TSTP Solution File: GRA008+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRA008+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %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  : 600s
% DateTime : Sat Jul 16 07:22:09 EDT 2022

% Result   : Theorem 45.05s 45.24s
% Output   : Refutation 46.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   38
% Syntax   : Number of clauses     :  161 (  37 unt;  41 nHn; 161 RR)
%            Number of literals    :  551 (   0 equ; 344 neg)
%            Maximal clause size   :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   15 (  14 usr;   2 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;  12 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

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

cnf(2,axiom,
    sequential(skc7,skc6),
    file('GRA008+1.p',unknown),
    [] ).

cnf(3,axiom,
    precedes(skc7,skc6,skc5),
    file('GRA008+1.p',unknown),
    [] ).

cnf(4,axiom,
    shortest_path(skc8,skc9,skc5),
    file('GRA008+1.p',unknown),
    [] ).

cnf(5,axiom,
    edge(skf12(u,v)),
    file('GRA008+1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ triangle(skc7,skc6,u),
    file('GRA008+1.p',unknown),
    [] ).

cnf(7,axiom,
    edge(skf13(u,v,w)),
    file('GRA008+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ edge(u)
    | vertex(head_of(u)) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ edge(u)
    | vertex(tail_of(u)) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ sequential(u,v)
    | edge(u) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ sequential(u,v)
    | edge(v) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ path(u,v,w)
    | vertex(u) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ path(u,v,w)
    | vertex(v) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ sequential(u,v)
    | ~ equal(u,v) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ skP0(u,v,w)
    | equal(w,head_of(v)) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ skP0(u,v,w)
    | equal(u,tail_of(v)) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ skP1(u,v,w)
    | equal(w,head_of(v)) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ sequential(u,v)
    | equal(head_of(u),tail_of(v)) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ shortest_path(u,v,w)
    | path(u,v,w) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ skP1(u,v,w)
    | equal(u,path_cons(v,empty)) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ in_path(u,v)
    | ~ path(w,x,v)
    | vertex(u) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(34,axiom,
    ( ~ path(u,v,w)
    | equal(tail_of(skf13(v,w,u)),u) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ on_path(u,v)
    | ~ path(w,x,v)
    | in_path(head_of(u),v) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ on_path(u,v)
    | ~ path(w,x,v)
    | in_path(tail_of(u),v) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ precedes(u,v,w)
    | ~ path(x,y,w)
    | on_path(u,w) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ precedes(u,v,w)
    | ~ path(x,y,w)
    | on_path(v,w) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(41,axiom,
    ( ~ sequential(u,v)
    | ~ skP2(w,x,u)
    | ~ precedes(v,x,w) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(49,axiom,
    ( ~ edge(u)
    | ~ edge(v)
    | ~ equal(head_of(u),tail_of(v))
    | sequential(u,v)
    | equal(u,v) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ sequential(u,v)
    | ~ precedes(u,v,w)
    | ~ path(x,y,w)
    | skP2(w,v,u) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(58,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+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ path(u,v,w)
    | equal(path_cons(skf13(v,w,u),skf14(u,v,w)),w)
    | skP1(w,skf13(v,w,u),v) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(60,axiom,
    ( ~ path(u,v,w)
    | skP1(w,skf13(v,w,u),v)
    | path(head_of(skf13(v,w,u)),v,skf14(u,v,w)) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ complete
    | equal(tail_of(skf12(u,v)),u)
    | equal(u,v)
    | skP0(v,skf12(u,v),u) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ complete
    | equal(head_of(skf12(u,v)),v)
    | equal(u,v)
    | skP0(v,skf12(u,v),u) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ edge(u)
    | ~ edge(v)
    | ~ edge(w)
    | ~ sequential(w,v)
    | ~ sequential(v,u)
    | ~ sequential(u,w)
    | triangle(w,v,u) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ sequential(u,v)
    | ~ precedes(v,w,x)
    | ~ path(y,z,x)
    | ~ on_path(u,x)
    | ~ on_path(w,x)
    | precedes(u,w,x) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(66,axiom,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ edge(w)
    | ~ equal(u,head_of(w))
    | ~ equal(v,tail_of(w))
    | ~ equal(x,path_cons(w,empty))
    | path(v,u,x) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(67,axiom,
    ( ~ edge(u)
    | ~ vertex(v)
    | ~ vertex(w)
    | ~ equal(v,tail_of(u))
    | ~ equal(x,path_cons(u,y))
    | ~ path(head_of(u),w,y)
    | path(v,w,x) ),
    file('GRA008+1.p',unknown),
    [] ).

cnf(69,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | equal(v,u)
    | equal(tail_of(skf12(v,u)),v)
    | skP0(u,skf12(v,u),v) ),
    inference(mrr,[status(thm)],[61,1]),
    [iquote('0:MRR:61.2,1.0')] ).

cnf(70,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | equal(v,u)
    | equal(head_of(skf12(v,u)),u)
    | skP0(u,skf12(v,u),v) ),
    inference(mrr,[status(thm)],[62,1]),
    [iquote('0:MRR:62.2,1.0')] ).

cnf(71,plain,
    ( ~ sequential(u,v)
    | ~ sequential(w,u)
    | ~ sequential(v,w)
    | triangle(v,w,u) ),
    inference(mrr,[status(thm)],[63,10]),
    [iquote('0:MRR:63.0,63.1,63.2,10.1,10.1,10.1')] ).

