TSTP Solution File: GRA010+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 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 : n008.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 00:05:24 EDT 2023
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 10 unt; 0 def)
% Number of atoms : 183 ( 33 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 193 ( 65 ~; 66 |; 43 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 116 (; 91 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f315,plain,
$false,
inference(avatar_sat_refutation,[],[f285,f299,f304,f314]) ).
fof(f314,plain,
~ spl14_7,
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f313,plain,
( $false
| ~ spl14_7 ),
inference(resolution,[],[f311,f90]) ).
fof(f90,plain,
path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
( number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0)
& ! [X3,X4] :
( triangle(X3,X4,sK3(X3,X4))
| ~ sequential(X3,X4)
| ~ on_path(X4,sK0)
| ~ on_path(X3,sK0) )
& path(sK1,sK2,sK0)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f38,f62,f61]) ).
fof(f61,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
& path(X1,X2,X0) )
=> ( number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0)
& ! [X4,X3] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,sK0)
| ~ on_path(X3,sK0) )
& path(sK1,sK2,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
=> triangle(X3,X4,sK3(X3,X4)) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
& path(X1,X2,X0) )
& complete ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
& path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
~ ( complete
=> ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
( complete
=> ! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pykSKtfX0q/Vampire---4.8_26528',complete_means_sequential_pairs_and_triangles) ).
fof(f311,plain,
( ! [X0,X1] : ~ path(X0,X1,sK0)
| ~ spl14_7 ),
inference(subsumption_resolution,[],[f310,f157]) ).
fof(f157,plain,
sF12 != sF13,
inference(definition_folding,[],[f92,f156,f155]) ).
fof(f155,plain,
number_of_in(sequential_pairs,sK0) = sF12,
introduced(function_definition,[]) ).
fof(f156,plain,
number_of_in(triangles,sK0) = sF13,
introduced(function_definition,[]) ).
fof(f92,plain,
number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0),
inference(cnf_transformation,[],[f63]) ).
fof(f310,plain,
( ! [X0,X1] :
( sF12 = sF13
| ~ path(X0,X1,sK0) )
| ~ spl14_7 ),
inference(forward_demodulation,[],[f309,f155]) ).
fof(f309,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK0) = sF13
| ~ path(X0,X1,sK0) )
| ~ spl14_7 ),
inference(forward_demodulation,[],[f305,f156]) ).
fof(f305,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK0) = number_of_in(triangles,sK0)
| ~ path(X0,X1,sK0) )
| ~ spl14_7 ),
inference(resolution,[],[f284,f131]) ).
fof(f131,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK8(X0),sK9(X0),X5)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ( ! [X5] : ~ triangle(sK8(X0),sK9(X0),X5)
& sequential(sK8(X0),sK9(X0))
& on_path(sK9(X0),X0)
& on_path(sK8(X0),X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f52,f81]) ).
fof(f81,plain,
! [X0] :
( ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ( ! [X5] : ~ triangle(sK8(X0),sK9(X0),X5)
& sequential(sK8(X0),sK9(X0))
& on_path(sK9(X0),X0)
& on_path(sK8(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.pykSKtfX0q/Vampire---4.8_26528',sequential_pairs_and_triangles) ).
fof(f284,plain,
( triangle(sK8(sK0),sK9(sK0),sK3(sK8(sK0),sK9(sK0)))
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f282,plain,
( spl14_7
<=> triangle(sK8(sK0),sK9(sK0),sK3(sK8(sK0),sK9(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_7])]) ).
fof(f304,plain,
spl14_6,
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f303,plain,
( $false
| spl14_6 ),
inference(resolution,[],[f297,f90]) ).
fof(f297,plain,
( ! [X0,X1] : ~ path(X0,X1,sK0)
| spl14_6 ),
inference(subsumption_resolution,[],[f296,f157]) ).
fof(f296,plain,
( ! [X0,X1] :
( sF12 = sF13
| ~ path(X0,X1,sK0) )
| spl14_6 ),
inference(forward_demodulation,[],[f295,f155]) ).
fof(f295,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK0) = sF13
| ~ path(X0,X1,sK0) )
| spl14_6 ),
inference(forward_demodulation,[],[f292,f156]) ).
