TSTP Solution File: SET980+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET980+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 : n014.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 15:46:37 EDT 2023
% Result : Theorem 0.23s 0.45s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 90 ( 7 unt; 0 def)
% Number of atoms : 272 ( 71 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 326 ( 144 ~; 134 |; 29 &)
% ( 12 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 114 (; 96 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f498,plain,
$false,
inference(avatar_sat_refutation,[],[f65,f131,f138,f145,f158,f189,f279,f451,f489,f496]) ).
fof(f496,plain,
( spl8_12
| spl8_9
| ~ spl8_7
| ~ spl8_11 ),
inference(avatar_split_clause,[],[f495,f156,f129,f136,f160]) ).
fof(f160,plain,
( spl8_12
<=> ! [X7] :
( ~ in(X7,sK2)
| in(X7,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
fof(f136,plain,
( spl8_9
<=> ! [X10] : ~ in(X10,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
fof(f129,plain,
( spl8_7
<=> ! [X8] :
( ~ in(X8,sK1)
| in(X8,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f156,plain,
( spl8_11
<=> ! [X4] :
( ~ in(X4,sK3)
| in(X4,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f495,plain,
( ! [X6,X7] :
( ~ in(X6,sK1)
| ~ in(X7,sK2)
| in(X7,sK0) )
| ~ spl8_7
| ~ spl8_11 ),
inference(forward_demodulation,[],[f350,f369]) ).
fof(f369,plain,
( sK1 = sK3
| ~ spl8_7
| ~ spl8_11 ),
inference(subsumption_resolution,[],[f356,f296]) ).
fof(f296,plain,
( ! [X1] :
( in(sK5(X1,sK3),sK1)
| sK3 = X1
| in(sK5(X1,sK3),X1) )
| ~ spl8_11 ),
inference(resolution,[],[f157,f46]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK5(X0,X1),X1)
| X0 = X1
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f24,f25]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.HDnLT5N38I/Vampire---4.8_26521',t2_tarski) ).
fof(f157,plain,
( ! [X4] :
( ~ in(X4,sK3)
| in(X4,sK1) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f356,plain,
( ~ in(sK5(sK1,sK3),sK1)
| sK1 = sK3
| ~ spl8_7 ),
inference(factoring,[],[f214]) ).
fof(f214,plain,
( ! [X2] :
( ~ in(sK5(X2,sK3),sK1)
| ~ in(sK5(X2,sK3),X2)
| sK3 = X2 )
| ~ spl8_7 ),
inference(resolution,[],[f130,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f130,plain,
( ! [X8] :
( in(X8,sK3)
| ~ in(X8,sK1) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f350,plain,
! [X6,X7] :
( ~ in(X6,sK3)
| ~ in(X7,sK2)
| in(X7,sK0) ),
inference(resolution,[],[f124,f51]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,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,[],[f29]) ).
fof(f29,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.HDnLT5N38I/Vampire---4.8_26521',l55_zfmisc_1) ).
fof(f124,plain,
! [X6,X7] :
( in(ordered_pair(X6,X7),cartesian_product2(sK0,sK1))
| ~ in(X7,sK3)
| ~ in(X6,sK2) ),
inference(superposition,[],[f53,f35]) ).
fof(f35,plain,
cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ( sK1 != sK3
| sK0 != sK2 )
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f18]) ).
fof(f18,plain,
( ? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0
& cartesian_product2(X2,X3) = cartesian_product2(X0,X1) )
=> ( ( sK1 != sK3
| sK0 != sK2 )
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0
& cartesian_product2(X2,X3) = cartesian_product2(X0,X1) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0
& cartesian_product2(X2,X3) = cartesian_product2(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
=> ( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0 ) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
( cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
=> ( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HDnLT5N38I/Vampire---4.8_26521',t134_zfmisc_1) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f489,plain,
( spl8_2
| ~ spl8_7
| ~ spl8_11 ),
inference(avatar_contradiction_clause,[],[f488]) ).