cnf(72,plain,
    ( ~ on_path(u,v)
    | ~ sequential(u,w)
    | ~ path(x,y,v)
    | ~ precedes(w,z,v)
    | precedes(u,z,v) ),
    inference(mrr,[status(thm)],[64,39]),
    [iquote('0:MRR:64.4,39.2')] ).

cnf(73,plain,
    ( ~ vertex(u)
    | ~ edge(v)
    | ~ equal(u,tail_of(v))
    | ~ equal(w,path_cons(v,x))
    | ~ path(head_of(v),y,x)
    | path(u,y,w) ),
    inference(mrr,[status(thm)],[67,17]),
    [iquote('0:MRR:67.2,17.1')] ).

cnf(76,plain,
    ( ~ sequential(skc6,u)
    | ~ sequential(u,skc7)
    | triangle(skc7,skc6,u) ),
    inference(res,[status(thm),theory(equality)],[2,71]),
    [iquote('0:Res:2.0,71.0')] ).

cnf(79,plain,
    ( ~ skP2(u,v,skc7)
    | ~ precedes(skc6,v,u) ),
    inference(res,[status(thm),theory(equality)],[2,41]),
    [iquote('0:Res:2.0,41.0')] ).

cnf(80,plain,
    equal(tail_of(skc6),head_of(skc7)),
    inference(res,[status(thm),theory(equality)],[2,27]),
    [iquote('0:Res:2.0,27.0')] ).

cnf(81,plain,
    ~ equal(skc7,skc6),
    inference(res,[status(thm),theory(equality)],[2,21]),
    [iquote('0:Res:2.0,21.1')] ).

cnf(82,plain,
    edge(skc7),
    inference(res,[status(thm),theory(equality)],[2,10]),
    [iquote('0:Res:2.0,10.0')] ).

cnf(83,plain,
    edge(skc6),
    inference(res,[status(thm),theory(equality)],[2,11]),
    [iquote('0:Res:2.0,11.0')] ).

cnf(86,plain,
    path(skc8,skc9,skc5),
    inference(res,[status(thm),theory(equality)],[4,28]),
    [iquote('0:Res:4.0,28.0')] ).

cnf(90,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)],[4,58]),
    [iquote('0:Res:4.0,58.3')] ).

cnf(93,plain,
    ( ~ path(u,v,skc5)
    | on_path(skc7,skc5) ),
    inference(res,[status(thm),theory(equality)],[3,38]),
    [iquote('0:Res:3.0,38.1')] ).

cnf(94,plain,
    ( ~ path(u,v,skc5)
    | on_path(skc6,skc5) ),
    inference(res,[status(thm),theory(equality)],[3,39]),
    [iquote('0:Res:3.0,39.1')] ).

cnf(97,plain,
    ( ~ on_path(u,skc5)
    | ~ sequential(u,skc7)
    | ~ path(v,w,skc5)
    | precedes(u,skc6,skc5) ),
    inference(res,[status(thm),theory(equality)],[3,72]),
    [iquote('0:Res:3.0,72.1')] ).

cnf(100,plain,
    ( ~ sequential(skc7,skc6)
    | ~ path(u,v,skc5)
    | skP2(skc5,skc6,skc7) ),
    inference(res,[status(thm),theory(equality)],[3,50]),
    [iquote('0:Res:3.0,50.2')] ).

cnf(102,plain,
    ( ~ sequential(u,skc7)
    | ~ sequential(skc6,u) ),
    inference(mrr,[status(thm)],[76,6]),
    [iquote('0:MRR:76.2,6.0')] ).

cnf(103,plain,
    ( ~ path(u,v,skc5)
    | skP2(skc5,skc6,skc7) ),
    inference(mrr,[status(thm)],[100,2]),
    [iquote('0:MRR:100.0,2.0')] ).

cnf(104,plain,
    ( ~ equal(head_of(u),head_of(skc6))
    | ~ equal(tail_of(u),tail_of(skc7)) ),
    inference(res,[status(thm),theory(equality)],[3,90]),
    [iquote('0:Res:3.0,90.2')] ).

cnf(115,plain,
    vertex(skc9),
    inference(res,[status(thm),theory(equality)],[86,17]),
    [iquote('0:Res:86.0,17.0')] ).

cnf(116,plain,
    vertex(skc8),
    inference(res,[status(thm),theory(equality)],[86,16]),
    [iquote('0:Res:86.0,16.0')] ).

cnf(117,plain,
    on_path(skc6,skc5),
    inference(res,[status(thm),theory(equality)],[86,94]),
    [iquote('0:Res:86.0,94.0')] ).

cnf(119,plain,
    on_path(skc7,skc5),
    inference(res,[status(thm),theory(equality)],[86,93]),
    [iquote('0:Res:86.0,93.0')] ).

cnf(120,plain,
    skP2(skc5,skc6,skc7),
    inference(res,[status(thm),theory(equality)],[86,103]),
    [iquote('0:Res:86.0,103.0')] ).

cnf(128,plain,
    ~ precedes(skc6,skc6,skc5),
    inference(res,[status(thm),theory(equality)],[120,79]),
    [iquote('0:Res:120.0,79.0')] ).

cnf(179,plain,
    ( ~ on_path(u,skc5)
    | ~ sequential(u,skc7)
    | precedes(u,skc6,skc5) ),
    inference(res,[status(thm),theory(equality)],[86,97]),
    [iquote('0:Res:86.0,97.2')] ).

