TSTP Solution File: GRA007+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRA007+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 0.41s 0.58s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of clauses : 58 ( 14 unt; 14 nHn; 58 RR)
% Number of literals : 183 ( 0 equ; 114 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 10 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('GRA007+1.p',unknown),
[] ).
cnf(2,axiom,
precedes(skc7,skc6,skc5),
file('GRA007+1.p',unknown),
[] ).
cnf(3,axiom,
shortest_path(skc8,skc9,skc5),
file('GRA007+1.p',unknown),
[] ).
cnf(4,axiom,
edge(skf12(u,v)),
file('GRA007+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ edge(u)
| vertex(head_of(u)) ),
file('GRA007+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ edge(u)
| vertex(tail_of(u)) ),
file('GRA007+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ skP0(u,v,w)
| equal(w,head_of(v)) ),
file('GRA007+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ skP0(u,v,w)
| equal(u,tail_of(v)) ),
file('GRA007+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ shortest_path(u,v,w)
| path(u,v,w) ),
file('GRA007+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ on_path(u,v)
| ~ path(w,x,v)
| edge(u) ),
file('GRA007+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ precedes(u,v,w)
| ~ path(x,y,w)
| on_path(u,w) ),
file('GRA007+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ precedes(u,v,w)
| ~ path(x,y,w)
| on_path(v,w) ),
file('GRA007+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ edge(u)
| ~ equal(head_of(u),tail_of(skc7))
| ~ equal(tail_of(u),head_of(skc6)) ),
file('GRA007+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ edge(u)
| ~ edge(v)
| ~ equal(head_of(u),tail_of(v))
| sequential(u,v)
| equal(u,v) ),
file('GRA007+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('GRA007+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ vertex(u)
| ~ vertex(v)
| ~ complete
| equal(tail_of(skf12(u,v)),u)
| equal(u,v)
| skP0(v,skf12(u,v),u) ),
file('GRA007+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ vertex(u)
| ~ vertex(v)
| ~ complete
| equal(head_of(skf12(u,v)),v)
| equal(u,v)
| skP0(v,skf12(u,v),u) ),
file('GRA007+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('GRA007+1.p',unknown),
[] ).
cnf(68,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)],[60,1]),
[iquote('0:MRR:60.2,1.0')] ).
cnf(69,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)],[61,1]),
[iquote('0:MRR:61.2,1.0')] ).
cnf(71,plain,
( ~ on_path(u,v)
| ~ sequential(u,w)
| ~ path(x,y,v)
| ~ precedes(w,z,v)
| precedes(u,z,v) ),
inference(mrr,[status(thm)],[63,37]),
[iquote('0:MRR:63.4,37.2')] ).
cnf(74,plain,
path(skc8,skc9,skc5),
inference(res,[status(thm),theory(equality)],[3,26]),
[iquote('0:Res:3.0,26.0')] ).
cnf(78,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)],[3,57]),
[iquote('0:Res:3.0,57.3')] ).
cnf(81,plain,
( ~ path(u,v,skc5)
| on_path(skc7,skc5) ),
inference(res,[status(thm),theory(equality)],[2,36]),
[iquote('0:Res:2.0,36.1')] ).
cnf(82,plain,
( ~ path(u,v,skc5)
| on_path(skc6,skc5) ),
inference(res,[status(thm),theory(equality)],[2,37]),
[iquote('0:Res:2.0,37.1')] ).
cnf(85,plain,
( ~ on_path(u,skc5)
| ~ sequential(u,skc7)
| ~ path(v,w,skc5)
| precedes(u,skc6,skc5) ),
inference(res,[status(thm),theory(equality)],[2,71]),
[iquote('0:Res:2.0,71.1')] ).
cnf(92,plain,
( ~ equal(head_of(u),head_of(skc6))
| ~ equal(tail_of(u),tail_of(skc7)) ),
inference(res,[status(thm),theory(equality)],[2,78]),
[iquote('0:Res:2.0,78.2')] ).
