TSTP Solution File: GRA002+4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.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 05:43:56 EDT 2024
% Result : Theorem 0.12s 0.36s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 11 unt; 0 def)
% Number of atoms : 130 ( 25 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 138 ( 49 ~; 35 |; 33 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 105 ( 95 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f216,plain,
$false,
inference(resolution,[],[f215,f203]) ).
fof(f203,plain,
less_or_equal(number_of_in(sequential_pairs,sK5),number_of_in(triangles,graph)),
inference(superposition,[],[f119,f201]) ).
fof(f201,plain,
number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5),
inference(resolution,[],[f195,f106]) ).
fof(f106,plain,
shortest_path(sK6,sK7,sK5),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ~ less_or_equal(minus(length_of(sK5),n1),number_of_in(triangles,graph))
& shortest_path(sK6,sK7,sK5)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f39,f73]) ).
fof(f73,plain,
( ? [X0,X1,X2] :
( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
& shortest_path(X1,X2,X0) )
=> ( ~ less_or_equal(minus(length_of(sK5),n1),number_of_in(triangles,graph))
& shortest_path(sK6,sK7,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
( ? [X0,X1,X2] :
( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
& shortest_path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
inference(resolution,[],[f108,f105]) ).
fof(f105,plain,
complete,
inference(cnf_transformation,[],[f74]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ complete
| ~ shortest_path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0) )
| ~ complete ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
fof(f119,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X10,X11] : less_or_equal(number_of_in(X10,X11),number_of_in(X10,graph)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f215,plain,
~ less_or_equal(number_of_in(sequential_pairs,sK5),number_of_in(triangles,graph)),
inference(backward_demodulation,[],[f107,f213]) ).
fof(f213,plain,
minus(length_of(sK5),n1) = number_of_in(sequential_pairs,sK5),
inference(resolution,[],[f211,f106]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ shortest_path(X1,X2,X0)
| minus(length_of(X0),n1) = number_of_in(sequential_pairs,X0) ),
inference(resolution,[],[f206,f158]) ).
fof(f158,plain,
! [X2,X0,X1] :
( sP4(X2,X1,X0)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ sP4(X2,X1,X0) )
& ( sP4(X2,X1,X0)
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> sP4(X2,X1,X0) ),
inference(definition_folding,[],[f57,f71]) ).
fof(f71,plain,
! [X2,X1,X0] :
( sP4(X2,X1,X0)
<=> ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f57,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X2,X9] :
( shortest_path(X1,X2,X9)
<=> ( ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) )
& X1 != X2
& path(X1,X2,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| minus(length_of(X0),n1) = number_of_in(sequential_pairs,X0) ),
inference(resolution,[],[f126,f153]) ).
fof(f153,plain,
! [X2,X0,X1] :
( path(X2,X1,X0)
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ( ~ less_or_equal(length_of(X0),length_of(sK14(X0,X1,X2)))
& path(X2,X1,sK14(X0,X1,X2)) )
| X1 = X2
| ~ path(X2,X1,X0) )
& ( ( ! [X4] :
( less_or_equal(length_of(X0),length_of(X4))
| ~ path(X2,X1,X4) )
& X1 != X2
& path(X2,X1,X0) )
| ~ sP4(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f99,f100]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ less_or_equal(length_of(X0),length_of(X3))
& path(X2,X1,X3) )
=> ( ~ less_or_equal(length_of(X0),length_of(sK14(X0,X1,X2)))
& path(X2,X1,sK14(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X0),length_of(X3))
& path(X2,X1,X3) )
| X1 = X2
| ~ path(X2,X1,X0) )
& ( ( ! [X4] :
( less_or_equal(length_of(X0),length_of(X4))
| ~ path(X2,X1,X4) )
& X1 != X2
& path(X2,X1,X0) )
| ~ sP4(X0,X1,X2) ) ),
inference(rectify,[],[f98]) ).
fof(f98,plain,
! [X2,X1,X0] :
( ( sP4(X2,X1,X0)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ sP4(X2,X1,X0) ) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X2,X1,X0] :
( ( sP4(X2,X1,X0)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ sP4(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X1,X2,X3] :
( path(X1,X2,X3)
=> number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(f107,plain,
~ less_or_equal(minus(length_of(sK5),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri May 3 18:25:38 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (1811)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (1818)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 theBenchmark for (497ds/0Mi)
% 0.12/0.35 % (1816)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 theBenchmark for (531ds/0Mi)
% 0.12/0.35 % (1817)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 theBenchmark for (522ds/0Mi)
% 0.12/0.35 % (1814)WARNING: value z3 for option sas not known
% 0.12/0.35 % (1815)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (1813)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35 % (1812)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % (1814)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 theBenchmark for (569ds/0Mi)
% 0.12/0.35 % (1817)First to succeed.
% 0.12/0.36 % (1817)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1811"
% 0.12/0.36 % (1817)Refutation found. Thanks to Tanya!
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36 % (1817)------------------------------
% 0.12/0.36 % (1817)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.36 % (1817)Termination reason: Refutation
% 0.12/0.36
% 0.12/0.36 % (1817)Memory used [KB]: 946
% 0.12/0.36 % (1817)Time elapsed: 0.007 s
% 0.12/0.36 % (1817)Instructions burned: 11 (million)
% 0.12/0.36 % (1811)Success in time 0.022 s
%------------------------------------------------------------------------------