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