TSTP Solution File: GRA004+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRA004+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 0.37s 0.53s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of clauses : 51 ( 22 unt; 5 nHn; 51 RR)
% Number of literals : 110 ( 0 equ; 69 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
precedes(skc8,skc7,skc6),
file('GRA004+1.p',unknown),
[] ).
cnf(2,axiom,
shortest_path(skc10,skc11,skc6),
file('GRA004+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ shortest_path(u,v,w)
| path(u,v,w) ),
file('GRA004+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ on_path(u,v)
| ~ path(w,x,v)
| edge(u) ),
file('GRA004+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ precedes(u,v,w)
| ~ path(x,y,w)
| on_path(u,w) ),
file('GRA004+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ precedes(u,v,w)
| ~ path(x,y,w)
| on_path(v,w) ),
file('GRA004+1.p',unknown),
[] ).
cnf(39,axiom,
( equal(head_of(skc8),head_of(skc7))
| equal(tail_of(skc9),tail_of(skc8))
| equal(head_of(skc7),tail_of(skc8)) ),
file('GRA004+1.p',unknown),
[] ).
cnf(40,axiom,
( equal(head_of(skc8),head_of(skc7))
| equal(head_of(skc9),head_of(skc7))
| equal(head_of(skc7),tail_of(skc8)) ),
file('GRA004+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ shortest_path(u,v,w)
| ~ precedes(x,y,w)
| ~ precedes(y,x,w) ),
file('GRA004+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ edge(u)
| ~ edge(v)
| ~ equal(head_of(u),tail_of(v))
| sequential(u,v)
| equal(u,v) ),
file('GRA004+1.p',unknown),
[] ).
cnf(57,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('GRA004+1.p',unknown),
[] ).
cnf(63,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('GRA004+1.p',unknown),
[] ).
cnf(69,plain,
( ~ on_path(u,v)
| ~ sequential(u,w)
| ~ path(x,y,v)
| ~ precedes(w,z,v)
| precedes(u,z,v) ),
inference(mrr,[status(thm)],[63,36]),
[iquote('0:MRR:63.4,36.2')] ).
cnf(72,plain,
path(skc10,skc11,skc6),
inference(res,[status(thm),theory(equality)],[2,25]),
[iquote('0:Res:2.0,25.0')] ).
cnf(74,plain,
( ~ precedes(u,v,skc6)
| ~ precedes(v,u,skc6) ),
inference(res,[status(thm),theory(equality)],[2,43]),
[iquote('0:Res:2.0,43.2')] ).
cnf(76,plain,
( ~ equal(head_of(u),head_of(v))
| ~ equal(tail_of(u),tail_of(w))
| ~ precedes(w,v,skc6) ),
inference(res,[status(thm),theory(equality)],[2,57]),
[iquote('0:Res:2.0,57.3')] ).
cnf(79,plain,
( ~ path(u,v,skc6)
| on_path(skc8,skc6) ),
inference(res,[status(thm),theory(equality)],[1,35]),
[iquote('0:Res:1.0,35.1')] ).
cnf(80,plain,
( ~ path(u,v,skc6)
| on_path(skc7,skc6) ),
inference(res,[status(thm),theory(equality)],[1,36]),
[iquote('0:Res:1.0,36.1')] ).
cnf(83,plain,
( ~ on_path(u,skc6)
| ~ sequential(u,skc8)
| ~ path(v,w,skc6)
| precedes(u,skc7,skc6) ),
inference(res,[status(thm),theory(equality)],[1,69]),
[iquote('0:Res:1.0,69.1')] ).
cnf(88,plain,
( ~ equal(head_of(u),head_of(skc7))
| ~ equal(tail_of(u),tail_of(skc8)) ),
inference(res,[status(thm),theory(equality)],[1,76]),
[iquote('0:Res:1.0,76.2')] ).