cnf(181,plain,
    ( ~ on_path(skc6,skc5)
    | ~ sequential(skc6,skc7) ),
    inference(res,[status(thm),theory(equality)],[179,128]),
    [iquote('0:Res:179.2,128.0')] ).

cnf(186,plain,
    ~ sequential(skc6,skc7),
    inference(mrr,[status(thm)],[181,117]),
    [iquote('0:MRR:181.0,117.0')] ).

cnf(194,plain,
    ( ~ equal(tail_of(u),tail_of(v))
    | ~ precedes(v,u,skc5) ),
    inference(eqr,[status(thm),theory(equality)],[90]),
    [iquote('0:EqR:90.0')] ).

cnf(195,plain,
    ~ equal(tail_of(skc7),tail_of(skc6)),
    inference(res,[status(thm),theory(equality)],[3,194]),
    [iquote('0:Res:3.0,194.1')] ).

cnf(197,plain,
    ~ equal(tail_of(skc7),head_of(skc7)),
    inference(rew,[status(thm),theory(equality)],[80,195]),
    [iquote('0:Rew:80.0,195.0')] ).

cnf(204,plain,
    ( ~ edge(u)
    | ~ edge(skc7)
    | ~ equal(head_of(u),tail_of(skc7))
    | ~ sequential(skc6,u)
    | equal(u,skc7) ),
    inference(res,[status(thm),theory(equality)],[49,102]),
    [iquote('0:Res:49.3,102.0')] ).

cnf(205,plain,
    ( ~ edge(skc6)
    | ~ edge(skc7)
    | ~ equal(tail_of(skc7),head_of(skc6))
    | equal(skc7,skc6) ),
    inference(res,[status(thm),theory(equality)],[49,186]),
    [iquote('0:Res:49.3,186.0')] ).

cnf(207,plain,
    ( ~ equal(tail_of(skc7),head_of(skc6))
    | equal(skc7,skc6) ),
    inference(ssi,[status(thm)],[205,82,83]),
    [iquote('0:SSi:205.1,205.0,82.0,83.0')] ).

cnf(208,plain,
    ~ equal(tail_of(skc7),head_of(skc6)),
    inference(mrr,[status(thm)],[207,81]),
    [iquote('0:MRR:207.1,81.0')] ).

cnf(209,plain,
    ( ~ edge(u)
    | ~ equal(head_of(u),tail_of(skc7))
    | ~ sequential(skc6,u)
    | equal(u,skc7) ),
    inference(ssi,[status(thm)],[204,82]),
    [iquote('0:SSi:204.1,82.0')] ).

cnf(210,plain,
    ( ~ equal(head_of(u),tail_of(skc7))
    | ~ sequential(skc6,u)
    | equal(u,skc7) ),
    inference(mrr,[status(thm)],[209,11]),
    [iquote('0:MRR:209.0,11.1')] ).

cnf(213,plain,
    ( ~ edge(skc6)
    | ~ edge(u)
    | ~ equal(tail_of(u),head_of(skc6))
    | ~ equal(head_of(u),tail_of(skc7))
    | equal(skc6,u)
    | equal(u,skc7) ),
    inference(res,[status(thm),theory(equality)],[49,210]),
    [iquote('0:Res:49.3,210.1')] ).

cnf(214,plain,
    ( ~ edge(u)
    | ~ equal(tail_of(u),head_of(skc6))
    | ~ equal(head_of(u),tail_of(skc7))
    | equal(skc6,u)
    | equal(u,skc7) ),
    inference(ssi,[status(thm)],[213,83]),
    [iquote('0:SSi:213.0,83.0')] ).

cnf(266,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | equal(v,u)
    | equal(head_of(skf12(v,u)),u)
    | equal(head_of(skf12(v,u)),v) ),
    inference(res,[status(thm),theory(equality)],[70,24]),
    [iquote('0:Res:70.4,24.0')] ).

cnf(267,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | equal(v,u)
    | equal(head_of(skf12(v,u)),u)
    | equal(tail_of(skf12(v,u)),u) ),
    inference(res,[status(thm),theory(equality)],[70,25]),
    [iquote('0:Res:70.4,25.0')] ).

cnf(276,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | equal(v,u)
    | equal(tail_of(skf12(v,u)),v)
    | equal(head_of(skf12(v,u)),v) ),
    inference(res,[status(thm),theory(equality)],[69,24]),
    [iquote('0:Res:69.4,24.0')] ).

cnf(277,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | equal(v,u)
    | equal(tail_of(skf12(v,u)),v)
    | equal(tail_of(skf12(v,u)),u) ),
    inference(res,[status(thm),theory(equality)],[69,25]),
    [iquote('0:Res:69.4,25.0')] ).

cnf(323,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ equal(u,head_of(w))
    | ~ equal(tail_of(skf12(v,u)),tail_of(x))
    | ~ precedes(x,w,skc5)
    | equal(v,u)
    | equal(head_of(skf12(v,u)),v) ),
    inference(spl,[status(thm),theory(equality)],[266,90]),
    [iquote('0:SpL:266.3,90.0')] ).

cnf(330,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ equal(u,head_of(w))
    | ~ equal(v,tail_of(x))
    | ~ precedes(x,w,skc5)
    | equal(v,u)
    | equal(head_of(skf12(v,u)),v) ),
    inference(rew,[status(thm),theory(equality)],[276,323]),
    [iquote('0:Rew:276.3,323.3')] ).

