TSTP Solution File: GRA008+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRA008+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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  : 600s
% DateTime : Sat Jul 16 07:22:09 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   51 (  21 unt;   8 nHn;  51 RR)
%            Number of literals    :  122 (   0 equ;  74 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   2 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;  11 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    complete,
    file('GRA008+2.p',unknown),
    [] ).

cnf(2,axiom,
    sequential(skc7,skc6),
    file('GRA008+2.p',unknown),
    [] ).

cnf(3,axiom,
    precedes(skc7,skc6,skc5),
    file('GRA008+2.p',unknown),
    [] ).

cnf(4,axiom,
    shortest_path(skc8,skc9,skc5),
    file('GRA008+2.p',unknown),
    [] ).

cnf(5,axiom,
    edge(skf13(u,v)),
    file('GRA008+2.p',unknown),
    [] ).

cnf(7,axiom,
    ~ triangle(skc7,skc6,u),
    file('GRA008+2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ sequential(u,v)
    | edge(u) ),
    file('GRA008+2.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ sequential(u,v)
    | edge(v) ),
    file('GRA008+2.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ edge(u)
    | ~ equal(head_of(u),tail_of(u)) ),
    file('GRA008+2.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ sequential(u,v)
    | equal(head_of(u),tail_of(v)) ),
    file('GRA008+2.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ edge(u)
    | ~ edge(v)
    | ~ equal(head_of(u),tail_of(v))
    | sequential(u,v)
    | equal(u,v) ),
    file('GRA008+2.p',unknown),
    [] ).

cnf(53,axiom,
    ( ~ complete
    | ~ precedes(u,v,w)
    | ~ shortest_path(x,y,w)
    | equal(tail_of(skf13(u,v)),head_of(v)) ),
    file('GRA008+2.p',unknown),
    [] ).

cnf(54,axiom,
    ( ~ complete
    | ~ precedes(u,v,w)
    | ~ shortest_path(x,y,w)
    | equal(head_of(skf13(u,v)),tail_of(u)) ),
    file('GRA008+2.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ equal(head_of(u),head_of(v))
    | ~ equal(tail_of(u),tail_of(w))
    | ~ shortest_path(x,y,z)
    | ~ precedes(w,v,z) ),
    file('GRA008+2.p',unknown),
    [] ).

cnf(66,axiom,
    ( ~ edge(u)
    | ~ edge(v)
    | ~ edge(w)
    | ~ sequential(w,v)
    | ~ sequential(v,u)
    | ~ sequential(u,w)
    | triangle(w,v,u) ),
    file('GRA008+2.p',unknown),
    [] ).

cnf(72,plain,
    ( ~ shortest_path(u,v,w)
    | ~ precedes(x,y,w)
    | equal(head_of(skf13(x,y)),tail_of(x)) ),
    inference(mrr,[status(thm)],[54,1]),
    [iquote('0:MRR:54.0,1.0')] ).

cnf(73,plain,
    ( ~ shortest_path(u,v,w)
    | ~ precedes(x,y,w)
    | equal(tail_of(skf13(x,y)),head_of(y)) ),
    inference(mrr,[status(thm)],[53,1]),
    [iquote('0:MRR:53.0,1.0')] ).

cnf(76,plain,
    ( ~ sequential(u,v)
    | ~ sequential(w,u)
    | ~ sequential(v,w)
    | triangle(v,w,u) ),
    inference(mrr,[status(thm)],[66,11]),
    [iquote('0:MRR:66.0,66.1,66.2,11.1,11.1,11.1')] ).

cnf(81,plain,
    ( ~ sequential(skc6,u)
    | ~ sequential(u,skc7)
    | triangle(skc7,skc6,u) ),
    inference(res,[status(thm),theory(equality)],[2,76]),
    [iquote('0:Res:2.0,76.0')] ).

cnf(85,plain,
    equal(head_of(skc7),tail_of(skc6)),
    inference(res,[status(thm),theory(equality)],[2,28]),
    [iquote('0:Res:2.0,28.0')] ).

cnf(87,plain,
    edge(skc7),
    inference(res,[status(thm),theory(equality)],[2,11]),
    [iquote('0:Res:2.0,11.0')] ).

cnf(88,plain,
    edge(skc6),
    inference(res,[status(thm),theory(equality)],[2,12]),
    [iquote('0:Res:2.0,12.0')] ).

cnf(93,plain,
    ( ~ precedes(u,v,skc5)
    | equal(tail_of(skf13(u,v)),head_of(v)) ),
    inference(res,[status(thm),theory(equality)],[4,73]),
    [iquote('0:Res:4.0,73.1')] ).

