TSTP Solution File: GRA008+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRA008+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.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 : Mon May 20 20:43:13 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 46
% Syntax : Number of formulae : 250 ( 27 unt; 0 def)
% Number of atoms : 829 ( 149 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 893 ( 314 ~; 314 |; 189 &)
% ( 34 <=>; 34 =>; 0 <=; 8 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 42 ( 40 usr; 27 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 421 ( 367 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f801,plain,
$false,
inference(avatar_sat_refutation,[],[f218,f225,f227,f253,f264,f268,f275,f318,f321,f355,f365,f503,f560,f570,f627,f687,f690,f738,f740,f742,f746,f786,f788,f790,f793]) ).
fof(f793,plain,
~ spl19_11,
inference(avatar_contradiction_clause,[],[f792]) ).
fof(f792,plain,
( $false
| ~ spl19_11 ),
inference(subsumption_resolution,[],[f791,f197]) ).
fof(f197,plain,
head_of(sK7) != head_of(sK8),
inference(subsumption_resolution,[],[f195,f193]) ).
fof(f193,plain,
edge(sK8),
inference(resolution,[],[f129,f112]) ).
fof(f112,plain,
sequential(sK7,sK8),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( ! [X5] : ~ triangle(sK7,sK8,X5)
& sequential(sK7,sK8)
& precedes(sK7,sK8,sK9)
& shortest_path(sK5,sK6,sK9)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f40,f75]) ).
fof(f75,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ! [X5] : ~ triangle(sK7,sK8,X5)
& sequential(sK7,sK8)
& precedes(sK7,sK8,sK9)
& shortest_path(sK5,sK6,sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
& complete ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
& complete ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X1,X2,X6,X7,X3] :
( ( sequential(X6,X7)
& precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
( complete
=> ! [X1,X2,X6,X7,X3] :
( ( sequential(X6,X7)
& precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(f129,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X6,X7] :
( sequential(X6,X7)
<=> ( head_of(X6) = tail_of(X7)
& X6 != X7
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).
fof(f195,plain,
( head_of(sK7) != head_of(sK8)
| ~ edge(sK8) ),
inference(superposition,[],[f124,f194]) ).
fof(f194,plain,
head_of(sK7) = tail_of(sK8),
inference(resolution,[],[f131,f112]) ).
fof(f131,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f124,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
fof(f791,plain,
( head_of(sK7) = head_of(sK8)
| ~ spl19_11 ),
inference(forward_demodulation,[],[f759,f194]) ).
fof(f759,plain,
( tail_of(sK8) = head_of(sK8)
| ~ spl19_11 ),
inference(superposition,[],[f324,f346]) ).
fof(f346,plain,
( sK8 = sK10(sK7,sK8)
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f344,plain,
( spl19_11
<=> sK8 = sK10(sK7,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_11])]) ).
fof(f324,plain,
head_of(sK8) = tail_of(sK10(sK7,sK8)),
inference(resolution,[],[f323,f111]) ).
fof(f111,plain,
precedes(sK7,sK8,sK9),
inference(cnf_transformation,[],[f76]) ).
fof(f323,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK9)
| head_of(X1) = tail_of(sK10(X0,X1)) ),
inference(resolution,[],[f188,f110]) ).
fof(f110,plain,
shortest_path(sK5,sK6,sK9),
inference(cnf_transformation,[],[f76]) ).
fof(f188,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| head_of(X3) = tail_of(sK10(X2,X3)) ),
inference(global_subsumption,[],[f113,f112,f111,f110,f109,f116,f187,f115]) ).
fof(f115,plain,
! [X2,X3,X0,X1,X4] :
( head_of(X3) = tail_of(sK10(X2,X3))
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ complete ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
( ! [X0,X1,X2,X3,X4] :
( ( tail_of(X2) = head_of(sK10(X2,X3))
& head_of(X3) = tail_of(sK10(X2,X3))
& edge(sK10(X2,X3)) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) )
| ~ complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f42,f77]) ).