cnf(360,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ equal(head_of(skf12(v,u)),head_of(skc6))
    | ~ equal(v,tail_of(skc7))
    | equal(v,u)
    | equal(tail_of(skf12(v,u)),u) ),
    inference(spl,[status(thm),theory(equality)],[277,104]),
    [iquote('0:SpL:277.3,104.1')] ).

cnf(364,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ edge(skf12(v,u))
    | ~ equal(u,head_of(skc6))
    | ~ equal(head_of(skf12(v,u)),tail_of(skc7))
    | equal(v,u)
    | equal(tail_of(skf12(v,u)),v)
    | equal(skf12(v,u),skc6)
    | equal(skf12(v,u),skc7) ),
    inference(spl,[status(thm),theory(equality)],[277,214]),
    [iquote('0:SpL:277.4,214.1')] ).

cnf(372,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ equal(u,head_of(skc6))
    | ~ equal(v,tail_of(skc7))
    | equal(v,u)
    | equal(tail_of(skf12(v,u)),u) ),
    inference(rew,[status(thm),theory(equality)],[267,360]),
    [iquote('0:Rew:267.3,360.2')] ).

cnf(376,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ edge(skf12(v,u))
    | ~ equal(u,head_of(skc6))
    | ~ equal(v,tail_of(skc7))
    | equal(v,u)
    | equal(u,v)
    | equal(skf12(v,u),skc6)
    | equal(skf12(v,u),skc7) ),
    inference(rew,[status(thm),theory(equality)],[372,364,276]),
    [iquote('0:Rew:372.5,364.6,276.4,364.4')] ).

cnf(377,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ edge(skf12(v,u))
    | ~ equal(u,head_of(skc6))
    | ~ equal(v,tail_of(skc7))
    | equal(u,v)
    | equal(skf12(v,u),skc6)
    | equal(skf12(v,u),skc7) ),
    inference(obv,[status(thm),theory(equality)],[376]),
    [iquote('0:Obv:376.5')] ).

cnf(378,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ equal(u,head_of(skc6))
    | ~ equal(v,tail_of(skc7))
    | equal(u,v)
    | equal(skf12(v,u),skc6)
    | equal(skf12(v,u),skc7) ),
    inference(ssi,[status(thm)],[377,5]),
    [iquote('0:SSi:377.2,5.0')] ).

cnf(573,plain,
    ( ~ vertex(u)
    | ~ edge(skf13(v,w,x))
    | ~ path(x,v,w)
    | ~ equal(u,tail_of(skf13(v,w,x)))
    | ~ equal(y,w)
    | ~ path(head_of(skf13(v,w,x)),z,skf14(x,v,w))
    | skP1(w,skf13(v,w,x),v)
    | path(u,z,y) ),
    inference(spl,[status(thm),theory(equality)],[59,73]),
    [iquote('0:SpL:59.1,73.3')] ).

cnf(574,plain,
    ( ~ vertex(u)
    | ~ edge(skf13(v,w,x))
    | ~ path(x,v,w)
    | ~ equal(u,x)
    | ~ equal(y,w)
    | ~ path(head_of(skf13(v,w,x)),z,skf14(x,v,w))
    | skP1(w,skf13(v,w,x),v)
    | path(u,z,y) ),
    inference(rew,[status(thm),theory(equality)],[34,573]),
    [iquote('0:Rew:34.1,573.3')] ).

cnf(575,plain,
    ( ~ vertex(u)
    | ~ path(v,w,x)
    | ~ equal(u,v)
    | ~ equal(y,x)
    | ~ path(head_of(skf13(w,x,v)),z,skf14(v,w,x))
    | skP1(x,skf13(w,x,v),w)
    | path(u,z,y) ),
    inference(ssi,[status(thm)],[574,7]),
    [iquote('0:SSi:574.1,7.0')] ).

cnf(1683,plain,
    ( ~ vertex(u)
    | ~ path(v,w,x)
    | ~ path(v,w,x)
    | ~ equal(u,v)
    | ~ equal(y,x)
    | skP1(x,skf13(w,x,v),w)
    | skP1(x,skf13(w,x,v),w)
    | path(u,w,y) ),
    inference(res,[status(thm),theory(equality)],[60,575]),
    [iquote('0:Res:60.2,575.4')] ).

cnf(1684,plain,
    ( ~ vertex(u)
    | ~ path(v,w,x)
    | ~ equal(u,v)
    | ~ equal(y,x)
    | skP1(x,skf13(w,x,v),w)
    | path(u,w,y) ),
    inference(obv,[status(thm),theory(equality)],[1683]),
    [iquote('0:Obv:1683.5')] ).

cnf(1735,plain,
    ( ~ vertex(u)
    | ~ equal(u,skc8)
    | ~ equal(v,skc5)
    | skP1(skc5,skf13(skc9,skc5,skc8),skc9)
    | path(u,skc9,v) ),
    inference(res,[status(thm),theory(equality)],[86,1684]),
    [iquote('0:Res:86.0,1684.1')] ).

cnf(1740,plain,
    ( ~ vertex(u)
    | ~ equal(u,skc8)
    | ~ equal(v,skc5)
    | path(u,skc9,v) ),
    inference(spt,[spt(split,[position(s1)])],[1735]),
    [iquote('1:Spt:1735.0,1735.1,1735.2,1735.4')] ).