cnf(98,plain,
on_path(skc6,skc5),
inference(res,[status(thm),theory(equality)],[74,82]),
[iquote('0:Res:74.0,82.0')] ).
cnf(99,plain,
on_path(skc7,skc5),
inference(res,[status(thm),theory(equality)],[74,81]),
[iquote('0:Res:74.0,81.0')] ).
cnf(107,plain,
( ~ on_path(u,skc5)
| edge(u) ),
inference(res,[status(thm),theory(equality)],[74,30]),
[iquote('0:Res:74.0,30.1')] ).
cnf(108,plain,
edge(skc6),
inference(res,[status(thm),theory(equality)],[98,107]),
[iquote('0:Res:98.0,107.0')] ).
cnf(109,plain,
edge(skc7),
inference(res,[status(thm),theory(equality)],[99,107]),
[iquote('0:Res:99.0,107.0')] ).
cnf(112,plain,
~ equal(tail_of(skc7),tail_of(skc6)),
inference(eqr,[status(thm),theory(equality)],[92]),
[iquote('0:EqR:92.0')] ).
cnf(168,plain,
( ~ on_path(u,skc5)
| ~ sequential(u,skc7)
| precedes(u,skc6,skc5) ),
inference(res,[status(thm),theory(equality)],[74,85]),
[iquote('0:Res:74.0,85.2')] ).
cnf(182,plain,
( ~ equal(tail_of(u),tail_of(v))
| ~ precedes(v,u,skc5) ),
inference(eqr,[status(thm),theory(equality)],[78]),
[iquote('0:EqR:78.0')] ).
cnf(186,plain,
( ~ on_path(u,skc5)
| ~ sequential(u,skc7)
| ~ equal(tail_of(skc6),tail_of(u)) ),
inference(res,[status(thm),theory(equality)],[168,182]),
[iquote('0:Res:168.2,182.1')] ).
cnf(187,plain,
( ~ sequential(skc6,skc7)
| ~ equal(tail_of(skc6),tail_of(skc6)) ),
inference(res,[status(thm),theory(equality)],[98,186]),
[iquote('0:Res:98.0,186.0')] ).
cnf(190,plain,
~ sequential(skc6,skc7),
inference(obv,[status(thm),theory(equality)],[187]),
[iquote('0:Obv:187.1')] ).
cnf(242,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)],[69,22]),
[iquote('0:Res:69.4,22.0')] ).
cnf(243,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)],[69,23]),
[iquote('0:Res:69.4,23.0')] ).
cnf(276,plain,
( ~ vertex(u)
| ~ vertex(v)
| ~ equal(u,head_of(skc6))
| ~ equal(tail_of(skf12(v,u)),tail_of(skc7))
| equal(v,u)
| equal(head_of(skf12(v,u)),v) ),
inference(spl,[status(thm),theory(equality)],[242,92]),
[iquote('0:SpL:242.3,92.0')] ).
cnf(283,plain,
( ~ vertex(u)
| ~ vertex(v)
| ~ edge(skf12(v,u))
| ~ equal(v,tail_of(skc7))
| ~ equal(tail_of(skf12(v,u)),head_of(skc6))
| equal(v,u)
| equal(head_of(skf12(v,u)),u) ),
inference(spl,[status(thm),theory(equality)],[242,40]),
[iquote('0:SpL:242.4,40.1')] ).
cnf(295,plain,
( ~ vertex(u)
| ~ vertex(v)
| ~ edge(skf12(v,u))
| ~ equal(v,tail_of(skc7))
| ~ equal(u,head_of(skc6))
| equal(v,u)
| equal(head_of(skf12(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[243,283]),
[iquote('0:Rew:243.4,283.4')] ).
cnf(296,plain,
( ~ vertex(u)
| ~ vertex(v)
| ~ equal(v,tail_of(skc7))
| ~ equal(u,head_of(skc6))
| equal(v,u)
| equal(head_of(skf12(v,u)),u) ),
inference(ssi,[status(thm)],[295,4]),
[iquote('0:SSi:295.2,4.0')] ).
