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f40,f47]) ).
fof(f47,plain,
! [X0,X2,X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
=> ( apply(X0,X6,sK5(X0,X2,X6))
& member(sK5(X0,X2,X6),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X4) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X4) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X5,X0,X1] :
( maps(X5,X0,X1)
<=> ( ! [X2,X6,X7] :
( ( member(X7,X1)
& member(X6,X1)
& member(X2,X0) )
=> ( ( apply(X5,X2,X7)
& apply(X5,X2,X6) )
=> X6 = X7 ) )
& ! [X2] :
( member(X2,X0)
=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SG18GfasnK/Vampire---4.8_7491',maps) ).
fof(f57,plain,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f81,plain,
! [X0,X1] :
( member(sK5(sK0,sK2,X0),image2(sK0,X1))
| ~ member(X0,sK1)
| ~ member(X0,X1) ),
inference(resolution,[],[f77,f68]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X3,X2)
| member(X2,image2(X0,X1))
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ( apply(X0,sK6(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f50,f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
=> ( apply(X0,sK6(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f50,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,[],[f49]) ).
fof(f49,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,[],[f33]) ).
fof(f33,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/tmp/tmp.SG18GfasnK/Vampire---4.8_7491',image2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET754+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.02/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.31 % Computer : n010.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.16/0.31 % DateTime : Tue Apr 30 17:05:19 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.31 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.31 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.SG18GfasnK/Vampire---4.8_7491
% 0.61/0.80 % (7608)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.61/0.80 % (7610)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.61/0.80 % (7611)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.61/0.80 % (7606)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.61/0.80 % (7609)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.61/0.80 % (7607)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.61/0.80 % (7612)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.61/0.80 % (7613)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.61/0.80 % (7611)Refutation not found, incomplete strategy% (7611)------------------------------
% 0.61/0.80 % (7611)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.80 % (7611)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.80
% 0.61/0.80 % (7611)Memory used [KB]: 1046
% 0.61/0.80 % (7611)Time elapsed: 0.003 s
% 0.61/0.80 % (7611)Instructions burned: 2 (million)
% 0.61/0.80 % (7611)------------------------------
% 0.61/0.80 % (7611)------------------------------
% 0.61/0.80 % (7613)First to succeed.
% 0.61/0.80 % (7610)Refutation not found, incomplete strategy% (7610)------------------------------
% 0.61/0.80 % (7610)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.80 % (7610)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.80
% 0.61/0.80 % (7610)Memory used [KB]: 1132
% 0.61/0.80 % (7610)Time elapsed: 0.004 s
% 0.61/0.80 % (7610)Instructions burned: 5 (million)
% 0.61/0.80 % (7610)------------------------------
% 0.61/0.80 % (7610)------------------------------
% 0.61/0.81 % (7609)Also succeeded, but the first one will report.
% 0.61/0.81 % (7613)Refutation found. Thanks to Tanya!
% 0.61/0.81 % SZS status Theorem for Vampire---4
% 0.61/0.81 % SZS output start Proof for Vampire---4
% See solution above
% 0.61/0.81 % (7613)------------------------------
% 0.61/0.81 % (7613)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.81 % (7613)Termination reason: Refutation
% 0.61/0.81
% 0.61/0.81 % (7613)Memory used [KB]: 1071
% 0.61/0.81 % (7613)Time elapsed: 0.004 s
% 0.61/0.81 % (7613)Instructions burned: 5 (million)
% 0.61/0.81 % (7613)------------------------------
% 0.61/0.81 % (7613)------------------------------
% 0.61/0.81 % (7601)Success in time 0.487 s
% 0.61/0.81 % Vampire---4.8 exiting
%------------------------------------------------------------------------------