fof(f77,plain,
! [X2,X3] :
( ? [X5] :
( tail_of(X2) = head_of(X5)
& tail_of(X5) = head_of(X3)
& edge(X5) )
=> ( tail_of(X2) = head_of(sK10(X2,X3))
& head_of(X3) = tail_of(sK10(X2,X3))
& edge(sK10(X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] :
( tail_of(X2) = head_of(X5)
& tail_of(X5) = head_of(X3)
& edge(X5) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) )
| ~ complete ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] :
( tail_of(X2) = head_of(X5)
& tail_of(X5) = head_of(X3)
& edge(X5) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) )
| ~ complete ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] :
( tail_of(X2) = head_of(X5)
& tail_of(X5) = head_of(X3)
& edge(X5) ) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
( complete
=> ! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] :
( tail_of(X6) = head_of(X8)
& tail_of(X8) = head_of(X7)
& edge(X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
fof(f187,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| tail_of(X2) = head_of(sK10(X2,X3)) ),
inference(global_subsumption,[],[f113,f112,f111,f110,f109,f116]) ).
fof(f116,plain,
! [X2,X3,X0,X1,X4] :
( tail_of(X2) = head_of(sK10(X2,X3))
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ complete ),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
complete,
inference(cnf_transformation,[],[f76]) ).
fof(f113,plain,
! [X5] : ~ triangle(sK7,sK8,X5),
inference(cnf_transformation,[],[f76]) ).
fof(f790,plain,
( ~ spl19_3
| spl19_9
| ~ spl19_11 ),
inference(avatar_contradiction_clause,[],[f789]) ).
fof(f789,plain,
( $false
| ~ spl19_3
| spl19_9
| ~ spl19_11 ),
inference(subsumption_resolution,[],[f758,f224]) ).
fof(f224,plain,
( on_path(sK8,sK9)
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f222,plain,
( spl19_3
<=> on_path(sK8,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_3])]) ).
fof(f758,plain,
( ~ on_path(sK8,sK9)
| spl19_9
| ~ spl19_11 ),
inference(superposition,[],[f313,f346]) ).
fof(f313,plain,
( ~ on_path(sK10(sK7,sK8),sK9)
| spl19_9 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f311,plain,
( spl19_9
<=> on_path(sK10(sK7,sK8),sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_9])]) ).
fof(f788,plain,
~ spl19_11,
inference(avatar_contradiction_clause,[],[f787]) ).
fof(f787,plain,
( $false
| ~ spl19_11 ),
inference(subsumption_resolution,[],[f757,f330]) ).
fof(f330,plain,
tail_of(sK7) != head_of(sK8),
inference(superposition,[],[f329,f306]) ).
fof(f306,plain,
tail_of(sK7) = head_of(sK10(sK7,sK8)),
inference(resolution,[],[f305,f111]) ).
fof(f305,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK9)
| tail_of(X0) = head_of(sK10(X0,X1)) ),
inference(resolution,[],[f187,f110]) ).
fof(f329,plain,
head_of(sK10(sK7,sK8)) != head_of(sK8),
inference(subsumption_resolution,[],[f327,f255]) ).
fof(f255,plain,
edge(sK10(sK7,sK8)),
inference(resolution,[],[f254,f111]) ).
fof(f254,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK9)
| edge(sK10(X0,X1)) ),
inference(resolution,[],[f189,f110]) ).
fof(f189,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| edge(sK10(X2,X3)) ),
inference(global_subsumption,[],[f113,f112,f111,f110,f109,f116,f187,f115,f188,f114]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X4] :
( edge(sK10(X2,X3))
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ complete ),
inference(cnf_transformation,[],[f78]) ).
fof(f327,plain,
( head_of(sK10(sK7,sK8)) != head_of(sK8)
| ~ edge(sK10(sK7,sK8)) ),
inference(superposition,[],[f124,f324]) ).
fof(f757,plain,
( tail_of(sK7) = head_of(sK8)
| ~ spl19_11 ),
inference(superposition,[],[f306,f346]) ).
fof(f786,plain,
~ spl19_11,
inference(avatar_contradiction_clause,[],[f785]) ).
fof(f785,plain,
( $false
| ~ spl19_11 ),
inference(trivial_inequality_removal,[],[f760]) ).
fof(f760,plain,
( head_of(sK8) != head_of(sK8)
| ~ spl19_11 ),
inference(superposition,[],[f329,f346]) ).
fof(f746,plain,
( spl19_11
| spl19_12 ),
inference(avatar_contradiction_clause,[],[f745]) ).
