TSTP Solution File: GRA010+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n019.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 : Sun May 5 05:43:20 EDT 2024
% Result : Theorem 0.57s 0.75s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 5 unt; 0 def)
% Number of atoms : 188 ( 19 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 216 ( 81 ~; 70 |; 43 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 122 ( 97 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f172,plain,
$false,
inference(avatar_sat_refutation,[],[f105,f110,f115,f119,f169,f171]) ).
fof(f171,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f170]) ).
fof(f170,plain,
( $false
| ~ spl8_1 ),
inference(resolution,[],[f100,f47]) ).
fof(f47,plain,
path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f35,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])],[f26,f34,f33]) ).
fof(f33,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(f34,plain,
! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
=> triangle(X3,X4,sK3(X3,X4)) ),
introduced(choice_axiom,[]) ).
fof(f26,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,[],[f25]) ).
fof(f25,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/sandbox/tmp/tmp.RxlYbE1btY/Vampire---4.8_32737',complete_means_sequential_pairs_and_triangles) ).
fof(f100,plain,
( ! [X0,X1] : ~ path(X0,X1,sK0)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f99,plain,
( spl8_1
<=> ! [X0,X1] : ~ path(X0,X1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f169,plain,
( ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f168,plain,
( $false
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(subsumption_resolution,[],[f167,f104]) ).
fof(f104,plain,
( on_path(sK5(sK0),sK0)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f102,plain,
( spl8_2
<=> on_path(sK5(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f167,plain,
( ~ on_path(sK5(sK0),sK0)
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(subsumption_resolution,[],[f166,f109]) ).
fof(f109,plain,
( on_path(sK6(sK0),sK0)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f107,plain,
( spl8_3
<=> on_path(sK6(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f166,plain,
( ~ on_path(sK6(sK0),sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ spl8_4
| ~ spl8_5 ),
inference(subsumption_resolution,[],[f161,f114]) ).
fof(f114,plain,
( sequential(sK5(sK0),sK6(sK0))
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f112,plain,
( spl8_4
<=> sequential(sK5(sK0),sK6(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f161,plain,
( ~ sequential(sK5(sK0),sK6(sK0))
| ~ on_path(sK6(sK0),sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ spl8_5 ),
inference(resolution,[],[f118,f48]) ).
fof(f48,plain,
! [X3,X4] :
( triangle(X3,X4,sK3(X3,X4))
| ~ sequential(X3,X4)
| ~ on_path(X4,sK0)
| ~ on_path(X3,sK0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f118,plain,
( ! [X0] : ~ triangle(sK5(sK0),sK6(sK0),X0)
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f117,plain,
( spl8_5
<=> ! [X0] : ~ triangle(sK5(sK0),sK6(sK0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f119,plain,
( spl8_1
| spl8_5 ),
inference(avatar_split_clause,[],[f95,f117,f99]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ triangle(sK5(sK0),sK6(sK0),X0)
| ~ path(X1,X2,sK0) ),
inference(resolution,[],[f77,f86]) ).
fof(f86,plain,
! [X2,X0,X1,X5] :
( sQ7_eqProxy(number_of_in(sequential_pairs,X0),number_of_in(triangles,X0))
| ~ triangle(sK5(X0),sK6(X0),X5)
| ~ path(X1,X2,X0) ),
inference(equality_proxy_replacement,[],[f64,f76]) ).
fof(f76,plain,
! [X0,X1] :
( sQ7_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ7_eqProxy])]) ).
fof(f64,plain,
! [X2,X0,X1,X5] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ triangle(sK5(X0),sK6(X0),X5)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ( ! [X5] : ~ triangle(sK5(X0),sK6(X0),X5)
& sequential(sK5(X0),sK6(X0))
& on_path(sK6(X0),X0)
& on_path(sK5(X0),X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f30,f42]) ).
fof(f42,plain,
! [X0] :
( ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ( ! [X5] : ~ triangle(sK5(X0),sK6(X0),X5)
& sequential(sK5(X0),sK6(X0))
& on_path(sK6(X0),X0)
& on_path(sK5(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f30,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,[],[f29]) ).
fof(f29,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,[],[f23]) ).
fof(f23,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/sandbox/tmp/tmp.RxlYbE1btY/Vampire---4.8_32737',sequential_pairs_and_triangles) ).
fof(f77,plain,
~ sQ7_eqProxy(number_of_in(sequential_pairs,sK0),number_of_in(triangles,sK0)),
inference(equality_proxy_replacement,[],[f49,f76]) ).
fof(f49,plain,
number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f115,plain,
( spl8_1
| spl8_4 ),
inference(avatar_split_clause,[],[f94,f112,f99]) ).
fof(f94,plain,
! [X0,X1] :
( sequential(sK5(sK0),sK6(sK0))
| ~ path(X0,X1,sK0) ),
inference(resolution,[],[f77,f87]) ).
fof(f87,plain,
! [X2,X0,X1] :
( sQ7_eqProxy(number_of_in(sequential_pairs,X0),number_of_in(triangles,X0))
| sequential(sK5(X0),sK6(X0))
| ~ path(X1,X2,X0) ),
inference(equality_proxy_replacement,[],[f63,f76]) ).
fof(f63,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| sequential(sK5(X0),sK6(X0))
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f110,plain,
( spl8_1
| spl8_3 ),
inference(avatar_split_clause,[],[f93,f107,f99]) ).
fof(f93,plain,
! [X0,X1] :
( on_path(sK6(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(resolution,[],[f77,f88]) ).
fof(f88,plain,
! [X2,X0,X1] :
( sQ7_eqProxy(number_of_in(sequential_pairs,X0),number_of_in(triangles,X0))
| on_path(sK6(X0),X0)
| ~ path(X1,X2,X0) ),
inference(equality_proxy_replacement,[],[f62,f76]) ).
fof(f62,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK6(X0),X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f105,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f92,f102,f99]) ).
fof(f92,plain,
! [X0,X1] :
( on_path(sK5(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(resolution,[],[f77,f89]) ).
fof(f89,plain,
! [X2,X0,X1] :
( sQ7_eqProxy(number_of_in(sequential_pairs,X0),number_of_in(triangles,X0))
| on_path(sK5(X0),X0)
| ~ path(X1,X2,X0) ),
inference(equality_proxy_replacement,[],[f61,f76]) ).
fof(f61,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK5(X0),X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n019.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 : Fri May 3 18:22:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.RxlYbE1btY/Vampire---4.8_32737
% 0.57/0.74 % (387)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.57/0.75 % (380)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.75 % (382)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.75 % (383)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.57/0.75 % (381)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.57/0.75 % (385)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.57/0.75 % (384)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.75 % (386)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.57/0.75 % (387)First to succeed.
% 0.57/0.75 % (387)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-379"
% 0.57/0.75 % (387)Refutation found. Thanks to Tanya!
% 0.57/0.75 % SZS status Theorem for Vampire---4
% 0.57/0.75 % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.75 % (387)------------------------------
% 0.57/0.75 % (387)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75 % (387)Termination reason: Refutation
% 0.57/0.75
% 0.57/0.75 % (387)Memory used [KB]: 1087
% 0.57/0.75 % (387)Time elapsed: 0.003 s
% 0.57/0.75 % (387)Instructions burned: 6 (million)
% 0.57/0.75 % (379)Success in time 0.383 s
% 0.57/0.75 % Vampire---4.8 exiting
%------------------------------------------------------------------------------