TSTP Solution File: SET594+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 : Tue Apr 30 15:08:43 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 102 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 43 ~; 37 |; 21 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 60 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f170,plain,
$false,
inference(resolution,[],[f168,f30]) ).
fof(f30,plain,
~ subset(sK0,union(sK1,sK2)),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
( ~ subset(sK0,union(sK1,sK2))
& sK0 = union(intersection(sK0,sK1),intersection(sK0,sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f13]) ).
fof(f13,plain,
( ? [X0,X1,X2] :
( ~ subset(X0,union(X1,X2))
& union(intersection(X0,X1),intersection(X0,X2)) = X0 )
=> ( ~ subset(sK0,union(sK1,sK2))
& sK0 = union(intersection(sK0,sK1),intersection(sK0,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ~ subset(X0,union(X1,X2))
& union(intersection(X0,X1),intersection(X0,X2)) = X0 ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( union(intersection(X0,X1),intersection(X0,X2)) = X0
=> subset(X0,union(X1,X2)) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( union(intersection(X0,X1),intersection(X0,X2)) = X0
=> subset(X0,union(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th53) ).
fof(f168,plain,
subset(sK0,union(sK1,sK2)),
inference(resolution,[],[f165,f42]) ).
fof(f42,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,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])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,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,[],[f21]) ).
fof(f21,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,[],[f12]) ).
fof(f12,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/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f165,plain,
~ member(sK4(sK0,union(sK1,sK2)),sK0),
inference(resolution,[],[f146,f61]) ).
fof(f61,plain,
~ member(sK4(sK0,union(sK1,sK2)),sK1),
inference(resolution,[],[f48,f54]) ).
fof(f54,plain,
~ member(sK4(sK0,union(sK1,sK2)),union(sK1,sK2)),
inference(resolution,[],[f43,f30]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f146,plain,
( member(sK4(sK0,union(sK1,sK2)),sK1)
| ~ member(sK4(sK0,union(sK1,sK2)),sK0) ),
inference(resolution,[],[f144,f65]) ).
fof(f65,plain,
~ member(sK4(sK0,union(sK1,sK2)),sK2),
inference(resolution,[],[f49,f54]) ).
fof(f49,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f144,plain,
! [X0] :
( member(X0,sK2)
| ~ member(X0,sK0)
| member(X0,sK1) ),
inference(resolution,[],[f138,f45]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f138,plain,
! [X0] :
( member(X0,intersection(sK0,sK1))
| ~ member(X0,sK0)
| member(X0,sK2) ),
inference(resolution,[],[f122,f45]) ).
fof(f122,plain,
! [X0] :
( member(X0,intersection(sK0,sK2))
| member(X0,intersection(sK0,sK1))
| ~ member(X0,sK0) ),
inference(superposition,[],[f47,f29]) ).
fof(f29,plain,
sK0 = union(intersection(sK0,sK1),intersection(sK0,sK2)),
inference(cnf_transformation,[],[f14]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 01:06:26 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (29822)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (29829)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)
% 0.14/0.38 % (29823)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (29827)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)
% 0.14/0.39 % (29828)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)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.40 % (29828)First to succeed.
% 0.14/0.40 % (29828)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40 % (29828)------------------------------
% 0.14/0.40 % (29828)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.40 % (29828)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (29828)Memory used [KB]: 847
% 0.14/0.40 % (29828)Time elapsed: 0.014 s
% 0.14/0.40 % (29828)Instructions burned: 11 (million)
% 0.14/0.40 % (29828)------------------------------
% 0.14/0.40 % (29828)------------------------------
% 0.14/0.40 % (29822)Success in time 0.041 s
%------------------------------------------------------------------------------