TSTP Solution File: SET696+4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n018.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 : Fri Sep 1 23:50:12 EDT 2023
% Result : Theorem 52.52s 8.02s
% Output : Refutation 52.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 10 unt; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 148 ( 60 ~; 43 |; 30 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 97 (; 90 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53360,plain,
$false,
inference(resolution,[],[f53332,f106]) ).
fof(f106,plain,
~ subset(intersection(difference(sK1,sK0),sK0),empty_set),
inference(resolution,[],[f101,f65]) ).
fof(f65,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X0] :
( member(X2,power_set(X0))
<=> subset(X2,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.Hb8AGhKzjo/Vampire---4.8_9119',power_set) ).
fof(f101,plain,
~ member(intersection(difference(sK1,sK0),sK0),power_set(empty_set)),
inference(resolution,[],[f96,f86]) ).
fof(f86,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f60,f55]) ).
fof(f55,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox2/tmp/tmp.Hb8AGhKzjo/Vampire---4.8_9119',empty_set) ).
fof(f60,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f32,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f32,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,[],[f31]) ).
fof(f31,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,[],[f25]) ).
fof(f25,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/tmp/tmp.Hb8AGhKzjo/Vampire---4.8_9119',subset) ).
fof(f96,plain,
( ~ subset(empty_set,intersection(difference(sK1,sK0),sK0))
| ~ member(intersection(difference(sK1,sK0),sK0),power_set(empty_set)) ),
inference(resolution,[],[f94,f64]) ).
fof(f64,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f94,plain,
( ~ subset(intersection(difference(sK1,sK0),sK0),empty_set)
| ~ subset(empty_set,intersection(difference(sK1,sK0),sK0)) ),
inference(resolution,[],[f58,f54]) ).
fof(f54,plain,
~ equal_set(intersection(difference(sK1,sK0),sK0),empty_set),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ~ equal_set(intersection(difference(sK1,sK0),sK0),empty_set)
& subset(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f24,f27]) ).
fof(f27,plain,
( ? [X0,X1] :
( ~ equal_set(intersection(difference(X1,X0),X0),empty_set)
& subset(X0,X1) )
=> ( ~ equal_set(intersection(difference(sK1,sK0),sK0),empty_set)
& subset(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
? [X0,X1] :
( ~ equal_set(intersection(difference(X1,X0),X0),empty_set)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ! [X0,X1] :
( subset(X0,X1)
=> equal_set(intersection(difference(X1,X0),X0),empty_set) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0,X3] :
( subset(X0,X3)
=> equal_set(intersection(difference(X3,X0),X0),empty_set) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X0,X3] :
( subset(X0,X3)
=> equal_set(intersection(difference(X3,X0),X0),empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.Hb8AGhKzjo/Vampire---4.8_9119',thI28) ).
fof(f58,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Hb8AGhKzjo/Vampire---4.8_9119',equal_set) ).
fof(f53332,plain,
subset(intersection(difference(sK1,sK0),sK0),empty_set),
inference(resolution,[],[f53276,f93]) ).
fof(f93,plain,
! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f82,f60]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Hb8AGhKzjo/Vampire---4.8_9119',intersection) ).
fof(f53276,plain,
~ member(sK2(intersection(difference(sK1,sK0),sK0),empty_set),sK0),
inference(resolution,[],[f993,f106]) ).
fof(f993,plain,
! [X31,X32,X30,X33] :
( subset(intersection(difference(X30,X31),X32),X33)
| ~ member(sK2(intersection(difference(X30,X31),X32),X33),X31) ),
inference(resolution,[],[f92,f79]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Hb8AGhKzjo/Vampire---4.8_9119',difference) ).
fof(f92,plain,
! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f81,f60]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 30 15:47:04 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.40 % (9241)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.41 % (9242)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.23/0.41 % (9245)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.41 % (9243)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.23/0.41 % (9244)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 Vampire---4 for (569ds/0Mi)
% 0.23/0.41 % (9246)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 Vampire---4 for (531ds/0Mi)
% 0.23/0.41 % (9247)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 Vampire---4 for (522ds/0Mi)
% 0.23/0.41 % (9248)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 Vampire---4 for (497ds/0Mi)
% 0.23/0.41 TRYING [1]
% 0.23/0.41 TRYING [2]
% 0.23/0.41 TRYING [3]
% 0.23/0.41 TRYING [1]
% 0.23/0.41 TRYING [2]
% 0.23/0.42 TRYING [4]
% 0.23/0.42 TRYING [3]
% 0.23/0.43 TRYING [5]
% 0.23/0.43 TRYING [4]
% 0.23/0.44 TRYING [6]
% 0.23/0.47 TRYING [5]
% 0.23/0.48 TRYING [7]
% 0.23/0.55 TRYING [8]
% 0.23/0.67 TRYING [9]
% 0.23/0.69 TRYING [6]
% 4.56/1.08 TRYING [10]
% 7.47/1.51 TRYING [1]
% 7.47/1.51 TRYING [2]
% 7.47/1.51 TRYING [3]
% 7.47/1.51 TRYING [4]
% 7.47/1.52 TRYING [5]
% 7.47/1.55 TRYING [6]
% 7.47/1.60 TRYING [7]
% 8.97/1.72 TRYING [8]
% 11.36/2.03 TRYING [9]
% 11.44/2.10 TRYING [7]
% 16.93/2.94 TRYING [10]
% 19.29/3.17 TRYING [11]
% 38.17/5.95 TRYING [8]
% 49.52/7.67 TRYING [11]
% 52.01/8.01 % (9247)First to succeed.
% 52.52/8.02 % (9247)Refutation found. Thanks to Tanya!
% 52.52/8.02 % SZS status Theorem for Vampire---4
% 52.52/8.02 % SZS output start Proof for Vampire---4
% See solution above
% 52.52/8.02 % (9247)------------------------------
% 52.52/8.02 % (9247)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 52.52/8.02 % (9247)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 52.52/8.02 % (9247)Termination reason: Refutation
% 52.52/8.02
% 52.52/8.02 % (9247)Memory used [KB]: 72024
% 52.52/8.02 % (9247)Time elapsed: 7.591 s
% 52.52/8.02 % (9247)------------------------------
% 52.52/8.02 % (9247)------------------------------
% 52.52/8.02 % (9241)Success in time 7.578 s
% 52.52/8.02 % Vampire---4.8 exiting
%------------------------------------------------------------------------------