cnf(94,plain,
on_path(skc7,skc6),
inference(res,[status(thm),theory(equality)],[72,80]),
[iquote('0:Res:72.0,80.0')] ).
cnf(95,plain,
on_path(skc8,skc6),
inference(res,[status(thm),theory(equality)],[72,79]),
[iquote('0:Res:72.0,79.0')] ).
cnf(103,plain,
( ~ on_path(u,skc6)
| edge(u) ),
inference(res,[status(thm),theory(equality)],[72,29]),
[iquote('0:Res:72.0,29.1')] ).
cnf(104,plain,
edge(skc7),
inference(res,[status(thm),theory(equality)],[94,103]),
[iquote('0:Res:94.0,103.0')] ).
cnf(105,plain,
edge(skc8),
inference(res,[status(thm),theory(equality)],[95,103]),
[iquote('0:Res:95.0,103.0')] ).
cnf(106,plain,
~ equal(tail_of(skc8),tail_of(skc7)),
inference(eqr,[status(thm),theory(equality)],[88]),
[iquote('0:EqR:88.0')] ).
cnf(126,plain,
equal(head_of(skc7),tail_of(skc8)),
inference(spt,[spt(split,[position(s1)])],[40]),
[iquote('1:Spt:40.2')] ).
cnf(175,plain,
( ~ on_path(u,skc6)
| ~ sequential(u,skc8)
| precedes(u,skc7,skc6) ),
inference(res,[status(thm),theory(equality)],[72,83]),
[iquote('0:Res:72.0,83.2')] ).
cnf(177,plain,
( ~ on_path(u,skc6)
| ~ sequential(u,skc8)
| ~ precedes(skc7,u,skc6) ),
inference(res,[status(thm),theory(equality)],[175,74]),
[iquote('0:Res:175.2,74.0')] ).
cnf(186,plain,
( ~ on_path(skc7,skc6)
| ~ sequential(skc7,skc8)
| ~ on_path(skc7,skc6)
| ~ sequential(skc7,skc8) ),
inference(res,[status(thm),theory(equality)],[175,177]),
[iquote('0:Res:175.2,177.2')] ).
cnf(187,plain,
( ~ on_path(skc7,skc6)
| ~ sequential(skc7,skc8) ),
inference(obv,[status(thm),theory(equality)],[186]),
[iquote('0:Obv:186.1')] ).
cnf(212,plain,
~ sequential(skc7,skc8),
inference(mrr,[status(thm)],[187,94]),
[iquote('0:MRR:187.0,94.0')] ).
cnf(217,plain,
( ~ edge(skc7)
| ~ edge(skc8)
| ~ equal(head_of(skc7),tail_of(skc8))
| equal(skc8,skc7) ),
inference(res,[status(thm),theory(equality)],[48,212]),
[iquote('0:Res:48.3,212.0')] ).
cnf(218,plain,
( ~ edge(skc7)
| ~ edge(skc8)
| ~ equal(tail_of(skc8),tail_of(skc8))
| equal(skc8,skc7) ),
inference(rew,[status(thm),theory(equality)],[126,217]),
[iquote('1:Rew:126.0,217.2')] ).
cnf(219,plain,
( ~ edge(skc7)
| ~ edge(skc8)
| equal(skc8,skc7) ),
inference(obv,[status(thm),theory(equality)],[218]),
[iquote('1:Obv:218.2')] ).
cnf(220,plain,
equal(skc8,skc7),
inference(ssi,[status(thm)],[219,105,104]),
[iquote('1:SSi:219.1,219.0,105.0,104.0')] ).
cnf(228,plain,
~ equal(tail_of(skc7),tail_of(skc7)),
inference(rew,[status(thm),theory(equality)],[220,106]),
[iquote('1:Rew:220.0,106.0')] ).
cnf(242,plain,
$false,
inference(obv,[status(thm),theory(equality)],[228]),
[iquote('1:Obv:228.0')] ).
