TSTP Solution File: SET957+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET957+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 : n032.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 15:46:30 EDT 2023
% Result : Theorem 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 4 unt; 0 def)
% Number of atoms : 215 ( 41 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 230 ( 81 ~; 85 |; 48 &)
% ( 9 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 127 (; 90 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f339,plain,
$false,
inference(avatar_sat_refutation,[],[f273,f291,f294,f308,f316,f332,f337]) ).
fof(f337,plain,
( ~ spl12_3
| spl12_4
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f319,f268,f289,f286]) ).
fof(f286,plain,
( spl12_3
<=> in(sK7(sK4,sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f289,plain,
( spl12_4
<=> in(sK7(sK4,sK1),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f268,plain,
( spl12_1
<=> sK7(sK4,sK1) = ordered_pair(sK8(sK7(sK4,sK1),sK6,sK5),sK9(sK7(sK4,sK1),sK6,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f319,plain,
( in(sK7(sK4,sK1),sK4)
| ~ in(sK7(sK4,sK1),sK1)
| ~ spl12_1 ),
inference(superposition,[],[f36,f269]) ).
fof(f269,plain,
( sK7(sK4,sK1) = ordered_pair(sK8(sK7(sK4,sK1),sK6,sK5),sK9(sK7(sK4,sK1),sK6,sK5))
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f36,plain,
! [X6,X7] :
( in(ordered_pair(X6,X7),sK4)
| ~ in(ordered_pair(X6,X7),sK1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( sK1 != sK4
& ! [X6,X7] :
( ( in(ordered_pair(X6,X7),sK1)
| ~ in(ordered_pair(X6,X7),sK4) )
& ( in(ordered_pair(X6,X7),sK4)
| ~ in(ordered_pair(X6,X7),sK1) ) )
& subset(sK4,cartesian_product2(sK5,sK6))
& subset(sK1,cartesian_product2(sK2,sK3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f20,f21]) ).
fof(f21,plain,
( ? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& ! [X6,X7] :
( ( in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X6,X7),X3) )
& ( in(ordered_pair(X6,X7),X3)
| ~ in(ordered_pair(X6,X7),X0) ) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) )
=> ( sK1 != sK4
& ! [X7,X6] :
( ( in(ordered_pair(X6,X7),sK1)
| ~ in(ordered_pair(X6,X7),sK4) )
& ( in(ordered_pair(X6,X7),sK4)
| ~ in(ordered_pair(X6,X7),sK1) ) )
& subset(sK4,cartesian_product2(sK5,sK6))
& subset(sK1,cartesian_product2(sK2,sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& ! [X6,X7] :
( ( in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X6,X7),X3) )
& ( in(ordered_pair(X6,X7),X3)
| ~ in(ordered_pair(X6,X7),X0) ) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) )
=> X0 = X3 ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) )
=> X0 = X3 ),
file('/export/starexec/sandbox/tmp/tmp.JXXq3JR53H/Vampire---4.8_32495',t110_zfmisc_1) ).
fof(f332,plain,
( ~ spl12_1
| ~ spl12_4 ),
inference(avatar_contradiction_clause,[],[f331]) ).
fof(f331,plain,
( $false
| ~ spl12_1
| ~ spl12_4 ),
inference(subsumption_resolution,[],[f330,f317]) ).
fof(f317,plain,
( ~ in(sK7(sK4,sK1),sK1)
| ~ spl12_4 ),
inference(subsumption_resolution,[],[f309,f38]) ).
fof(f38,plain,
sK1 != sK4,
inference(cnf_transformation,[],[f22]) ).
fof(f309,plain,
( ~ in(sK7(sK4,sK1),sK1)
| sK1 = sK4
| ~ spl12_4 ),
inference(resolution,[],[f290,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(sK7(X0,X1),X1)
| ~ in(sK7(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK7(X0,X1),X1)
| ~ in(sK7(X0,X1),X0) )
& ( in(sK7(X0,X1),X1)
| in(sK7(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK7(X0,X1),X1)
| ~ in(sK7(X0,X1),X0) )
& ( in(sK7(X0,X1),X1)
| in(sK7(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,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.JXXq3JR53H/Vampire---4.8_32495',t2_tarski) ).