fof(f745,plain,
( $false
| spl19_11
| spl19_12 ),
inference(subsumption_resolution,[],[f714,f112]) ).
fof(f714,plain,
( ~ sequential(sK7,sK8)
| spl19_11
| spl19_12 ),
inference(superposition,[],[f349,f705]) ).
fof(f705,plain,
( sK7 = sK10(sK7,sK8)
| spl19_11 ),
inference(subsumption_resolution,[],[f704,f192]) ).
fof(f192,plain,
edge(sK7),
inference(resolution,[],[f128,f112]) ).
fof(f128,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f704,plain,
( sK7 = sK10(sK7,sK8)
| ~ edge(sK7)
| spl19_11 ),
inference(trivial_inequality_removal,[],[f703]) ).
fof(f703,plain,
( tail_of(sK7) != tail_of(sK7)
| sK7 = sK10(sK7,sK8)
| ~ edge(sK7)
| spl19_11 ),
inference(resolution,[],[f701,f336]) ).
fof(f336,plain,
! [X0] :
( sequential(sK10(sK7,sK8),X0)
| tail_of(X0) != tail_of(sK7)
| sK10(sK7,sK8) = X0
| ~ edge(X0) ),
inference(subsumption_resolution,[],[f332,f255]) ).
fof(f332,plain,
! [X0] :
( tail_of(X0) != tail_of(sK7)
| sequential(sK10(sK7,sK8),X0)
| sK10(sK7,sK8) = X0
| ~ edge(X0)
| ~ edge(sK10(sK7,sK8)) ),
inference(superposition,[],[f132,f306]) ).
fof(f132,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| sequential(X0,X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f701,plain,
( ~ sequential(sK10(sK7,sK8),sK7)
| spl19_11 ),
inference(subsumption_resolution,[],[f700,f193]) ).
fof(f700,plain,
( ~ sequential(sK10(sK7,sK8),sK7)
| ~ edge(sK8)
| spl19_11 ),
inference(subsumption_resolution,[],[f699,f345]) ).
fof(f345,plain,
( sK8 != sK10(sK7,sK8)
| spl19_11 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f699,plain,
( ~ sequential(sK10(sK7,sK8),sK7)
| sK8 = sK10(sK7,sK8)
| ~ edge(sK8) ),
inference(trivial_inequality_removal,[],[f697]) ).
fof(f697,plain,
( ~ sequential(sK10(sK7,sK8),sK7)
| head_of(sK8) != head_of(sK8)
| sK8 = sK10(sK7,sK8)
| ~ edge(sK8) ),
inference(resolution,[],[f694,f339]) ).
fof(f339,plain,
! [X0] :
( sequential(X0,sK10(sK7,sK8))
| head_of(X0) != head_of(sK8)
| sK10(sK7,sK8) = X0
| ~ edge(X0) ),
inference(subsumption_resolution,[],[f335,f255]) ).
fof(f335,plain,
! [X0] :
( head_of(X0) != head_of(sK8)
| sequential(X0,sK10(sK7,sK8))
| sK10(sK7,sK8) = X0
| ~ edge(sK10(sK7,sK8))
| ~ edge(X0) ),
inference(superposition,[],[f132,f324]) ).
fof(f694,plain,
! [X0] :
( ~ sequential(sK8,X0)
| ~ sequential(X0,sK7) ),
inference(subsumption_resolution,[],[f692,f112]) ).
fof(f692,plain,
! [X0] :
( ~ sequential(X0,sK7)
| ~ sequential(sK8,X0)
| ~ sequential(sK7,sK8) ),
inference(resolution,[],[f667,f113]) ).
fof(f667,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1) ),
inference(subsumption_resolution,[],[f666,f128]) ).
fof(f666,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X0) ),
inference(subsumption_resolution,[],[f665,f128]) ).
fof(f665,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X1)
| ~ edge(X0) ),
inference(subsumption_resolution,[],[f160,f128]) ).
fof(f160,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X6,X7,X8] :
( triangle(X6,X7,X8)
<=> ( sequential(X8,X6)
& sequential(X7,X8)
& sequential(X6,X7)
& edge(X8)
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(f349,plain,
( ~ sequential(sK10(sK7,sK8),sK8)
| spl19_12 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f348,plain,
( spl19_12
<=> sequential(sK10(sK7,sK8),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_12])]) ).