cnf(94,plain,
    ( ~ precedes(u,v,skc5)
    | equal(head_of(skf13(u,v)),tail_of(u)) ),
    inference(res,[status(thm),theory(equality)],[4,72]),
    [iquote('0:Res:4.0,72.1')] ).

cnf(97,plain,
    ( ~ equal(head_of(u),head_of(v))
    | ~ equal(tail_of(u),tail_of(w))
    | ~ precedes(w,v,skc5) ),
    inference(res,[status(thm),theory(equality)],[4,61]),
    [iquote('0:Res:4.0,61.3')] ).

cnf(115,plain,
    ( ~ sequential(u,skc7)
    | ~ sequential(skc6,u) ),
    inference(mrr,[status(thm)],[81,7]),
    [iquote('0:MRR:81.2,7.0')] ).

cnf(117,plain,
    ( ~ equal(head_of(u),head_of(skc6))
    | ~ equal(tail_of(u),tail_of(skc7)) ),
    inference(res,[status(thm),theory(equality)],[3,97]),
    [iquote('0:Res:3.0,97.2')] ).

cnf(121,plain,
    equal(head_of(skf13(skc7,skc6)),tail_of(skc7)),
    inference(res,[status(thm),theory(equality)],[3,94]),
    [iquote('0:Res:3.0,94.0')] ).

cnf(122,plain,
    equal(tail_of(skf13(skc7,skc6)),head_of(skc6)),
    inference(res,[status(thm),theory(equality)],[3,93]),
    [iquote('0:Res:3.0,93.0')] ).

cnf(148,plain,
    ( ~ edge(skc7)
    | ~ equal(tail_of(skc7),tail_of(skc6)) ),
    inference(spl,[status(thm),theory(equality)],[85,24]),
    [iquote('0:SpL:85.0,24.1')] ).

cnf(150,plain,
    ~ equal(tail_of(skc7),tail_of(skc6)),
    inference(ssi,[status(thm)],[148,87]),
    [iquote('0:SSi:148.0,87.0')] ).

cnf(168,plain,
    ( ~ equal(head_of(skc6),tail_of(skc6))
    | ~ equal(tail_of(skc7),tail_of(skc7)) ),
    inference(spl,[status(thm),theory(equality)],[85,117]),
    [iquote('0:SpL:85.0,117.0')] ).

cnf(170,plain,
    ~ equal(head_of(skc6),tail_of(skc6)),
    inference(obv,[status(thm),theory(equality)],[168]),
    [iquote('0:Obv:168.1')] ).

cnf(288,plain,
    ( ~ edge(u)
    | ~ edge(skc7)
    | ~ equal(head_of(u),tail_of(skc7))
    | ~ sequential(skc6,u)
    | equal(u,skc7) ),
    inference(res,[status(thm),theory(equality)],[50,115]),
    [iquote('0:Res:50.3,115.0')] ).

cnf(293,plain,
    ( ~ edge(u)
    | ~ equal(head_of(u),tail_of(skc7))
    | ~ sequential(skc6,u)
    | equal(u,skc7) ),
    inference(ssi,[status(thm)],[288,87]),
    [iquote('0:SSi:288.1,87.0')] ).

cnf(294,plain,
    ( ~ equal(head_of(u),tail_of(skc7))
    | ~ sequential(skc6,u)
    | equal(u,skc7) ),
    inference(mrr,[status(thm)],[293,12]),
    [iquote('0:MRR:293.0,12.1')] ).

cnf(301,plain,
    ( ~ edge(skc6)
    | ~ edge(u)
    | ~ equal(head_of(skc6),tail_of(u))
    | ~ equal(head_of(u),tail_of(skc7))
    | equal(skc6,u)
    | equal(u,skc7) ),
    inference(res,[status(thm),theory(equality)],[50,294]),
    [iquote('0:Res:50.3,294.1')] ).

cnf(302,plain,
    ( ~ edge(u)
    | ~ equal(head_of(skc6),tail_of(u))
    | ~ equal(head_of(u),tail_of(skc7))
    | equal(skc6,u)
    | equal(u,skc7) ),
    inference(ssi,[status(thm)],[301,88]),
    [iquote('0:SSi:301.0,88.0')] ).