fof(f488,plain,
( $false
| spl8_2
| ~ spl8_7
| ~ spl8_11 ),
inference(subsumption_resolution,[],[f64,f369]) ).
fof(f64,plain,
( sK1 != sK3
| spl8_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f63,plain,
( spl8_2
<=> sK1 = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f451,plain,
( spl8_1
| ~ spl8_8
| ~ spl8_12 ),
inference(avatar_contradiction_clause,[],[f450]) ).
fof(f450,plain,
( $false
| spl8_1
| ~ spl8_8
| ~ spl8_12 ),
inference(subsumption_resolution,[],[f447,f443]) ).
fof(f443,plain,
( ~ in(sK5(sK2,sK0),sK0)
| spl8_1
| ~ spl8_8 ),
inference(subsumption_resolution,[],[f438,f61]) ).
fof(f61,plain,
( sK0 != sK2
| spl8_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f60,plain,
( spl8_1
<=> sK0 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f438,plain,
( ~ in(sK5(sK2,sK0),sK0)
| sK0 = sK2
| ~ spl8_8 ),
inference(factoring,[],[f293]) ).
fof(f293,plain,
( ! [X3] :
( ~ in(sK5(sK2,X3),sK0)
| ~ in(sK5(sK2,X3),X3)
| sK2 = X3 )
| ~ spl8_8 ),
inference(resolution,[],[f134,f47]) ).
fof(f134,plain,
( ! [X11] :
( in(X11,sK2)
| ~ in(X11,sK0) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f133,plain,
( spl8_8
<=> ! [X11] :
( ~ in(X11,sK0)
| in(X11,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
fof(f447,plain,
( in(sK5(sK2,sK0),sK0)
| spl8_1
| ~ spl8_8
| ~ spl8_12 ),
inference(resolution,[],[f445,f161]) ).
fof(f161,plain,
( ! [X7] :
( ~ in(X7,sK2)
| in(X7,sK0) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f445,plain,
( in(sK5(sK2,sK0),sK2)
| spl8_1
| ~ spl8_8 ),
inference(subsumption_resolution,[],[f444,f61]) ).
fof(f444,plain,
( sK0 = sK2
| in(sK5(sK2,sK0),sK2)
| spl8_1
| ~ spl8_8 ),
inference(resolution,[],[f443,f46]) ).
fof(f279,plain,
~ spl8_9,
inference(avatar_contradiction_clause,[],[f278]) ).
fof(f278,plain,
( $false
| ~ spl8_9 ),
inference(subsumption_resolution,[],[f275,f37]) ).
fof(f37,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f19]) ).
fof(f275,plain,
( empty_set = sK1
| ~ spl8_9 ),
inference(resolution,[],[f137,f103]) ).
fof(f103,plain,
! [X4] :
( in(sK5(X4,empty_set),X4)
| empty_set = X4 ),
inference(resolution,[],[f46,f56]) ).
fof(f56,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f40]) ).
fof(f40,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( ( empty_set = X0
| in(sK4(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f21,f22]) ).
fof(f22,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f20]) ).
fof(f20,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.HDnLT5N38I/Vampire---4.8_26521',d1_xboole_0) ).
fof(f137,plain,
( ! [X10] : ~ in(X10,sK1)
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f189,plain,
( ~ spl8_8
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f188]) ).
fof(f188,plain,
( $false
| ~ spl8_8
| ~ spl8_10 ),
inference(subsumption_resolution,[],[f185,f36]) ).
fof(f36,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f19]) ).
fof(f185,plain,
( empty_set = sK0
| ~ spl8_8
| ~ spl8_10 ),
inference(resolution,[],[f178,f103]) ).
fof(f178,plain,
( ! [X11] : ~ in(X11,sK0)
| ~ spl8_8
| ~ spl8_10 ),
inference(subsumption_resolution,[],[f172,f56]) ).