fof(f742,plain,
spl19_11,
inference(avatar_contradiction_clause,[],[f741]) ).
fof(f741,plain,
( $false
| spl19_11 ),
inference(subsumption_resolution,[],[f709,f330]) ).
fof(f709,plain,
( tail_of(sK7) = head_of(sK8)
| spl19_11 ),
inference(superposition,[],[f324,f705]) ).
fof(f740,plain,
( ~ spl19_2
| spl19_9
| spl19_11 ),
inference(avatar_contradiction_clause,[],[f739]) ).
fof(f739,plain,
( $false
| ~ spl19_2
| spl19_9
| spl19_11 ),
inference(subsumption_resolution,[],[f708,f217]) ).
fof(f217,plain,
( on_path(sK7,sK9)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f215,plain,
( spl19_2
<=> on_path(sK7,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).
fof(f708,plain,
( ~ on_path(sK7,sK9)
| spl19_9
| spl19_11 ),
inference(superposition,[],[f313,f705]) ).
fof(f738,plain,
( spl19_11
| spl19_13 ),
inference(avatar_contradiction_clause,[],[f737]) ).
fof(f737,plain,
( $false
| spl19_11
| spl19_13 ),
inference(subsumption_resolution,[],[f707,f354]) ).
fof(f354,plain,
( head_of(sK7) != tail_of(sK7)
| spl19_13 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f352,plain,
( spl19_13
<=> head_of(sK7) = tail_of(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_13])]) ).
fof(f707,plain,
( head_of(sK7) = tail_of(sK7)
| spl19_11 ),
inference(superposition,[],[f306,f705]) ).
fof(f690,plain,
( ~ spl19_3
| spl19_25 ),
inference(avatar_contradiction_clause,[],[f689]) ).
fof(f689,plain,
( $false
| ~ spl19_3
| spl19_25 ),
inference(subsumption_resolution,[],[f688,f224]) ).
fof(f688,plain,
( ~ on_path(sK8,sK9)
| spl19_25 ),
inference(resolution,[],[f685,f229]) ).
fof(f229,plain,
! [X0] :
( in_path(head_of(X0),sK9)
| ~ on_path(X0,sK9) ),
inference(resolution,[],[f172,f202]) ).
fof(f202,plain,
path(sK5,sK6,sK9),
inference(resolution,[],[f200,f110]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(resolution,[],[f166,f161]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| path(X2,X1,X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ( ~ less_or_equal(length_of(X0),length_of(sK17(X0,X1,X2)))
& path(X2,X1,sK17(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,[sK17])],[f103,f104]) ).
fof(f104,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(sK17(X0,X1,X2)))
& path(X2,X1,sK17(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f103,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,[],[f102]) ).
fof(f102,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,[],[f101]) ).
fof(f101,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,[],[f73]) ).
fof(f73,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(f166,plain,
! [X2,X0,X1] :
( sP4(X2,X1,X0)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,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,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> sP4(X2,X1,X0) ),
inference(definition_folding,[],[f59,f73]) ).
fof(f59,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/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| in_path(head_of(X3),X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ( on_path(X3,X2)
& path(X0,X1,X2) )
=> ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X2,X3,X0] :
( ( on_path(X0,X3)
& path(X1,X2,X3) )
=> ( in_path(tail_of(X0),X3)
& in_path(head_of(X0),X3)
& edge(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',on_path_properties) ).
fof(f685,plain,
( ~ in_path(head_of(sK8),sK9)
| spl19_25 ),
inference(avatar_component_clause,[],[f684]) ).
fof(f684,plain,
( spl19_25
<=> in_path(head_of(sK8),sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_25])]) ).
fof(f687,plain,
( ~ spl19_24
| spl19_25 ),
inference(avatar_split_clause,[],[f603,f684,f680]) ).
fof(f680,plain,
( spl19_24
<=> on_path(sK12(tail_of(sK7),path_cons(sK10(sK7,sK8),empty),head_of(sK8)),sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_24])]) ).
fof(f603,plain,
( in_path(head_of(sK8),sK9)
| ~ on_path(sK12(tail_of(sK7),path_cons(sK10(sK7,sK8),empty),head_of(sK8)),sK9) ),
inference(superposition,[],[f230,f486]) ).