cnf(245,plain,
~ equal(head_of(skc7),tail_of(skc8)),
inference(spt,[spt(split,[position(sa)])],[242,126]),
[iquote('1:Spt:242.0,40.2,126.0')] ).
cnf(246,plain,
( equal(head_of(skc8),head_of(skc7))
| equal(head_of(skc9),head_of(skc7)) ),
inference(spt,[spt(split,[position(s2)])],[40]),
[iquote('1:Spt:242.0,40.0,40.1')] ).
cnf(247,plain,
( equal(head_of(skc8),head_of(skc7))
| equal(tail_of(skc9),tail_of(skc8)) ),
inference(mrr,[status(thm)],[39,245]),
[iquote('1:MRR:39.2,245.0')] ).
cnf(263,plain,
equal(head_of(skc8),head_of(skc7)),
inference(spt,[spt(split,[position(s2s1)])],[247]),
[iquote('2:Spt:247.0')] ).
cnf(283,plain,
( ~ equal(head_of(skc7),head_of(skc7))
| ~ equal(tail_of(skc8),tail_of(skc8)) ),
inference(spl,[status(thm),theory(equality)],[263,88]),
[iquote('2:SpL:263.0,88.0')] ).
cnf(284,plain,
$false,
inference(obv,[status(thm),theory(equality)],[283]),
[iquote('2:Obv:283.1')] ).
cnf(285,plain,
~ equal(head_of(skc8),head_of(skc7)),
inference(spt,[spt(split,[position(s2sa)])],[284,263]),
[iquote('2:Spt:284.0,247.0,263.0')] ).
cnf(286,plain,
equal(tail_of(skc9),tail_of(skc8)),
inference(spt,[spt(split,[position(s2s2)])],[247]),
[iquote('2:Spt:284.0,247.1')] ).
cnf(287,plain,
equal(head_of(skc9),head_of(skc7)),
inference(mrr,[status(thm)],[246,285]),
[iquote('2:MRR:246.0,285.0')] ).
cnf(303,plain,
( ~ equal(head_of(skc7),head_of(skc7))
| ~ equal(tail_of(skc9),tail_of(skc8)) ),
inference(spl,[status(thm),theory(equality)],[287,88]),
[iquote('2:SpL:287.0,88.0')] ).
cnf(306,plain,
~ equal(tail_of(skc9),tail_of(skc8)),
inference(obv,[status(thm),theory(equality)],[303]),
[iquote('2:Obv:303.0')] ).
cnf(307,plain,
~ equal(tail_of(skc8),tail_of(skc8)),
inference(rew,[status(thm),theory(equality)],[286,306]),
[iquote('2:Rew:286.0,306.0')] ).
cnf(308,plain,
$false,
inference(obv,[status(thm),theory(equality)],[307]),
[iquote('2:Obv:307.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRA004+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 03:42:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.37/0.53
% 0.37/0.53 SPASS V 3.9
% 0.37/0.53 SPASS beiseite: Proof found.
% 0.37/0.53 % SZS status Theorem
% 0.37/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.53 SPASS derived 189 clauses, backtracked 45 clauses, performed 5 splits and kept 215 clauses.
% 0.37/0.53 SPASS allocated 98359 KBytes.
% 0.37/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.37/0.53 0:00:00.04 for the input.
% 0.37/0.53 0:00:00.08 for the FLOTTER CNF translation.
% 0.37/0.53 0:00:00.00 for inferences.
% 0.37/0.53 0:00:00.00 for the backtracking.
% 0.37/0.53 0:00:00.02 for the reduction.
% 0.37/0.53
% 0.37/0.53
% 0.37/0.53 Here is a proof with depth 5, length 51 :
% 0.37/0.53 % SZS output start Refutation
% See solution above
% 0.37/0.53 Formulae used in the proof : shortest_path_properties_lemma shortest_path_defn on_path_properties precedes_properties shortest_path_properties sequential_defn precedes_defn
% 0.37/0.53
%------------------------------------------------------------------------------