TSTP Solution File: GRA010+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---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 : n018.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 : Fri Sep 1 14:56:23 EDT 2023
% Result : Theorem 0.13s 0.35s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 162 ( 33 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 202 ( 74 ~; 69 |; 43 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 143 (; 118 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f337,plain,
$false,
inference(trivial_inequality_removal,[],[f335]) ).
fof(f335,plain,
number_of_in(sequential_pairs,sK5) != number_of_in(sequential_pairs,sK5),
inference(superposition,[],[f106,f333]) ).
fof(f333,plain,
number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5),
inference(resolution,[],[f328,f104]) ).
fof(f104,plain,
path(sK6,sK7,sK5),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( number_of_in(sequential_pairs,sK5) != number_of_in(triangles,sK5)
& ! [X3,X4] :
( triangle(X3,X4,sK8(X3,X4))
| ~ sequential(X3,X4)
| ~ on_path(X4,sK5)
| ~ on_path(X3,sK5) )
& path(sK6,sK7,sK5)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f37,f69,f68]) ).
fof(f68,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,sK5) != number_of_in(triangles,sK5)
& ! [X4,X3] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,sK5)
| ~ on_path(X3,sK5) )
& path(sK6,sK7,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
=> triangle(X3,X4,sK8(X3,X4)) ),
introduced(choice_axiom,[]) ).
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(flattening,[],[f36]) ).
fof(f36,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.eE3d6aH07R/Vampire---4.8_7378',complete_means_sequential_pairs_and_triangles) ).
fof(f328,plain,
! [X0,X1] :
( ~ path(X0,X1,sK5)
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
inference(resolution,[],[f319,f104]) ).
fof(f319,plain,
! [X2,X3,X0,X1] :
( ~ path(X2,X3,sK5)
| ~ path(X0,X1,sK5)
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
inference(resolution,[],[f305,f104]) ).
fof(f305,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ path(X4,X5,sK5)
| ~ path(X2,X3,sK5)
| ~ path(X0,X1,sK5)
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
inference(resolution,[],[f304,f104]) ).
fof(f304,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ path(X6,X7,sK5)
| ~ path(X4,X5,sK5)
| ~ path(X2,X3,sK5)
| ~ path(X0,X1,sK5)
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
inference(duplicate_literal_removal,[],[f303]) ).
fof(f303,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ path(X0,X1,sK5)
| ~ path(X2,X3,sK5)
| ~ path(X4,X5,sK5)
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ path(X6,X7,sK5) ),
inference(resolution,[],[f302,f148]) ).
fof(f148,plain,
! [X2,X0,X1] :
( sequential(sK13(X0),sK14(X0))
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ( ! [X5] : ~ triangle(sK13(X0),sK14(X0),X5)
& sequential(sK13(X0),sK14(X0))
& on_path(sK14(X0),X0)
& on_path(sK13(X0),X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f51,f91]) ).
fof(f91,plain,
! [X0] :
( ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ( ! [X5] : ~ triangle(sK13(X0),sK14(X0),X5)
& sequential(sK13(X0),sK14(X0))
& on_path(sK14(X0),X0)
& on_path(sK13(X0),X0) ) ),
introduced(choice_axiom,[]) ).
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(flattening,[],[f50]) ).
fof(f50,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.eE3d6aH07R/Vampire---4.8_7378',sequential_pairs_and_triangles) ).
fof(f302,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sequential(sK13(sK5),sK14(sK5))
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ path(X0,X1,sK5)
| ~ path(X2,X3,sK5)
| ~ path(X4,X5,sK5) ),
inference(duplicate_literal_removal,[],[f301]) ).
fof(f301,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sequential(sK13(sK5),sK14(sK5))
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ path(X0,X1,sK5)
| ~ path(X2,X3,sK5)
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ path(X4,X5,sK5) ),
inference(resolution,[],[f300,f146]) ).
fof(f146,plain,
! [X2,X0,X1] :
( on_path(sK13(X0),X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f300,plain,
! [X2,X3,X0,X1] :
( ~ on_path(sK13(sK5),sK5)
| ~ sequential(sK13(sK5),sK14(sK5))
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ path(X0,X1,sK5)
| ~ path(X2,X3,sK5) ),
inference(duplicate_literal_removal,[],[f299]) ).
fof(f299,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,sK5)
| ~ sequential(sK13(sK5),sK14(sK5))
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ on_path(sK13(sK5),sK5)
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ path(X2,X3,sK5) ),
inference(resolution,[],[f298,f147]) ).
fof(f147,plain,
! [X2,X0,X1] :
( on_path(sK14(X0),X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ on_path(sK14(X0),sK5)
| ~ path(X1,X2,X0)
| ~ sequential(sK13(X0),sK14(X0))
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ on_path(sK13(X0),sK5) ),
inference(resolution,[],[f149,f105]) ).
fof(f105,plain,
! [X3,X4] :
( triangle(X3,X4,sK8(X3,X4))
| ~ sequential(X3,X4)
| ~ on_path(X4,sK5)
| ~ on_path(X3,sK5) ),
inference(cnf_transformation,[],[f70]) ).
fof(f149,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK13(X0),sK14(X0),X5)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f106,plain,
number_of_in(sequential_pairs,sK5) != number_of_in(triangles,sK5),
inference(cnf_transformation,[],[f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.04/0.10 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.08/0.29 % Computer : n018.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Wed Aug 30 16:16:49 EDT 2023
% 0.08/0.29 % CPUTime :
% 0.13/0.33 % (8626)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.33 % (8737)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)
% 0.13/0.33 % (8734)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.13/0.33 % (8732)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.13/0.33 % (8731)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.13/0.33 % (8736)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)
% 0.13/0.33 % (8733)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)
% 0.13/0.33 % (8735)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)
% 0.13/0.34 TRYING [1]
% 0.13/0.34 TRYING [1]
% 0.13/0.34 TRYING [2]
% 0.13/0.34 TRYING [2]
% 0.13/0.34 TRYING [3]
% 0.13/0.34 % (8736)First to succeed.
% 0.13/0.34 TRYING [3]
% 0.13/0.35 % (8736)Refutation found. Thanks to Tanya!
% 0.13/0.35 % SZS status Theorem for Vampire---4
% 0.13/0.35 % SZS output start Proof for Vampire---4
% See solution above
% 0.13/0.35 % (8736)------------------------------
% 0.13/0.35 % (8736)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.13/0.35 % (8736)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.13/0.35 % (8736)Termination reason: Refutation
% 0.13/0.35
% 0.13/0.35 % (8736)Memory used [KB]: 1279
% 0.13/0.35 % (8736)Time elapsed: 0.014 s
% 0.13/0.35 % (8736)------------------------------
% 0.13/0.35 % (8736)------------------------------
% 0.13/0.35 % (8626)Success in time 0.049 s
% 0.13/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------