fof(f290,plain,
( in(sK7(sK4,sK1),sK4)
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f330,plain,
( in(sK7(sK4,sK1),sK1)
| ~ spl12_1
| ~ spl12_4 ),
inference(subsumption_resolution,[],[f320,f290]) ).
fof(f320,plain,
( ~ in(sK7(sK4,sK1),sK4)
| in(sK7(sK4,sK1),sK1)
| ~ spl12_1 ),
inference(superposition,[],[f37,f269]) ).
fof(f37,plain,
! [X6,X7] :
( ~ in(ordered_pair(X6,X7),sK4)
| in(ordered_pair(X6,X7),sK1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f316,plain,
( ~ spl12_3
| ~ spl12_4 ),
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f315,plain,
( $false
| ~ spl12_3
| ~ spl12_4 ),
inference(subsumption_resolution,[],[f314,f38]) ).
fof(f314,plain,
( sK1 = sK4
| ~ spl12_3
| ~ spl12_4 ),
inference(subsumption_resolution,[],[f309,f292]) ).
fof(f292,plain,
( in(sK7(sK4,sK1),sK1)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f308,plain,
( spl12_3
| spl12_4 ),
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f307,plain,
( $false
| spl12_3
| spl12_4 ),
inference(subsumption_resolution,[],[f306,f293]) ).
fof(f293,plain,
( ~ in(sK7(sK4,sK1),sK4)
| spl12_4 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f306,plain,
( in(sK7(sK4,sK1),sK4)
| spl12_3 ),
inference(subsumption_resolution,[],[f305,f38]) ).
fof(f305,plain,
( sK1 = sK4
| in(sK7(sK4,sK1),sK4)
| spl12_3 ),
inference(resolution,[],[f287,f44]) ).
fof(f44,plain,
! [X0,X1] :
( in(sK7(X0,X1),X1)
| X0 = X1
| in(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f287,plain,
( ~ in(sK7(sK4,sK1),sK1)
| spl12_3 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f294,plain,
( spl12_3
| ~ spl12_4
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f275,f271,f289,f286]) ).
fof(f271,plain,
( spl12_2
<=> sK7(sK4,sK1) = ordered_pair(sK8(sK7(sK4,sK1),sK3,sK2),sK9(sK7(sK4,sK1),sK3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f275,plain,
( ~ in(sK7(sK4,sK1),sK4)
| in(sK7(sK4,sK1),sK1)
| ~ spl12_2 ),
inference(superposition,[],[f37,f272]) ).
fof(f272,plain,
( sK7(sK4,sK1) = ordered_pair(sK8(sK7(sK4,sK1),sK3,sK2),sK9(sK7(sK4,sK1),sK3,sK2))
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f291,plain,
( ~ spl12_3
| spl12_4
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f274,f271,f289,f286]) ).
fof(f274,plain,
( in(sK7(sK4,sK1),sK4)
| ~ in(sK7(sK4,sK1),sK1)
| ~ spl12_2 ),
inference(superposition,[],[f36,f272]) ).
fof(f273,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f266,f271,f268]) ).
fof(f266,plain,
( sK7(sK4,sK1) = ordered_pair(sK8(sK7(sK4,sK1),sK3,sK2),sK9(sK7(sK4,sK1),sK3,sK2))
| sK7(sK4,sK1) = ordered_pair(sK8(sK7(sK4,sK1),sK6,sK5),sK9(sK7(sK4,sK1),sK6,sK5)) ),
inference(subsumption_resolution,[],[f262,f38]) ).
fof(f262,plain,
( sK1 = sK4
| sK7(sK4,sK1) = ordered_pair(sK8(sK7(sK4,sK1),sK3,sK2),sK9(sK7(sK4,sK1),sK3,sK2))
| sK7(sK4,sK1) = ordered_pair(sK8(sK7(sK4,sK1),sK6,sK5),sK9(sK7(sK4,sK1),sK6,sK5)) ),
inference(resolution,[],[f181,f180]) ).