fof(f172,plain,
( ! [X11] :
( in(X11,empty_set)
| ~ in(X11,sK0) )
| ~ spl8_8
| ~ spl8_10 ),
inference(backward_demodulation,[],[f134,f166]) ).
fof(f166,plain,
( empty_set = sK2
| ~ spl8_10 ),
inference(resolution,[],[f154,f41]) ).
fof(f41,plain,
! [X0] :
( in(sK4(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f154,plain,
( ! [X5] : ~ in(X5,sK2)
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f153,plain,
( spl8_10
<=> ! [X5] : ~ in(X5,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
fof(f158,plain,
( spl8_10
| spl8_11 ),
inference(avatar_split_clause,[],[f148,f156,f153]) ).
fof(f148,plain,
! [X4,X5] :
( ~ in(X4,sK3)
| ~ in(X5,sK2)
| in(X4,sK1) ),
inference(resolution,[],[f124,f52]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f30]) ).
fof(f145,plain,
~ spl8_6,
inference(avatar_contradiction_clause,[],[f144]) ).
fof(f144,plain,
( $false
| ~ spl8_6 ),
inference(subsumption_resolution,[],[f141,f36]) ).
fof(f141,plain,
( empty_set = sK0
| ~ spl8_6 ),
inference(resolution,[],[f127,f103]) ).
fof(f127,plain,
( ! [X9] : ~ in(X9,sK0)
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f126,plain,
( spl8_6
<=> ! [X9] : ~ in(X9,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
fof(f138,plain,
( spl8_8
| spl8_9 ),
inference(avatar_split_clause,[],[f119,f136,f133]) ).
fof(f119,plain,
! [X10,X11] :
( ~ in(X10,sK1)
| ~ in(X11,sK0)
| in(X11,sK2) ),
inference(resolution,[],[f53,f73]) ).
fof(f73,plain,
! [X6,X7] :
( ~ in(ordered_pair(X6,X7),cartesian_product2(sK0,sK1))
| in(X6,sK2) ),
inference(superposition,[],[f51,f35]) ).
fof(f131,plain,
( spl8_6
| spl8_7 ),
inference(avatar_split_clause,[],[f118,f129,f126]) ).
fof(f118,plain,
! [X8,X9] :
( ~ in(X8,sK1)
| ~ in(X9,sK0)
| in(X8,sK3) ),
inference(resolution,[],[f53,f76]) ).
fof(f76,plain,
! [X6,X7] :
( ~ in(ordered_pair(X6,X7),cartesian_product2(sK0,sK1))
| in(X7,sK3) ),
inference(superposition,[],[f52,f35]) ).
fof(f65,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f38,f63,f60]) ).
fof(f38,plain,
( sK1 != sK3
| sK0 != sK2 ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n014.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat Aug 26 13:40:32 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.HDnLT5N38I/Vampire---4.8_26521
% 0.16/0.37 % (26724)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43 % (26730)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)
% 0.23/0.43 % (26733)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)
% 0.23/0.43 % (26729)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)
% 0.23/0.43 % (26736)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)
% 0.23/0.43 % (26726)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)
% 0.23/0.43 % (26728)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)
% 0.23/0.43 % (26740)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)
% 0.23/0.45 % (26728)First to succeed.
% 0.23/0.45 % (26728)Refutation found. Thanks to Tanya!
% 0.23/0.45 % SZS status Theorem for Vampire---4
% 0.23/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.45 % (26728)------------------------------
% 0.23/0.45 % (26728)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.45 % (26728)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.45 % (26728)Termination reason: Refutation
% 0.23/0.45
% 0.23/0.45 % (26728)Memory used [KB]: 10106
% 0.23/0.45 % (26728)Time elapsed: 0.018 s
% 0.23/0.45 % (26728)------------------------------
% 0.23/0.45 % (26728)------------------------------
% 0.23/0.45 % (26724)Success in time 0.079 s
% 0.23/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------