cnf(1753,plain,
    ( ~ vertex(u)
    | ~ equal(u,skc8)
    | ~ equal(v,skc5)
    | ~ on_path(w,v)
    | in_path(head_of(w),v) ),
    inference(res,[status(thm),theory(equality)],[1740,36]),
    [iquote('1:Res:1740.3,36.1')] ).

cnf(1754,plain,
    ( ~ vertex(u)
    | ~ equal(u,skc8)
    | ~ equal(v,skc5)
    | ~ on_path(w,v)
    | in_path(tail_of(w),v) ),
    inference(res,[status(thm),theory(equality)],[1740,37]),
    [iquote('1:Res:1740.3,37.1')] ).

cnf(1756,plain,
    ( ~ vertex(u)
    | ~ equal(u,skc8)
    | ~ equal(v,skc5)
    | ~ in_path(w,v)
    | vertex(w) ),
    inference(res,[status(thm),theory(equality)],[1740,33]),
    [iquote('1:Res:1740.3,33.1')] ).

cnf(1845,plain,
    ( ~ vertex(skc8)
    | ~ equal(u,skc5)
    | ~ in_path(v,u)
    | vertex(v) ),
    inference(eqr,[status(thm),theory(equality)],[1756]),
    [iquote('1:EqR:1756.1')] ).

cnf(1846,plain,
    ( ~ equal(u,skc5)
    | ~ in_path(v,u)
    | vertex(v) ),
    inference(ssi,[status(thm)],[1845,116]),
    [iquote('1:SSi:1845.0,116.0')] ).

cnf(1889,plain,
    ( ~ vertex(skc8)
    | ~ equal(u,skc5)
    | ~ on_path(v,u)
    | in_path(head_of(v),u) ),
    inference(eqr,[status(thm),theory(equality)],[1753]),
    [iquote('1:EqR:1753.1')] ).

cnf(1890,plain,
    ( ~ equal(u,skc5)
    | ~ on_path(v,u)
    | in_path(head_of(v),u) ),
    inference(ssi,[status(thm)],[1889,116]),
    [iquote('1:SSi:1889.0,116.0')] ).

cnf(1899,plain,
    ( ~ equal(u,skc5)
    | ~ on_path(v,u)
    | ~ equal(u,skc5)
    | vertex(head_of(v)) ),
    inference(res,[status(thm),theory(equality)],[1890,1846]),
    [iquote('1:Res:1890.2,1846.1')] ).

cnf(1906,plain,
    ( ~ on_path(u,v)
    | ~ equal(v,skc5)
    | vertex(head_of(u)) ),
    inference(obv,[status(thm),theory(equality)],[1899]),
    [iquote('1:Obv:1899.0')] ).

cnf(1912,plain,
    ( ~ equal(skc5,skc5)
    | vertex(head_of(skc6)) ),
    inference(res,[status(thm),theory(equality)],[117,1906]),
    [iquote('1:Res:117.0,1906.0')] ).

cnf(1923,plain,
    vertex(head_of(skc6)),
    inference(obv,[status(thm),theory(equality)],[1912]),
    [iquote('1:Obv:1912.0')] ).

cnf(1982,plain,
    ( ~ vertex(skc8)
    | ~ equal(u,skc5)
    | ~ on_path(v,u)
    | in_path(tail_of(v),u) ),
    inference(eqr,[status(thm),theory(equality)],[1754]),
    [iquote('1:EqR:1754.1')] ).

cnf(1983,plain,
    ( ~ equal(u,skc5)
    | ~ on_path(v,u)
    | in_path(tail_of(v),u) ),
    inference(ssi,[status(thm)],[1982,116]),
    [iquote('1:SSi:1982.0,116.0')] ).

cnf(1997,plain,
    ( ~ equal(u,skc5)
    | ~ on_path(v,u)
    | ~ equal(u,skc5)
    | vertex(tail_of(v)) ),
    inference(res,[status(thm),theory(equality)],[1983,1846]),
    [iquote('1:Res:1983.2,1846.1')] ).

cnf(2004,plain,
    ( ~ on_path(u,v)
    | ~ equal(v,skc5)
    | vertex(tail_of(u)) ),
    inference(obv,[status(thm),theory(equality)],[1997]),
    [iquote('1:Obv:1997.0')] ).

cnf(2014,plain,
    ( ~ equal(skc5,skc5)
    | vertex(tail_of(skc7)) ),
    inference(res,[status(thm),theory(equality)],[119,2004]),
    [iquote('1:Res:119.0,2004.0')] ).

cnf(2026,plain,
    vertex(tail_of(skc7)),
    inference(obv,[status(thm),theory(equality)],[2014]),
    [iquote('1:Obv:2014.0')] ).

cnf(2071,plain,
    ( ~ vertex(head_of(u))
    | ~ vertex(v)
    | ~ equal(v,tail_of(w))
    | ~ precedes(w,u,skc5)
    | equal(v,head_of(u))
    | equal(head_of(skf12(v,head_of(u))),v) ),
    inference(eqr,[status(thm),theory(equality)],[330]),
    [iquote('0:EqR:330.2')] ).