fof(f180,plain,
! [X4] :
( ~ in(X4,sK4)
| ordered_pair(sK8(X4,sK6,sK5),sK9(X4,sK6,sK5)) = X4 ),
inference(resolution,[],[f126,f35]) ).
fof(f35,plain,
subset(sK4,cartesian_product2(sK5,sK6)),
inference(cnf_transformation,[],[f22]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X3)
| ~ subset(X3,cartesian_product2(X2,X1))
| ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2)) = X0 ),
inference(resolution,[],[f48,f49]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( sP0(X3,X2,X1)
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( sP0(X3,X2,X1)
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(definition_folding,[],[f17,f18]) ).
fof(f18,plain,
! [X3,X2,X1] :
( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
| ~ sP0(X3,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.JXXq3JR53H/Vampire---4.8_32495',t103_zfmisc_1) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2)) = X0
& in(sK9(X0,X1,X2),X1)
& in(sK8(X0,X1,X2),X2) )
| ~ sP0(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ordered_pair(X3,X4) = X0
& in(X4,X1)
& in(X3,X2) )
=> ( ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2)) = X0
& in(sK9(X0,X1,X2),X1)
& in(sK8(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ordered_pair(X3,X4) = X0
& in(X4,X1)
& in(X3,X2) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X3,X2,X1] :
( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
| ~ sP0(X3,X2,X1) ),
inference(nnf_transformation,[],[f18]) ).
fof(f181,plain,
! [X0] :
( in(sK7(X0,sK1),X0)
| sK1 = X0
| sK7(X0,sK1) = ordered_pair(sK8(sK7(X0,sK1),sK3,sK2),sK9(sK7(X0,sK1),sK3,sK2)) ),
inference(resolution,[],[f179,f44]) ).
fof(f179,plain,
! [X3] :
( ~ in(X3,sK1)
| ordered_pair(sK8(X3,sK3,sK2),sK9(X3,sK3,sK2)) = X3 ),
inference(resolution,[],[f126,f34]) ).
fof(f34,plain,
subset(sK1,cartesian_product2(sK2,sK3)),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.12/0.13 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.33 % Computer : n032.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 11:24:43 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.33 This is a FOF_THM_RFO_SEQ problem
% 0.12/0.33 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.JXXq3JR53H/Vampire---4.8_32495
% 0.12/0.33 % (32604)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.37 % (32611)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)
% 0.18/0.38 % (32605)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.18/0.38 % (32607)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)
% 0.18/0.38 % (32608)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)
% 0.18/0.38 % (32609)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)
% 0.18/0.38 % (32610)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)
% 0.18/0.38 % (32606)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)
% 0.18/0.39 % (32606)First to succeed.
% 0.18/0.40 % (32606)Refutation found. Thanks to Tanya!
% 0.18/0.40 % SZS status Theorem for Vampire---4
% 0.18/0.40 % SZS output start Proof for Vampire---4
% See solution above
% 0.18/0.40 % (32606)------------------------------
% 0.18/0.40 % (32606)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.40 % (32606)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.40 % (32606)Termination reason: Refutation
% 0.18/0.40
% 0.18/0.40 % (32606)Memory used [KB]: 10490
% 0.18/0.40 % (32606)Time elapsed: 0.014 s
% 0.18/0.40 % (32606)------------------------------
% 0.18/0.40 % (32606)------------------------------
% 0.18/0.40 % (32604)Success in time 0.063 s
% 0.18/0.40 32605 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.JXXq3JR53H/Vampire---4.8_32495
% 0.18/0.40 % (32605)------------------------------
% 0.18/0.40 % (32605)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.40 % (32605)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.40 % (32605)Termination reason: Unknown
% 0.18/0.40 % (32605)Termination phase: Saturation
% 0.18/0.40
% 0.18/0.40 % (32605)Memory used [KB]: 5373
% 0.18/0.40 % (32605)Time elapsed: 0.022 s
% 0.18/0.40 % (32605)------------------------------
% 0.18/0.40 % (32605)------------------------------
% 0.18/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------