TSTP Solution File: GRA003+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 07:22:08 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 33 ( 16 unt; 3 nHn; 33 RR)
% Number of literals : 65 ( 0 equ; 38 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
shortest_path(skc9,skc8,skc7),
file('GRA003+1.p',unknown),
[] ).
cnf(2,axiom,
precedes(skc5,skc6,skc7),
file('GRA003+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ path(u,v,w)
| vertex(u) ),
file('GRA003+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ path(u,v,w)
| vertex(v) ),
file('GRA003+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ shortest_path(u,v,w)
| path(u,v,w) ),
file('GRA003+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ equal(u,v)
| ~ shortest_path(u,v,w) ),
file('GRA003+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ on_path(u,v)
| ~ path(w,x,v)
| edge(u) ),
file('GRA003+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ precedes(u,v,w)
| ~ path(x,y,w)
| on_path(u,w) ),
file('GRA003+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ precedes(u,v,w)
| ~ path(x,y,w)
| on_path(v,w) ),
file('GRA003+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ shortest_path(u,v,w)
| ~ precedes(x,y,w)
| ~ precedes(y,x,w) ),
file('GRA003+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ vertex(skc9)
| ~ vertex(skc8)
| ~ edge(skc5)
| ~ edge(skc6)
| ~ path(skc9,skc8,skc7)
| equal(skc9,skc8)
| equal(skc6,skc5) ),
file('GRA003+1.p',unknown),
[] ).
cnf(67,plain,
( ~ edge(skc5)
| ~ edge(skc6)
| ~ path(skc9,skc8,skc7)
| equal(skc9,skc8)
| equal(skc6,skc5) ),
inference(mrr,[status(thm)],[60,13,14]),
[iquote('0:MRR:60.0,60.1,13.1,14.1')] ).
cnf(74,plain,
( ~ path(u,v,skc7)
| on_path(skc5,skc7) ),
inference(res,[status(thm),theory(equality)],[2,35]),
[iquote('0:Res:2.0,35.1')] ).
cnf(75,plain,
( ~ path(u,v,skc7)
| on_path(skc6,skc7) ),
inference(res,[status(thm),theory(equality)],[2,36]),
[iquote('0:Res:2.0,36.1')] ).
cnf(76,plain,
( ~ precedes(skc6,skc5,skc7)
| ~ shortest_path(u,v,skc7) ),
inference(res,[status(thm),theory(equality)],[2,41]),
[iquote('0:Res:2.0,41.0')] ).
cnf(82,plain,
path(skc9,skc8,skc7),
inference(res,[status(thm),theory(equality)],[1,25]),
[iquote('0:Res:1.0,25.0')] ).
cnf(83,plain,
~ equal(skc9,skc8),
inference(res,[status(thm),theory(equality)],[1,26]),
[iquote('0:Res:1.0,26.1')] ).
cnf(87,plain,
( ~ edge(skc5)
| ~ edge(skc6)
| equal(skc9,skc8)
| equal(skc6,skc5) ),
inference(mrr,[status(thm)],[67,82]),
[iquote('0:MRR:67.2,82.0')] ).
cnf(88,plain,
( ~ edge(skc6)
| ~ edge(skc5)
| equal(skc6,skc5) ),
inference(mrr,[status(thm)],[87,83]),
[iquote('0:MRR:87.2,83.0')] ).
cnf(89,plain,
~ precedes(skc6,skc5,skc7),
inference(res,[status(thm),theory(equality)],[1,76]),
[iquote('0:Res:1.0,76.1')] ).
cnf(94,plain,
equal(skc6,skc5),
inference(spt,[spt(split,[position(s1)])],[88]),
[iquote('1:Spt:88.2')] ).
cnf(98,plain,
precedes(skc5,skc5,skc7),
inference(rew,[status(thm),theory(equality)],[94,2]),
[iquote('1:Rew:94.0,2.0')] ).
cnf(99,plain,
~ precedes(skc5,skc5,skc7),
inference(rew,[status(thm),theory(equality)],[94,89]),
[iquote('1:Rew:94.0,89.0')] ).
cnf(104,plain,
$false,
inference(mrr,[status(thm)],[99,98]),
[iquote('1:MRR:99.0,98.0')] ).
cnf(111,plain,
~ equal(skc6,skc5),
inference(spt,[spt(split,[position(sa)])],[104,94]),
[iquote('1:Spt:104.0,88.2,94.0')] ).
cnf(112,plain,
( ~ edge(skc6)
| ~ edge(skc5) ),
inference(spt,[spt(split,[position(s2)])],[88]),
[iquote('1:Spt:104.0,88.0,88.1')] ).
cnf(115,plain,
on_path(skc5,skc7),
inference(res,[status(thm),theory(equality)],[82,74]),
[iquote('0:Res:82.0,74.0')] ).
cnf(116,plain,
on_path(skc6,skc7),
inference(res,[status(thm),theory(equality)],[82,75]),
[iquote('0:Res:82.0,75.0')] ).
cnf(124,plain,
( ~ on_path(u,skc7)
| edge(u) ),
inference(res,[status(thm),theory(equality)],[82,29]),
[iquote('0:Res:82.0,29.1')] ).
cnf(125,plain,
edge(skc5),
inference(res,[status(thm),theory(equality)],[115,124]),
[iquote('0:Res:115.0,124.0')] ).
cnf(126,plain,
edge(skc6),
inference(res,[status(thm),theory(equality)],[116,124]),
[iquote('0:Res:116.0,124.0')] ).
cnf(127,plain,
~ edge(skc6),
inference(mrr,[status(thm)],[112,125]),
[iquote('1:MRR:112.1,125.0')] ).
cnf(128,plain,
$false,
inference(mrr,[status(thm)],[127,126]),
[iquote('1:MRR:127.0,126.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue May 31 02:41:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 46 clauses, backtracked 11 clauses, performed 1 splits and kept 113 clauses.
% 0.20/0.49 SPASS allocated 98253 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.49 0:00:00.03 for the input.
% 0.20/0.49 0:00:00.08 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.00 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.01 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 3, length 33 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : vertices_and_edges path_properties shortest_path_defn on_path_properties precedes_properties shortest_path_properties
% 0.20/0.49
%------------------------------------------------------------------------------