fof(f486,plain,
head_of(sK8) = tail_of(sK12(tail_of(sK7),path_cons(sK10(sK7,sK8),empty),head_of(sK8))),
inference(resolution,[],[f444,f209]) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ path(X2,X0,X1)
| tail_of(sK12(X0,X1,X2)) = X2 ),
inference(resolution,[],[f136,f145]) ).
fof(f145,plain,
! [X2,X0,X1] :
( sP2(X1,X2,X0)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( sP2(X1,X2,X0)
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(definition_folding,[],[f49,f69,f68]) ).
fof(f68,plain,
! [X2,X3,X1] :
( ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) ) )
| ~ sP1(X2,X3,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f69,plain,
! [X1,X2,X0] :
( ? [X3] :
( sP1(X2,X3,X1)
& tail_of(X3) = X0
& edge(X3) )
| ~ sP2(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> ( ? [X3] :
( ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X2,X3] :
( path(X1,X2,X3)
=> ( ? [X0] :
( ( ( path_cons(X0,empty) = X3
& head_of(X0) = X2 )
<~> ? [X4] :
( path_cons(X0,X4) = X3
& path(head_of(X0),X2,X4) ) )
& tail_of(X0) = X1
& edge(X0) )
& vertex(X2)
& vertex(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_properties) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| tail_of(sK12(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( sP1(X1,sK12(X0,X1,X2),X0)
& tail_of(sK12(X0,X1,X2)) = X2
& edge(sK12(X0,X1,X2)) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f87,f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ? [X3] :
( sP1(X1,X3,X0)
& tail_of(X3) = X2
& edge(X3) )
=> ( sP1(X1,sK12(X0,X1,X2),X0)
& tail_of(sK12(X0,X1,X2)) = X2
& edge(sK12(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ? [X3] :
( sP1(X1,X3,X0)
& tail_of(X3) = X2
& edge(X3) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f86]) ).
fof(f86,plain,
! [X1,X2,X0] :
( ? [X3] :
( sP1(X2,X3,X1)
& tail_of(X3) = X0
& edge(X3) )
| ~ sP2(X1,X2,X0) ),
inference(nnf_transformation,[],[f69]) ).
fof(f444,plain,
path(head_of(sK8),tail_of(sK7),path_cons(sK10(sK7,sK8),empty)),
inference(forward_demodulation,[],[f443,f306]) ).
fof(f443,plain,
path(head_of(sK8),head_of(sK10(sK7,sK8)),path_cons(sK10(sK7,sK8),empty)),
inference(subsumption_resolution,[],[f439,f255]) ).
fof(f439,plain,
( path(head_of(sK8),head_of(sK10(sK7,sK8)),path_cons(sK10(sK7,sK8),empty))
| ~ edge(sK10(sK7,sK8)) ),
inference(superposition,[],[f423,f324]) ).
fof(f423,plain,
! [X3] :
( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
| ~ edge(X3) ),
inference(subsumption_resolution,[],[f422,f126]) ).
fof(f126,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ( vertex(tail_of(X0))
& vertex(head_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
fof(f422,plain,
! [X3] :
( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
| ~ edge(X3)
| ~ vertex(tail_of(X3)) ),
inference(subsumption_resolution,[],[f185,f125]) ).
fof(f125,plain,
! [X0] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f185,plain,
! [X3] :
( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
| ~ edge(X3)
| ~ vertex(head_of(X3))
| ~ vertex(tail_of(X3)) ),
inference(equality_resolution,[],[f184]) ).
fof(f184,plain,
! [X3,X0] :
( path(X0,head_of(X3),path_cons(X3,empty))
| tail_of(X3) != X0
| ~ edge(X3)
| ~ vertex(head_of(X3))
| ~ vertex(X0) ),
inference(equality_resolution,[],[f183]) ).
