TSTP Solution File: SEU169+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU169+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n029.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 : Sat Sep 2 00:07:15 EDT 2023
% Result : Theorem 0.12s 0.40s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 18 unt; 0 def)
% Number of atoms : 141 ( 6 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 144 ( 57 ~; 42 |; 25 &)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 93 (; 82 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3348,plain,
$false,
inference(resolution,[],[f3344,f354]) ).
fof(f354,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',fc1_subset_1) ).
fof(f3344,plain,
empty(powerset(sK6)),
inference(resolution,[],[f3259,f276]) ).
fof(f276,plain,
element(sK7,powerset(sK6)),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
( ~ in(sK8,sK6)
& in(sK8,sK7)
& element(sK7,powerset(sK6)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f115,f178,f177]) ).
fof(f177,plain,
( ? [X0,X1] :
( ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) )
& element(X1,powerset(X0)) )
=> ( ? [X2] :
( ~ in(X2,sK6)
& in(X2,sK7) )
& element(sK7,powerset(sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
( ? [X2] :
( ~ in(X2,sK6)
& in(X2,sK7) )
=> ( ~ in(sK8,sK6)
& in(sK8,sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
? [X0,X1] :
( ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) )
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(negated_conjecture,[],[f47]) ).
fof(f47,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',l3_subset_1) ).
fof(f3259,plain,
( ~ element(sK7,powerset(sK6))
| empty(powerset(sK6)) ),
inference(resolution,[],[f3252,f379]) ).
fof(f379,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',d2_subset_1) ).
fof(f3252,plain,
~ in(sK7,powerset(sK6)),
inference(resolution,[],[f3126,f503]) ).
fof(f503,plain,
! [X0] : in(X0,singleton(X0)),
inference(resolution,[],[f317,f371]) ).
fof(f371,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',reflexivity_r1_tarski) ).
fof(f317,plain,
! [X0,X1] :
( ~ subset(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f191]) ).
fof(f191,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',l2_zfmisc_1) ).
fof(f3126,plain,
( ~ in(sK8,singleton(sK8))
| ~ in(sK7,powerset(sK6)) ),
inference(resolution,[],[f3120,f500]) ).
fof(f500,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,powerset(X0)) ),
inference(superposition,[],[f301,f282]) ).
fof(f282,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f104]) ).
fof(f104,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',t99_zfmisc_1) ).
fof(f301,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',l50_zfmisc_1) ).
fof(f3120,plain,
( ~ subset(sK7,sK6)
| ~ in(sK8,singleton(sK8)) ),
inference(resolution,[],[f2211,f1501]) ).
fof(f1501,plain,
subset(singleton(sK8),sK7),
inference(superposition,[],[f289,f1490]) ).
fof(f1490,plain,
sK7 = set_union2(singleton(sK8),sK7),
inference(resolution,[],[f303,f277]) ).
fof(f277,plain,
in(sK8,sK7),
inference(cnf_transformation,[],[f179]) ).
fof(f303,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',t46_zfmisc_1) ).
fof(f289,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f98]) ).
fof(f98,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',t7_xboole_1) ).
fof(f2211,plain,
! [X2,X3] :
( ~ subset(X3,sK6)
| ~ subset(X2,X3)
| ~ in(sK8,X2) ),
inference(resolution,[],[f2202,f337]) ).
fof(f337,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f141]) ).
fof(f141,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',t1_xboole_1) ).
fof(f2202,plain,
! [X61] :
( ~ subset(X61,sK6)
| ~ in(sK8,X61) ),
inference(resolution,[],[f398,f278]) ).
fof(f278,plain,
~ in(sK8,sK6),
inference(cnf_transformation,[],[f179]) ).
fof(f398,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK18(X0,X1),X1)
& in(sK18(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f223,f224]) ).
fof(f224,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK18(X0,X1),X1)
& in(sK18(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f223,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f222]) ).
fof(f222,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9pP4U6yI18/Vampire---4.8_5542',d3_tarski) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU169+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.09 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.08/0.28 % Computer : n029.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Wed Aug 30 14:14:42 EDT 2023
% 0.12/0.28 % CPUTime :
% 0.12/0.32 % (6530)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.32 % (6642)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.12/0.32 % (6643)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.12/0.32 % (6646)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.12/0.32 % (6647)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)
% 0.12/0.32 % (6644)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)
% 0.12/0.32 % (6649)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)
% 0.12/0.32 % (6648)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)
% 0.12/0.33 TRYING [1]
% 0.12/0.33 TRYING [2]
% 0.12/0.34 TRYING [3]
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 TRYING [3]
% 0.12/0.37 TRYING [4]
% 0.12/0.37 TRYING [4]
% 0.12/0.40 % (6648)First to succeed.
% 0.12/0.40 % (6648)Refutation found. Thanks to Tanya!
% 0.12/0.40 % SZS status Theorem for Vampire---4
% 0.12/0.40 % SZS output start Proof for Vampire---4
% See solution above
% 0.12/0.40 % (6648)------------------------------
% 0.12/0.40 % (6648)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.12/0.40 % (6648)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.12/0.40 % (6648)Termination reason: Refutation
% 0.12/0.40
% 0.12/0.40 % (6648)Memory used [KB]: 3070
% 0.12/0.40 % (6648)Time elapsed: 0.076 s
% 0.12/0.40 % (6648)------------------------------
% 0.12/0.40 % (6648)------------------------------
% 0.12/0.40 % (6530)Success in time 0.111 s
% 0.12/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------