TSTP Solution File: SET961+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : Thu Aug 31 15:46:31 EDT 2023
% Result : Theorem 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 8 unt; 0 def)
% Number of atoms : 174 ( 53 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 204 ( 89 ~; 74 |; 27 &)
% ( 7 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 84 (; 72 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f170,plain,
$false,
inference(avatar_sat_refutation,[],[f153,f154,f161,f162,f169]) ).
fof(f169,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f168,plain,
( $false
| ~ spl6_4 ),
inference(subsumption_resolution,[],[f165,f34]) ).
fof(f34,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( sK0 != sK1
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f17]) ).
fof(f17,plain,
( ? [X0,X1] :
( X0 != X1
& empty_set != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) )
=> ( sK0 != sK1
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1] :
( X0 != X1
& empty_set != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0,X1] :
( X0 != X1
& empty_set != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = X1
| empty_set = X1
| empty_set = X0 ) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = X1
| empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.KEb1HjMbXT/Vampire---4.8_9416',t114_zfmisc_1) ).
fof(f165,plain,
( empty_set = sK1
| ~ spl6_4 ),
inference(resolution,[],[f103,f71]) ).
fof(f71,plain,
! [X4] :
( in(sK3(X4,empty_set),X4)
| empty_set = X4 ),
inference(resolution,[],[f43,f50]) ).
fof(f50,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f37]) ).
fof(f37,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( ( empty_set = X0
| in(sK2(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f21]) ).
fof(f21,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.KEb1HjMbXT/Vampire---4.8_9416',d1_xboole_0) ).
fof(f43,plain,
! [X0,X1] :
( in(sK3(X0,X1),X1)
| X0 = X1
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),X0) )
& ( in(sK3(X0,X1),X1)
| in(sK3(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),X0) )
& ( in(sK3(X0,X1),X1)
| in(sK3(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.KEb1HjMbXT/Vampire---4.8_9416',t2_tarski) ).
fof(f103,plain,
( ! [X10] : ~ in(X10,sK1)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f102,plain,
( spl6_4
<=> ! [X10] : ~ in(X10,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
fof(f162,plain,
( spl6_4
| spl6_3 ),
inference(avatar_split_clause,[],[f116,f99,f102]) ).
fof(f99,plain,
( spl6_3
<=> ! [X11] :
( ~ in(X11,sK0)
| in(X11,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
fof(f116,plain,
! [X4,X5] :
( ~ in(X4,sK0)
| ~ in(X5,sK1)
| in(X4,sK1) ),
inference(resolution,[],[f90,f46]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KEb1HjMbXT/Vampire---4.8_9416',l55_zfmisc_1) ).
fof(f90,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| ~ in(X1,sK0)
| ~ in(X0,sK1) ),
inference(superposition,[],[f47,f32]) ).
fof(f32,plain,
cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0),
inference(cnf_transformation,[],[f18]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f161,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f160]) ).
fof(f160,plain,
( $false
| ~ spl6_1 ),
inference(subsumption_resolution,[],[f157,f33]) ).
fof(f33,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f18]) ).
fof(f157,plain,
( empty_set = sK0
| ~ spl6_1 ),
inference(resolution,[],[f93,f71]) ).
fof(f93,plain,
( ! [X9] : ~ in(X9,sK0)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f92,plain,
( spl6_1
<=> ! [X9] : ~ in(X9,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f154,plain,
( spl6_2
| spl6_1 ),
inference(avatar_split_clause,[],[f117,f92,f95]) ).
fof(f95,plain,
( spl6_2
<=> ! [X8] :
( ~ in(X8,sK1)
| in(X8,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f117,plain,
! [X6,X7] :
( ~ in(X6,sK0)
| ~ in(X7,sK1)
| in(X7,sK0) ),
inference(resolution,[],[f90,f45]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f153,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f152]) ).
fof(f152,plain,
( $false
| ~ spl6_2
| ~ spl6_3 ),
inference(subsumption_resolution,[],[f151,f149]) ).
fof(f149,plain,
( ~ in(sK3(sK0,sK1),sK0)
| ~ spl6_3 ),
inference(subsumption_resolution,[],[f144,f35]) ).
fof(f35,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f18]) ).
fof(f144,plain,
( ~ in(sK3(sK0,sK1),sK0)
| sK0 = sK1
| ~ spl6_3 ),
inference(factoring,[],[f124]) ).
fof(f124,plain,
( ! [X3] :
( ~ in(sK3(X3,sK1),sK0)
| ~ in(sK3(X3,sK1),X3)
| sK1 = X3 )
| ~ spl6_3 ),
inference(resolution,[],[f100,f44]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f100,plain,
( ! [X11] :
( in(X11,sK1)
| ~ in(X11,sK0) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f151,plain,
( in(sK3(sK0,sK1),sK0)
| ~ spl6_2
| ~ spl6_3 ),
inference(subsumption_resolution,[],[f150,f35]) ).
fof(f150,plain,
( sK0 = sK1
| in(sK3(sK0,sK1),sK0)
| ~ spl6_2
| ~ spl6_3 ),
inference(resolution,[],[f149,f106]) ).
fof(f106,plain,
( ! [X0] :
( in(sK3(X0,sK1),sK0)
| sK1 = X0
| in(sK3(X0,sK1),X0) )
| ~ spl6_2 ),
inference(resolution,[],[f96,f43]) ).
fof(f96,plain,
( ! [X8] :
( ~ in(X8,sK1)
| in(X8,sK0) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.35 % Computer : n029.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Aug 26 14:33:25 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.12/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.12/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.KEb1HjMbXT/Vampire---4.8_9416
% 0.12/0.36 % (9564)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.41 % (9567)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.19/0.41 % (9568)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.19/0.41 % (9569)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.19/0.41 % (9570)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.19/0.41 % (9566)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.19/0.41 % (9571)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.19/0.42 % (9566)First to succeed.
% 0.19/0.42 % (9571)Also succeeded, but the first one will report.
% 0.19/0.42 % (9566)Refutation found. Thanks to Tanya!
% 0.19/0.42 % SZS status Theorem for Vampire---4
% 0.19/0.42 % SZS output start Proof for Vampire---4
% See solution above
% 0.19/0.42 % (9566)------------------------------
% 0.19/0.42 % (9566)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.19/0.42 % (9566)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.19/0.42 % (9566)Termination reason: Refutation
% 0.19/0.42
% 0.19/0.42 % (9566)Memory used [KB]: 9978
% 0.19/0.42 % (9566)Time elapsed: 0.008 s
% 0.19/0.42 % (9566)------------------------------
% 0.19/0.42 % (9566)------------------------------
% 0.19/0.42 % (9564)Success in time 0.065 s
% 0.19/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------