fof(f183,plain,
! [X3,X0,X1] :
( path(X0,X1,path_cons(X3,empty))
| head_of(X3) != X1
| tail_of(X3) != X0
| ~ edge(X3)
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f154,plain,
! [X2,X3,X0,X1] :
( path(X0,X1,X2)
| path_cons(X3,empty) != X2
| head_of(X3) != X1
| tail_of(X3) != X0
| ~ edge(X3)
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ! [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
& ( path_cons(X3,empty) != X2
| head_of(X3) != X1 ) )
| tail_of(X3) != X0
| ~ edge(X3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ! [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
& ( path_cons(X3,empty) != X2
| head_of(X3) != X1 ) )
| tail_of(X3) != X0
| ~ edge(X3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) )
=> path(X0,X1,X2) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2,X3] :
( ( ? [X0] :
( ( ? [X4] :
( path_cons(X0,X4) = X3
& path(head_of(X0),X2,X4) )
| ( path_cons(X0,empty) = X3
& head_of(X0) = X2 ) )
& tail_of(X0) = X1
& edge(X0) )
& vertex(X2)
& vertex(X1) )
=> path(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_defn) ).
fof(f230,plain,
! [X0] :
( in_path(tail_of(X0),sK9)
| ~ on_path(X0,sK9) ),
inference(resolution,[],[f173,f202]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| in_path(tail_of(X3),X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f627,plain,
( ~ spl19_22
| spl19_23 ),
inference(avatar_split_clause,[],[f613,f624,f620]) ).
fof(f620,plain,
( spl19_22
<=> on_path(sK8,path_cons(sK10(sK7,sK8),empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_22])]) ).
fof(f624,plain,
( spl19_23
<=> in_path(head_of(sK7),path_cons(sK10(sK7,sK8),empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_23])]) ).
fof(f613,plain,
( in_path(head_of(sK7),path_cons(sK10(sK7,sK8),empty))
| ~ on_path(sK8,path_cons(sK10(sK7,sK8),empty)) ),
inference(superposition,[],[f485,f194]) ).
fof(f485,plain,
! [X0] :
( in_path(tail_of(X0),path_cons(sK10(sK7,sK8),empty))
| ~ on_path(X0,path_cons(sK10(sK7,sK8),empty)) ),
inference(resolution,[],[f444,f173]) ).
fof(f570,plain,
( ~ spl19_20
| spl19_21 ),
inference(avatar_split_clause,[],[f492,f567,f563]) ).
fof(f563,plain,
( spl19_20
<=> on_path(sK12(sK6,sK9,sK5),path_cons(sK8,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_20])]) ).
fof(f567,plain,
( spl19_21
<=> in_path(sK5,path_cons(sK8,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_21])]) ).
fof(f492,plain,
( in_path(sK5,path_cons(sK8,empty))
| ~ on_path(sK12(sK6,sK9,sK5),path_cons(sK8,empty)) ),
inference(superposition,[],[f458,f241]) ).
fof(f241,plain,
sK5 = tail_of(sK12(sK6,sK9,sK5)),
inference(resolution,[],[f209,f202]) ).
fof(f458,plain,
! [X0] :
( in_path(tail_of(X0),path_cons(sK8,empty))
| ~ on_path(X0,path_cons(sK8,empty)) ),
inference(resolution,[],[f441,f173]) ).
fof(f441,plain,
path(head_of(sK7),head_of(sK8),path_cons(sK8,empty)),
inference(subsumption_resolution,[],[f437,f193]) ).
fof(f437,plain,
( path(head_of(sK7),head_of(sK8),path_cons(sK8,empty))
| ~ edge(sK8) ),
inference(superposition,[],[f423,f194]) ).
fof(f560,plain,
( ~ spl19_18
| spl19_19 ),
inference(avatar_split_clause,[],[f489,f557,f553]) ).
fof(f553,plain,
( spl19_18
<=> on_path(sK10(sK7,sK8),path_cons(sK8,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_18])]) ).
fof(f557,plain,
( spl19_19
<=> in_path(tail_of(sK7),path_cons(sK8,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_19])]) ).
fof(f489,plain,
( in_path(tail_of(sK7),path_cons(sK8,empty))
| ~ on_path(sK10(sK7,sK8),path_cons(sK8,empty)) ),
inference(superposition,[],[f457,f306]) ).
fof(f457,plain,
! [X0] :
( in_path(head_of(X0),path_cons(sK8,empty))
| ~ on_path(X0,path_cons(sK8,empty)) ),
inference(resolution,[],[f441,f172]) ).
