TSTP Solution File: GRA010+2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -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 : Wed Aug 31 16:13:32 EDT 2022
% Result : Theorem 1.25s 0.52s
% Output : Refutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 11 unt; 0 def)
% Number of atoms : 170 ( 35 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 187 ( 64 ~; 57 |; 49 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 124 ( 93 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f700,plain,
$false,
inference(avatar_sat_refutation,[],[f552,f699]) ).
fof(f699,plain,
spl15_16,
inference(avatar_split_clause,[],[f698,f520]) ).
fof(f520,plain,
( spl15_16
<=> ! [X2,X3] : ~ path(X2,X3,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).
fof(f698,plain,
! [X0,X1] : ~ path(X0,X1,sK6),
inference(subsumption_resolution,[],[f697,f176]) ).
fof(f176,plain,
sF13 != sF14,
inference(definition_folding,[],[f146,f175,f174]) ).
fof(f174,plain,
number_of_in(sequential_pairs,sK6) = sF13,
introduced(function_definition,[]) ).
fof(f175,plain,
number_of_in(triangles,sK6) = sF14,
introduced(function_definition,[]) ).
fof(f146,plain,
number_of_in(sequential_pairs,sK6) != number_of_in(triangles,sK6),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( complete
& ! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,sK6)
| ~ on_path(X3,sK6)
| triangle(X3,X4,sK9(X3,X4)) )
& number_of_in(sequential_pairs,sK6) != number_of_in(triangles,sK6)
& path(sK7,sK8,sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f90,f92,f91]) ).
fof(f91,plain,
( ? [X0,X1,X2] :
( ! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| ? [X5] : triangle(X3,X4,X5) )
& number_of_in(triangles,X0) != number_of_in(sequential_pairs,X0)
& path(X1,X2,X0) )
=> ( ! [X4,X3] :
( ~ sequential(X3,X4)
| ~ on_path(X4,sK6)
| ~ on_path(X3,sK6)
| ? [X5] : triangle(X3,X4,X5) )
& number_of_in(sequential_pairs,sK6) != number_of_in(triangles,sK6)
& path(sK7,sK8,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
=> triangle(X3,X4,sK9(X3,X4)) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
( complete
& ? [X0,X1,X2] :
( ! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| ? [X5] : triangle(X3,X4,X5) )
& number_of_in(triangles,X0) != number_of_in(sequential_pairs,X0)
& path(X1,X2,X0) ) ),
inference(rectify,[],[f60]) ).
fof(f60,plain,
( complete
& ? [X2,X1,X0] :
( ! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| ? [X5] : triangle(X3,X4,X5) )
& number_of_in(triangles,X2) != number_of_in(sequential_pairs,X2)
& path(X1,X0,X2) ) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
( ? [X1,X0,X2] :
( number_of_in(triangles,X2) != number_of_in(sequential_pairs,X2)
& path(X1,X0,X2)
& ! [X4,X3] :
( ? [X5] : triangle(X3,X4,X5)
| ~ on_path(X3,X2)
| ~ on_path(X4,X2)
| ~ sequential(X3,X4) ) )
& complete ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
~ ( complete
=> ! [X1,X0,X2] :
( ( path(X1,X0,X2)
& ! [X4,X3] :
( ( on_path(X3,X2)
& on_path(X4,X2)
& sequential(X3,X4) )
=> ? [X5] : triangle(X3,X4,X5) ) )
=> number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X2,X1,X3] :
( ( path(X1,X2,X3)
& ! [X6,X7] :
( ( on_path(X7,X3)
& sequential(X6,X7)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
( complete
=> ! [X2,X1,X3] :
( ( path(X1,X2,X3)
& ! [X6,X7] :
( ( on_path(X7,X3)
& sequential(X6,X7)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(f697,plain,
! [X0,X1] :
( ~ path(X0,X1,sK6)
| sF13 = sF14 ),
inference(forward_demodulation,[],[f696,f174]) ).
fof(f696,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK6) = sF14
| ~ path(X0,X1,sK6) ),
inference(forward_demodulation,[],[f695,f175]) ).
fof(f695,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK6) = number_of_in(triangles,sK6)
| ~ path(X0,X1,sK6) ),
inference(subsumption_resolution,[],[f694,f296]) ).
fof(f296,plain,
on_path(sK0(sK6),sK6),
inference(subsumption_resolution,[],[f295,f176]) ).
fof(f295,plain,
( on_path(sK0(sK6),sK6)
| sF13 = sF14 ),
inference(forward_demodulation,[],[f294,f174]) ).
fof(f294,plain,
( on_path(sK0(sK6),sK6)
| number_of_in(sequential_pairs,sK6) = sF14 ),
inference(forward_demodulation,[],[f290,f175]) ).
fof(f290,plain,
( number_of_in(sequential_pairs,sK6) = number_of_in(triangles,sK6)
| on_path(sK0(sK6),sK6) ),
inference(resolution,[],[f109,f145]) ).
fof(f145,plain,
path(sK7,sK8,sK6),
inference(cnf_transformation,[],[f93]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ path(X1,X0,X2)
| number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2)
| on_path(sK0(X2),X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( sequential(sK1(X2),sK0(X2))
& on_path(sK0(X2),X2)
& ! [X5] : ~ triangle(sK1(X2),sK0(X2),X5)
& on_path(sK1(X2),X2) )
| ~ path(X1,X0,X2)
| number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f65,f66]) ).