cnf(369,plain,
    ( ~ edge(skf13(skc7,skc6))
    | ~ equal(head_of(skc6),head_of(skc6))
    | ~ equal(head_of(skf13(skc7,skc6)),tail_of(skc7))
    | equal(skf13(skc7,skc6),skc6)
    | equal(skf13(skc7,skc6),skc7) ),
    inference(spl,[status(thm),theory(equality)],[122,302]),
    [iquote('0:SpL:122.0,302.1')] ).

cnf(373,plain,
    ( ~ edge(skf13(skc7,skc6))
    | ~ equal(head_of(skf13(skc7,skc6)),tail_of(skc7))
    | equal(skf13(skc7,skc6),skc6)
    | equal(skf13(skc7,skc6),skc7) ),
    inference(obv,[status(thm),theory(equality)],[369]),
    [iquote('0:Obv:369.1')] ).

cnf(374,plain,
    ( ~ edge(skf13(skc7,skc6))
    | ~ equal(tail_of(skc7),tail_of(skc7))
    | equal(skf13(skc7,skc6),skc6)
    | equal(skf13(skc7,skc6),skc7) ),
    inference(rew,[status(thm),theory(equality)],[121,373]),
    [iquote('0:Rew:121.0,373.1')] ).

cnf(375,plain,
    ( ~ edge(skf13(skc7,skc6))
    | equal(skf13(skc7,skc6),skc6)
    | equal(skf13(skc7,skc6),skc7) ),
    inference(obv,[status(thm),theory(equality)],[374]),
    [iquote('0:Obv:374.1')] ).

cnf(376,plain,
    ( equal(skf13(skc7,skc6),skc6)
    | equal(skf13(skc7,skc6),skc7) ),
    inference(ssi,[status(thm)],[375,5,87,88]),
    [iquote('0:SSi:375.0,5.0,87.0,88.0')] ).

cnf(384,plain,
    equal(skf13(skc7,skc6),skc6),
    inference(spt,[spt(split,[position(s1)])],[376]),
    [iquote('1:Spt:376.0')] ).

cnf(386,plain,
    equal(head_of(skc6),tail_of(skc6)),
    inference(rew,[status(thm),theory(equality)],[384,122]),
    [iquote('1:Rew:384.0,122.0')] ).

cnf(392,plain,
    $false,
    inference(mrr,[status(thm)],[386,170]),
    [iquote('1:MRR:386.0,170.0')] ).

cnf(394,plain,
    ~ equal(skf13(skc7,skc6),skc6),
    inference(spt,[spt(split,[position(sa)])],[392,384]),
    [iquote('1:Spt:392.0,376.0,384.0')] ).

cnf(395,plain,
    equal(skf13(skc7,skc6),skc7),
    inference(spt,[spt(split,[position(s2)])],[376]),
    [iquote('1:Spt:392.0,376.1')] ).

cnf(399,plain,
    equal(head_of(skc7),tail_of(skc7)),
    inference(rew,[status(thm),theory(equality)],[395,121]),
    [iquote('1:Rew:395.0,121.0')] ).

cnf(400,plain,
    equal(tail_of(skc7),tail_of(skc6)),
    inference(rew,[status(thm),theory(equality)],[85,399]),
    [iquote('1:Rew:85.0,399.0')] ).

cnf(401,plain,
    $false,
    inference(mrr,[status(thm)],[400,150]),
    [iquote('1:MRR:400.0,150.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GRA008+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue May 31 01:18:56 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.51  
% 0.19/0.51  SPASS V 3.9 
% 0.19/0.51  SPASS beiseite: Proof found.
% 0.19/0.51  % SZS status Theorem
% 0.19/0.51  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.51  SPASS derived 260 clauses, backtracked 8 clauses, performed 2 splits and kept 210 clauses.
% 0.19/0.51  SPASS allocated 98358 KBytes.
% 0.19/0.51  SPASS spent	0:00:00.16 on the problem.
% 0.19/0.51  		0:00:00.04 for the input.
% 0.19/0.51  		0:00:00.07 for the FLOTTER CNF translation.
% 0.19/0.51  		0:00:00.00 for inferences.
% 0.19/0.51  		0:00:00.00 for the backtracking.
% 0.19/0.51  		0:00:00.02 for the reduction.
% 0.19/0.51  
% 0.19/0.51  
% 0.19/0.51  Here is a proof with depth 5, length 51 :
% 0.19/0.51  % SZS output start Refutation
% See solution above
% 0.19/0.51  Formulae used in the proof : sequential_is_triangle back_edge sequential_defn no_loops shortest_path_properties triangle_defn
% 0.19/0.51  
%------------------------------------------------------------------------------