fof(f503,plain,
( ~ spl19_16
| spl19_17 ),
inference(avatar_split_clause,[],[f491,f500,f496]) ).
fof(f496,plain,
( spl19_16
<=> on_path(sK8,path_cons(sK8,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_16])]) ).
fof(f500,plain,
( spl19_17
<=> in_path(head_of(sK7),path_cons(sK8,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_17])]) ).
fof(f491,plain,
( in_path(head_of(sK7),path_cons(sK8,empty))
| ~ on_path(sK8,path_cons(sK8,empty)) ),
inference(superposition,[],[f458,f194]) ).
fof(f365,plain,
( spl19_14
| spl19_15 ),
inference(avatar_split_clause,[],[f356,f362,f358]) ).
fof(f358,plain,
( spl19_14
<=> number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_14])]) ).
fof(f362,plain,
( spl19_15
<=> on_path(sK15(sK9),sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_15])]) ).
fof(f356,plain,
( on_path(sK15(sK9),sK9)
| number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9) ),
inference(resolution,[],[f156,f202]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| on_path(sK15(X0),X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ( ! [X5] : ~ triangle(sK15(X0),sK16(X0),X5)
& sequential(sK15(X0),sK16(X0))
& on_path(sK16(X0),X0)
& on_path(sK15(X0),X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f56,f99]) ).
fof(f99,plain,
! [X0] :
( ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ( ! [X5] : ~ triangle(sK15(X0),sK16(X0),X5)
& sequential(sK15(X0),sK16(X0))
& on_path(sK16(X0),X0)
& on_path(sK15(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f56,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,[],[f55]) ).
fof(f55,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,[],[f32]) ).
fof(f32,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/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f355,plain,
( spl19_11
| spl19_12
| ~ spl19_13 ),
inference(avatar_split_clause,[],[f342,f352,f348,f344]) ).
fof(f342,plain,
( head_of(sK7) != tail_of(sK7)
| sequential(sK10(sK7,sK8),sK8)
| sK8 = sK10(sK7,sK8) ),
inference(subsumption_resolution,[],[f340,f255]) ).
fof(f340,plain,
( head_of(sK7) != tail_of(sK7)
| sequential(sK10(sK7,sK8),sK8)
| sK8 = sK10(sK7,sK8)
| ~ edge(sK10(sK7,sK8)) ),
inference(superposition,[],[f337,f306]) ).
fof(f337,plain,
! [X0] :
( head_of(X0) != head_of(sK7)
| sequential(X0,sK8)
| sK8 = X0
| ~ edge(X0) ),
inference(subsumption_resolution,[],[f333,f193]) ).
fof(f333,plain,
! [X0] :
( head_of(X0) != head_of(sK7)
| sequential(X0,sK8)
| sK8 = X0
| ~ edge(sK8)
| ~ edge(X0) ),
inference(superposition,[],[f132,f194]) ).
fof(f321,plain,
( ~ spl19_2
| spl19_10 ),
inference(avatar_contradiction_clause,[],[f320]) ).
fof(f320,plain,
( $false
| ~ spl19_2
| spl19_10 ),
inference(subsumption_resolution,[],[f319,f217]) ).
fof(f319,plain,
( ~ on_path(sK7,sK9)
| spl19_10 ),
inference(resolution,[],[f316,f230]) ).
fof(f316,plain,
( ~ in_path(tail_of(sK7),sK9)
| spl19_10 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f315,plain,
( spl19_10
<=> in_path(tail_of(sK7),sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_10])]) ).
fof(f318,plain,
( ~ spl19_9
| spl19_10 ),
inference(avatar_split_clause,[],[f308,f315,f311]) ).
fof(f308,plain,
( in_path(tail_of(sK7),sK9)
| ~ on_path(sK10(sK7,sK8),sK9) ),
inference(superposition,[],[f229,f306]) ).
fof(f275,plain,
( spl19_1
| spl19_8 ),
inference(avatar_split_clause,[],[f270,f272,f212]) ).
fof(f212,plain,
( spl19_1
<=> ! [X0,X1] : ~ path(X0,X1,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).
fof(f272,plain,
( spl19_8
<=> sP3(sK9,sK8,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_8])]) ).