cnf(5051,plain,
    ( ~ vertex(u)
    | ~ equal(u,tail_of(v))
    | ~ precedes(v,skc6,skc5)
    | equal(u,head_of(skc6))
    | equal(head_of(skf12(u,head_of(skc6))),u) ),
    inference(sor,[status(thm)],[2071,1923]),
    [iquote('1:SoR:2071.0,1923.0')] ).

cnf(5436,plain,
    ( ~ vertex(tail_of(u))
    | ~ precedes(u,skc6,skc5)
    | equal(tail_of(u),head_of(skc6))
    | equal(head_of(skf12(tail_of(u),head_of(skc6))),tail_of(u)) ),
    inference(eqr,[status(thm),theory(equality)],[5051]),
    [iquote('1:EqR:5051.1')] ).

cnf(5449,plain,
    ( ~ precedes(skc7,skc6,skc5)
    | equal(tail_of(skc7),head_of(skc6))
    | equal(head_of(skf12(tail_of(skc7),head_of(skc6))),tail_of(skc7)) ),
    inference(sor,[status(thm)],[5436,2026]),
    [iquote('1:SoR:5436.0,2026.0')] ).

cnf(5457,plain,
    equal(head_of(skf12(tail_of(skc7),head_of(skc6))),tail_of(skc7)),
    inference(mrr,[status(thm)],[5449,3,208]),
    [iquote('1:MRR:5449.0,5449.1,3.0,208.0')] ).

cnf(12526,plain,
    ( ~ vertex(head_of(skc6))
    | ~ vertex(tail_of(skc7))
    | ~ equal(head_of(skc6),head_of(skc6))
    | ~ equal(tail_of(skc7),tail_of(skc7))
    | equal(tail_of(skc7),head_of(skc6))
    | equal(skf12(tail_of(skc7),head_of(skc6)),skc6)
    | equal(tail_of(skc7),head_of(skc7)) ),
    inference(spr,[status(thm),theory(equality)],[378,5457]),
    [iquote('1:SpR:378.6,5457.0')] ).

cnf(12663,plain,
    ( ~ vertex(head_of(skc6))
    | ~ vertex(tail_of(skc7))
    | equal(tail_of(skc7),head_of(skc6))
    | equal(skf12(tail_of(skc7),head_of(skc6)),skc6)
    | equal(tail_of(skc7),head_of(skc7)) ),
    inference(obv,[status(thm),theory(equality)],[12526]),
    [iquote('1:Obv:12526.3')] ).

cnf(12664,plain,
    ( equal(tail_of(skc7),head_of(skc6))
    | equal(skf12(tail_of(skc7),head_of(skc6)),skc6)
    | equal(tail_of(skc7),head_of(skc7)) ),
    inference(ssi,[status(thm)],[12663,9,82,8,83]),
    [iquote('1:SSi:12663.1,12663.0,9.0,82.1,8.0,83.1')] ).

cnf(12665,plain,
    equal(skf12(tail_of(skc7),head_of(skc6)),skc6),
    inference(mrr,[status(thm)],[12664,208,197]),
    [iquote('1:MRR:12664.0,12664.2,208.0,197.0')] ).

cnf(12666,plain,
    equal(tail_of(skc7),head_of(skc6)),
    inference(rew,[status(thm),theory(equality)],[12665,5457]),
    [iquote('1:Rew:12665.0,5457.0')] ).

cnf(12808,plain,
    $false,
    inference(mrr,[status(thm)],[12666,208]),
    [iquote('1:MRR:12666.0,208.0')] ).

cnf(13153,plain,
    skP1(skc5,skf13(skc9,skc5,skc8),skc9),
    inference(spt,[spt(split,[position(s2)])],[1735]),
    [iquote('1:Spt:12808.0,1735.3')] ).

cnf(13162,plain,
    equal(path_cons(skf13(skc9,skc5,skc8),empty),skc5),
    inference(res,[status(thm),theory(equality)],[13153,30]),
    [iquote('1:Res:13153.0,30.0')] ).

cnf(13163,plain,
    equal(head_of(skf13(skc9,skc5,skc8)),skc9),
    inference(res,[status(thm),theory(equality)],[13153,26]),
    [iquote('1:Res:13153.0,26.0')] ).

cnf(13305,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ edge(skf13(skc9,skc5,skc8))
    | ~ equal(u,head_of(skf13(skc9,skc5,skc8)))
    | ~ equal(v,tail_of(skf13(skc9,skc5,skc8)))
    | ~ equal(w,skc5)
    | path(v,u,w) ),
    inference(spl,[status(thm),theory(equality)],[13162,66]),
    [iquote('1:SpL:13162.0,66.5')] ).

cnf(13328,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ edge(skf13(skc9,skc5,skc8))
    | ~ equal(u,skc9)
    | ~ equal(v,tail_of(skf13(skc9,skc5,skc8)))
    | ~ equal(w,skc5)
    | path(v,u,w) ),
    inference(rew,[status(thm),theory(equality)],[13163,13305]),
    [iquote('1:Rew:13163.0,13305.3')] ).

cnf(13329,plain,
    ( ~ vertex(u)
    | ~ vertex(v)
    | ~ equal(u,skc9)
    | ~ equal(v,tail_of(skf13(skc9,skc5,skc8)))
    | ~ equal(w,skc5)
    | path(v,u,w) ),
    inference(ssi,[status(thm)],[13328,7,115,116]),
    [iquote('1:SSi:13328.2,7.0,115.0,116.0')] ).