fof(f66,plain,
! [X2] :
( ? [X3,X4] :
( sequential(X4,X3)
& on_path(X3,X2)
& ! [X5] : ~ triangle(X4,X3,X5)
& on_path(X4,X2) )
=> ( sequential(sK1(X2),sK0(X2))
& on_path(sK0(X2),X2)
& ! [X5] : ~ triangle(sK1(X2),sK0(X2),X5)
& on_path(sK1(X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( sequential(X4,X3)
& on_path(X3,X2)
& ! [X5] : ~ triangle(X4,X3,X5)
& on_path(X4,X2) )
| ~ path(X1,X0,X2)
| number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ? [X4,X3] :
( sequential(X3,X4)
& on_path(X4,X1)
& ! [X5] : ~ triangle(X3,X4,X5)
& on_path(X3,X1) )
| ~ path(X0,X2,X1)
| number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0,X2,X1] :
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& on_path(X3,X1)
& sequential(X3,X4)
& on_path(X4,X1) )
| ~ path(X0,X2,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X2,X1] :
( ( ! [X3,X4] :
( ( on_path(X3,X1)
& sequential(X3,X4)
& on_path(X4,X1) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X0,X2,X1) )
=> number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X1,X3,X2] :
( ( path(X1,X2,X3)
& ! [X6,X7] :
( ( on_path(X6,X3)
& on_path(X7,X3)
& sequential(X6,X7) )
=> ? [X8] : triangle(X6,X7,X8) ) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f694,plain,
! [X0,X1] :
( ~ path(X0,X1,sK6)
| number_of_in(sequential_pairs,sK6) = number_of_in(triangles,sK6)
| ~ on_path(sK0(sK6),sK6) ),
inference(resolution,[],[f310,f285]) ).
fof(f285,plain,
on_path(sK1(sK6),sK6),
inference(subsumption_resolution,[],[f284,f176]) ).
fof(f284,plain,
( sF13 = sF14
| on_path(sK1(sK6),sK6) ),
inference(forward_demodulation,[],[f283,f174]) ).
fof(f283,plain,
( on_path(sK1(sK6),sK6)
| number_of_in(sequential_pairs,sK6) = sF14 ),
inference(forward_demodulation,[],[f280,f175]) ).
fof(f280,plain,
( on_path(sK1(sK6),sK6)
| number_of_in(sequential_pairs,sK6) = number_of_in(triangles,sK6) ),
inference(resolution,[],[f107,f145]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ path(X1,X0,X2)
| on_path(sK1(X2),X2)
| number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f310,plain,
! [X6,X4,X5] :
( ~ on_path(sK1(X4),sK6)
| ~ path(X5,X6,X4)
| number_of_in(triangles,X4) = number_of_in(sequential_pairs,X4)
| ~ on_path(sK0(X4),sK6) ),
inference(subsumption_resolution,[],[f309,f110]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ path(X1,X0,X2)
| number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2)
| sequential(sK1(X2),sK0(X2)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f309,plain,
! [X6,X4,X5] :
( ~ on_path(sK0(X4),sK6)
| number_of_in(triangles,X4) = number_of_in(sequential_pairs,X4)
| ~ path(X5,X6,X4)
| ~ sequential(sK1(X4),sK0(X4))
| ~ on_path(sK1(X4),sK6) ),
inference(resolution,[],[f108,f147]) ).
fof(f147,plain,
! [X3,X4] :
( triangle(X3,X4,sK9(X3,X4))
| ~ on_path(X4,sK6)
| ~ sequential(X3,X4)
| ~ on_path(X3,sK6) ),
inference(cnf_transformation,[],[f93]) ).
fof(f108,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK1(X2),sK0(X2),X5)
| number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2)
| ~ path(X1,X0,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f552,plain,
~ spl15_16,
inference(avatar_contradiction_clause,[],[f551]) ).
fof(f551,plain,
( $false
| ~ spl15_16 ),
inference(resolution,[],[f521,f145]) ).
fof(f521,plain,
( ! [X2,X3] : ~ path(X2,X3,sK6)
| ~ spl15_16 ),
inference(avatar_component_clause,[],[f520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 22:01:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48 % (26440)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.48 % (26433)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.51 % (26425)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (26440)First to succeed.
% 0.20/0.51 % (26441)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.51 % (26442)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.51 % (26430)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52 % (26424)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (26426)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.25/0.52 % (26440)Refutation found. Thanks to Tanya!
% 1.25/0.52 % SZS status Theorem for theBenchmark
% 1.25/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.25/0.52 % (26440)------------------------------
% 1.25/0.52 % (26440)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.52 % (26440)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.52 % (26440)Termination reason: Refutation
% 1.25/0.52
% 1.25/0.52 % (26440)Memory used [KB]: 6140
% 1.25/0.52 % (26440)Time elapsed: 0.091 s
% 1.25/0.52 % (26440)Instructions burned: 36 (million)
% 1.25/0.52 % (26440)------------------------------
% 1.25/0.52 % (26440)------------------------------
% 1.25/0.52 % (26420)Success in time 0.163 s
%------------------------------------------------------------------------------