fof(f270,plain,
! [X0,X1] :
( sP3(sK9,sK8,sK7)
| ~ path(X0,X1,sK9) ),
inference(resolution,[],[f151,f111]) ).
fof(f151,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| sP3(X0,X4,X3)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( sP3(X0,X4,X3)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(definition_folding,[],[f50,f71]) ).
fof(f71,plain,
! [X0,X4,X3] :
( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
| ~ sP3(X0,X4,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( precedes(X6,X7,X3)
=> ( ( sequential(X6,X7)
<~> ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) ) )
& on_path(X7,X3)
& on_path(X6,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
fof(f268,plain,
spl19_6,
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f267,plain,
( $false
| spl19_6 ),
inference(subsumption_resolution,[],[f266,f202]) ).
fof(f266,plain,
( ~ path(sK5,sK6,sK9)
| spl19_6 ),
inference(resolution,[],[f265,f145]) ).
fof(f265,plain,
( ~ sP2(sK6,sK9,sK5)
| spl19_6 ),
inference(resolution,[],[f259,f135]) ).
fof(f135,plain,
! [X2,X0,X1] :
( edge(sK12(X0,X1,X2))
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f259,plain,
( ~ edge(sK12(sK6,sK9,sK5))
| spl19_6 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f257,plain,
( spl19_6
<=> edge(sK12(sK6,sK9,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_6])]) ).
fof(f264,plain,
( ~ spl19_6
| ~ spl19_7 ),
inference(avatar_split_clause,[],[f243,f261,f257]) ).
fof(f261,plain,
( spl19_7
<=> sK5 = head_of(sK12(sK6,sK9,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_7])]) ).
fof(f243,plain,
( sK5 != head_of(sK12(sK6,sK9,sK5))
| ~ edge(sK12(sK6,sK9,sK5)) ),
inference(superposition,[],[f124,f241]) ).
fof(f253,plain,
( ~ spl19_4
| spl19_5 ),
inference(avatar_split_clause,[],[f242,f250,f246]) ).
fof(f246,plain,
( spl19_4
<=> on_path(sK12(sK6,sK9,sK5),sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_4])]) ).
fof(f250,plain,
( spl19_5
<=> in_path(sK5,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_5])]) ).
fof(f242,plain,
( in_path(sK5,sK9)
| ~ on_path(sK12(sK6,sK9,sK5),sK9) ),
inference(superposition,[],[f230,f241]) ).
fof(f227,plain,
~ spl19_1,
inference(avatar_contradiction_clause,[],[f226]) ).
fof(f226,plain,
( $false
| ~ spl19_1 ),
inference(resolution,[],[f213,f202]) ).
fof(f213,plain,
( ! [X0,X1] : ~ path(X0,X1,sK9)
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f225,plain,
( spl19_1
| spl19_3 ),
inference(avatar_split_clause,[],[f220,f222,f212]) ).
fof(f220,plain,
! [X0,X1] :
( on_path(sK8,sK9)
| ~ path(X0,X1,sK9) ),
inference(resolution,[],[f150,f111]) ).
fof(f150,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f218,plain,
( spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f210,f215,f212]) ).
fof(f210,plain,
! [X0,X1] :
( on_path(sK7,sK9)
| ~ path(X0,X1,sK9) ),
inference(resolution,[],[f149,f111]) ).
fof(f149,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA008+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 12:42:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (15344)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (15348)WARNING: value z3 for option sas not known
% 0.21/0.37 % (15345)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (15349)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (15348)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)
% 0.21/0.37 % (15350)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)
% 0.21/0.37 % (15352)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)
% 0.21/0.37 % (15351)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)
% 0.21/0.37 TRYING [1]
% 0.21/0.38 TRYING [1]
% 0.21/0.38 % (15347)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.38 TRYING [3]
% 0.21/0.40 % (15348)First to succeed.
% 0.21/0.40 % (15348)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15344"
% 0.21/0.40 % (15348)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41 % (15348)------------------------------
% 0.21/0.41 % (15348)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.41 % (15348)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (15348)Memory used [KB]: 1256
% 0.21/0.41 % (15348)Time elapsed: 0.035 s
% 0.21/0.41 % (15348)Instructions burned: 55 (million)
% 0.21/0.41 % (15344)Success in time 0.04 s
%------------------------------------------------------------------------------