cnf(17558,plain,
    ( ~ vertex(u)
    | ~ vertex(tail_of(skf13(skc9,skc5,skc8)))
    | ~ equal(u,skc9)
    | ~ equal(v,skc5)
    | path(tail_of(skf13(skc9,skc5,skc8)),u,v) ),
    inference(eqr,[status(thm),theory(equality)],[13329]),
    [iquote('1:EqR:13329.3')] ).

cnf(17560,plain,
    ( ~ vertex(u)
    | ~ equal(u,skc9)
    | ~ equal(v,skc5)
    | path(tail_of(skf13(skc9,skc5,skc8)),u,v) ),
    inference(ssi,[status(thm)],[17558,9,7,115,116]),
    [iquote('1:SSi:17558.1,9.0,7.0,115.0,116.1')] ).

cnf(17577,plain,
    ( ~ vertex(u)
    | ~ equal(u,skc9)
    | ~ equal(v,skc5)
    | ~ on_path(w,v)
    | in_path(head_of(w),v) ),
    inference(res,[status(thm),theory(equality)],[17560,36]),
    [iquote('1:Res:17560.3,36.1')] ).

cnf(17578,plain,
    ( ~ vertex(u)
    | ~ equal(u,skc9)
    | ~ equal(v,skc5)
    | ~ on_path(w,v)
    | in_path(tail_of(w),v) ),
    inference(res,[status(thm),theory(equality)],[17560,37]),
    [iquote('1:Res:17560.3,37.1')] ).

cnf(17580,plain,
    ( ~ vertex(u)
    | ~ equal(u,skc9)
    | ~ equal(v,skc5)
    | ~ in_path(w,v)
    | vertex(w) ),
    inference(res,[status(thm),theory(equality)],[17560,33]),
    [iquote('1:Res:17560.3,33.1')] ).

cnf(17700,plain,
    ( ~ vertex(skc9)
    | ~ equal(u,skc5)
    | ~ in_path(v,u)
    | vertex(v) ),
    inference(eqr,[status(thm),theory(equality)],[17580]),
    [iquote('1:EqR:17580.1')] ).

cnf(17701,plain,
    ( ~ equal(u,skc5)
    | ~ in_path(v,u)
    | vertex(v) ),
    inference(ssi,[status(thm)],[17700,115]),
    [iquote('1:SSi:17700.0,115.0')] ).

cnf(17738,plain,
    ( ~ vertex(skc9)
    | ~ equal(u,skc5)
    | ~ on_path(v,u)
    | in_path(head_of(v),u) ),
    inference(eqr,[status(thm),theory(equality)],[17577]),
    [iquote('1:EqR:17577.1')] ).

cnf(17739,plain,
    ( ~ equal(u,skc5)
    | ~ on_path(v,u)
    | in_path(head_of(v),u) ),
    inference(ssi,[status(thm)],[17738,115]),
    [iquote('1:SSi:17738.0,115.0')] ).

cnf(17768,plain,
    ( ~ equal(u,skc5)
    | ~ on_path(v,u)
    | ~ equal(u,skc5)
    | vertex(head_of(v)) ),
    inference(res,[status(thm),theory(equality)],[17739,17701]),
    [iquote('1:Res:17739.2,17701.1')] ).

cnf(17781,plain,
    ( ~ on_path(u,v)
    | ~ equal(v,skc5)
    | vertex(head_of(u)) ),
    inference(obv,[status(thm),theory(equality)],[17768]),
    [iquote('1:Obv:17768.0')] ).

cnf(17830,plain,
    ( ~ equal(skc5,skc5)
    | vertex(head_of(skc6)) ),
    inference(res,[status(thm),theory(equality)],[117,17781]),
    [iquote('1:Res:117.0,17781.0')] ).

cnf(17843,plain,
    vertex(head_of(skc6)),
    inference(obv,[status(thm),theory(equality)],[17830]),
    [iquote('1:Obv:17830.0')] ).

cnf(17854,plain,
    ( ~ vertex(u)
    | ~ equal(u,tail_of(v))
    | ~ precedes(v,skc6,skc5)
    | equal(u,head_of(skc6))
    | equal(head_of(skf12(u,head_of(skc6))),u) ),
    inference(sor,[status(thm)],[2071,17843]),
    [iquote('1:SoR:2071.0,17843.0')] ).

cnf(17906,plain,
    ( ~ vertex(skc9)
    | ~ equal(u,skc5)
    | ~ on_path(v,u)
    | in_path(tail_of(v),u) ),
    inference(eqr,[status(thm),theory(equality)],[17578]),
    [iquote('1:EqR:17578.1')] ).

cnf(17907,plain,
    ( ~ equal(u,skc5)
    | ~ on_path(v,u)
    | in_path(tail_of(v),u) ),
    inference(ssi,[status(thm)],[17906,115]),
    [iquote('1:SSi:17906.0,115.0')] ).

cnf(17923,plain,
    ( ~ equal(u,skc5)
    | ~ on_path(v,u)
    | ~ equal(u,skc5)
    | vertex(tail_of(v)) ),
    inference(res,[status(thm),theory(equality)],[17907,17701]),
    [iquote('1:Res:17907.2,17701.1')] ).

cnf(17936,plain,
    ( ~ on_path(u,v)
    | ~ equal(v,skc5)
    | vertex(tail_of(u)) ),
    inference(obv,[status(thm),theory(equality)],[17923]),
    [iquote('1:Obv:17923.0')] ).