fof(f292,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK0) = number_of_in(triangles,sK0)
| ~ path(X0,X1,sK0) )
| spl14_6 ),
inference(resolution,[],[f280,f129]) ).
fof(f129,plain,
! [X2,X0,X1] :
( on_path(sK9(X0),X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f280,plain,
( ~ on_path(sK9(sK0),sK0)
| spl14_6 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f278,plain,
( spl14_6
<=> on_path(sK9(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_6])]) ).
fof(f299,plain,
spl14_5,
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f298,plain,
( $false
| spl14_5 ),
inference(resolution,[],[f291,f90]) ).
fof(f291,plain,
( ! [X0,X1] : ~ path(X0,X1,sK0)
| spl14_5 ),
inference(subsumption_resolution,[],[f290,f157]) ).
fof(f290,plain,
( ! [X0,X1] :
( sF12 = sF13
| ~ path(X0,X1,sK0) )
| spl14_5 ),
inference(forward_demodulation,[],[f289,f155]) ).
fof(f289,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK0) = sF13
| ~ path(X0,X1,sK0) )
| spl14_5 ),
inference(forward_demodulation,[],[f286,f156]) ).
fof(f286,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK0) = number_of_in(triangles,sK0)
| ~ path(X0,X1,sK0) )
| spl14_5 ),
inference(resolution,[],[f276,f128]) ).
fof(f128,plain,
! [X2,X0,X1] :
( on_path(sK8(X0),X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f276,plain,
( ~ on_path(sK8(sK0),sK0)
| spl14_5 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f274,plain,
( spl14_5
<=> on_path(sK8(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_5])]) ).
fof(f285,plain,
( ~ spl14_5
| ~ spl14_6
| spl14_7 ),
inference(avatar_split_clause,[],[f197,f282,f278,f274]) ).
fof(f197,plain,
( triangle(sK8(sK0),sK9(sK0),sK3(sK8(sK0),sK9(sK0)))
| ~ on_path(sK9(sK0),sK0)
| ~ on_path(sK8(sK0),sK0) ),
inference(resolution,[],[f196,f91]) ).
fof(f91,plain,
! [X3,X4] :
( ~ sequential(X3,X4)
| triangle(X3,X4,sK3(X3,X4))
| ~ on_path(X4,sK0)
| ~ on_path(X3,sK0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f196,plain,
sequential(sK8(sK0),sK9(sK0)),
inference(subsumption_resolution,[],[f195,f157]) ).
fof(f195,plain,
( sF12 = sF13
| sequential(sK8(sK0),sK9(sK0)) ),
inference(forward_demodulation,[],[f194,f155]) ).
fof(f194,plain,
( number_of_in(sequential_pairs,sK0) = sF13
| sequential(sK8(sK0),sK9(sK0)) ),
inference(forward_demodulation,[],[f193,f156]) ).
fof(f193,plain,
( sequential(sK8(sK0),sK9(sK0))
| number_of_in(sequential_pairs,sK0) = number_of_in(triangles,sK0) ),
inference(resolution,[],[f130,f90]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| sequential(sK8(X0),sK9(X0))
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 03:18:47 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.pykSKtfX0q/Vampire---4.8_26528
% 0.22/0.36 % (26647)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (26652)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.22/0.42 % (26653)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.42 % (26648)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_730 on Vampire---4 for (730ds/0Mi)
% 0.22/0.42 % (26649)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.22/0.43 % (26654)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_386 on Vampire---4 for (386ds/0Mi)
% 0.22/0.43 % (26653)First to succeed.
% 0.22/0.43 % (26650)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.22/0.43 % (26653)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for Vampire---4
% 0.22/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.43 % (26653)------------------------------
% 0.22/0.43 % (26653)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (26653)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (26653)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (26653)Memory used [KB]: 5628
% 0.22/0.43 % (26653)Time elapsed: 0.012 s
% 0.22/0.43 % (26653)------------------------------
% 0.22/0.43 % (26653)------------------------------
% 0.22/0.43 % (26647)Success in time 0.073 s
% 0.22/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------