cnf(17975,plain,
    ( ~ equal(skc5,skc5)
    | vertex(tail_of(skc7)) ),
    inference(res,[status(thm),theory(equality)],[119,17936]),
    [iquote('1:Res:119.0,17936.0')] ).

cnf(17989,plain,
    vertex(tail_of(skc7)),
    inference(obv,[status(thm),theory(equality)],[17975]),
    [iquote('1:Obv:17975.0')] ).

cnf(21740,plain,
    ( ~ vertex(tail_of(u))
    | ~ precedes(u,skc6,skc5)
    | equal(tail_of(u),head_of(skc6))
    | equal(head_of(skf12(tail_of(u),head_of(skc6))),tail_of(u)) ),
    inference(eqr,[status(thm),theory(equality)],[17854]),
    [iquote('1:EqR:17854.1')] ).

cnf(21752,plain,
    ( ~ precedes(skc7,skc6,skc5)
    | equal(tail_of(skc7),head_of(skc6))
    | equal(head_of(skf12(tail_of(skc7),head_of(skc6))),tail_of(skc7)) ),
    inference(sor,[status(thm)],[21740,17989]),
    [iquote('1:SoR:21740.0,17989.0')] ).

cnf(21763,plain,
    equal(head_of(skf12(tail_of(skc7),head_of(skc6))),tail_of(skc7)),
    inference(mrr,[status(thm)],[21752,3,208]),
    [iquote('1:MRR:21752.0,21752.1,3.0,208.0')] ).

cnf(21795,plain,
    ( ~ vertex(head_of(skc6))
    | ~ vertex(tail_of(skc7))
    | ~ equal(head_of(skc6),head_of(skc6))
    | ~ equal(tail_of(skc7),tail_of(skc7))
    | equal(tail_of(skc7),head_of(skc6))
    | equal(skf12(tail_of(skc7),head_of(skc6)),skc6)
    | equal(tail_of(skc7),head_of(skc7)) ),
    inference(spr,[status(thm),theory(equality)],[378,21763]),
    [iquote('1:SpR:378.6,21763.0')] ).

cnf(21900,plain,
    ( ~ vertex(head_of(skc6))
    | ~ vertex(tail_of(skc7))
    | equal(tail_of(skc7),head_of(skc6))
    | equal(skf12(tail_of(skc7),head_of(skc6)),skc6)
    | equal(tail_of(skc7),head_of(skc7)) ),
    inference(obv,[status(thm),theory(equality)],[21795]),
    [iquote('1:Obv:21795.3')] ).

cnf(22046,plain,
    ( equal(tail_of(skc7),head_of(skc6))
    | equal(skf12(tail_of(skc7),head_of(skc6)),skc6)
    | equal(tail_of(skc7),head_of(skc7)) ),
    inference(ssi,[status(thm)],[21900,9,82,8,83]),
    [iquote('1:SSi:21900.1,21900.0,9.0,82.1,8.0,83.1')] ).

cnf(22047,plain,
    ( equal(skf12(tail_of(skc7),head_of(skc6)),skc6)
    | equal(tail_of(skc7),head_of(skc7)) ),
    inference(mrr,[status(thm)],[22046,208]),
    [iquote('1:MRR:22046.0,208.0')] ).

cnf(22048,plain,
    equal(skf12(tail_of(skc7),head_of(skc6)),skc6),
    inference(mrr,[status(thm)],[22047,197]),
    [iquote('1:MRR:22047.1,197.0')] ).

cnf(22049,plain,
    equal(tail_of(skc7),head_of(skc6)),
    inference(rew,[status(thm),theory(equality)],[22048,21763]),
    [iquote('1:Rew:22048.0,21763.0')] ).

cnf(22055,plain,
    $false,
    inference(mrr,[status(thm)],[22049,208]),
    [iquote('1:MRR:22049.0,208.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRA008+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.11/0.12  % Command  : run_spass %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  : 600
% 0.12/0.33  % DateTime : Tue May 31 03:12:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 45.05/45.24  
% 45.05/45.24  SPASS V 3.9 
% 45.05/45.24  SPASS beiseite: Proof found.
% 45.05/45.24  % SZS status Theorem
% 45.05/45.24  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 45.05/45.24  SPASS derived 13612 clauses, backtracked 908 clauses, performed 14 splits and kept 7835 clauses.
% 45.05/45.24  SPASS allocated 125270 KBytes.
% 45.05/45.24  SPASS spent	0:0:44.88 on the problem.
% 45.05/45.24  		0:00:00.03 for the input.
% 45.05/45.24  		0:00:00.07 for the FLOTTER CNF translation.
% 45.05/45.24  		0:00:00.45 for inferences.
% 45.05/45.24  		0:00:00.85 for the backtracking.
% 45.05/45.24  		0:0:43.33 for the reduction.
% 45.05/45.24  
% 45.05/45.24  
% 45.05/45.24  Here is a proof with depth 15, length 161 :
% 45.05/45.24  % SZS output start Refutation
% See solution above
% 46.67/46.87  Formulae used in the proof : sequential_is_triangle complete_properties sequential_defn path_properties edge_ends_are_vertices shortest_path_defn in_path_properties on_path_properties precedes_properties shortest_path_properties triangle_defn precedes_defn path_defn
% 46.67/46.87  
%------------------------------------------------------------------------------