cnf(301,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)],[68,22]),
[iquote('0:Res:68.4,22.0')] ).
cnf(309,plain,
( ~ vertex(u)
| ~ vertex(v)
| ~ equal(u,head_of(skc6))
| ~ equal(v,tail_of(skc7))
| equal(v,u)
| equal(head_of(skf12(v,u)),v) ),
inference(rew,[status(thm),theory(equality)],[301,276]),
[iquote('0:Rew:301.3,276.3')] ).
cnf(313,plain,
( ~ vertex(u)
| ~ vertex(v)
| ~ equal(u,head_of(skc6))
| ~ equal(v,tail_of(skc7))
| equal(v,u)
| equal(u,v) ),
inference(rew,[status(thm),theory(equality)],[296,309]),
[iquote('0:Rew:296.5,309.5')] ).
cnf(314,plain,
( ~ vertex(u)
| ~ vertex(v)
| ~ equal(u,head_of(skc6))
| ~ equal(v,tail_of(skc7))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[313]),
[iquote('0:Obv:313.4')] ).
cnf(385,plain,
( ~ vertex(head_of(skc6))
| ~ vertex(u)
| ~ equal(u,tail_of(skc7))
| equal(head_of(skc6),u) ),
inference(eqr,[status(thm),theory(equality)],[314]),
[iquote('0:EqR:314.2')] ).
cnf(386,plain,
( ~ vertex(u)
| ~ equal(u,tail_of(skc7))
| equal(head_of(skc6),u) ),
inference(ssi,[status(thm)],[385,6,108]),
[iquote('0:SSi:385.0,6.0,108.1')] ).
cnf(498,plain,
( ~ edge(skc6)
| ~ edge(skc7)
| ~ equal(head_of(skc6),tail_of(skc7))
| equal(skc7,skc6) ),
inference(res,[status(thm),theory(equality)],[48,190]),
[iquote('0:Res:48.3,190.0')] ).
cnf(499,plain,
( ~ equal(head_of(skc6),tail_of(skc7))
| equal(skc7,skc6) ),
inference(ssi,[status(thm)],[498,109,108]),
[iquote('0:SSi:498.1,498.0,109.0,108.0')] ).
cnf(661,plain,
( ~ vertex(u)
| ~ equal(u,tail_of(skc7))
| ~ equal(u,tail_of(skc7))
| equal(skc7,skc6) ),
inference(spl,[status(thm),theory(equality)],[386,499]),
[iquote('0:SpL:386.2,499.0')] ).
cnf(691,plain,
( ~ vertex(u)
| ~ equal(u,tail_of(skc7))
| equal(skc7,skc6) ),
inference(obv,[status(thm),theory(equality)],[661]),
[iquote('0:Obv:661.1')] ).
cnf(735,plain,
( ~ vertex(tail_of(skc7))
| equal(skc7,skc6) ),
inference(eqr,[status(thm),theory(equality)],[691]),
[iquote('0:EqR:691.1')] ).
cnf(736,plain,
equal(skc7,skc6),
inference(ssi,[status(thm)],[735,7,109]),
[iquote('0:SSi:735.0,7.0,109.1')] ).
cnf(751,plain,
~ equal(tail_of(skc6),tail_of(skc6)),
inference(rew,[status(thm),theory(equality)],[736,112]),
[iquote('0:Rew:736.0,112.0')] ).
cnf(853,plain,
$false,
inference(obv,[status(thm),theory(equality)],[751]),
[iquote('0:Obv:751.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA007+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.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 : Mon May 30 23:03:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.58
% 0.41/0.58 SPASS V 3.9
% 0.41/0.58 SPASS beiseite: Proof found.
% 0.41/0.58 % SZS status Theorem
% 0.41/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.58 SPASS derived 649 clauses, backtracked 83 clauses, performed 3 splits and kept 406 clauses.
% 0.41/0.58 SPASS allocated 98529 KBytes.
% 0.41/0.58 SPASS spent 0:00:00.23 on the problem.
% 0.41/0.58 0:00:00.04 for the input.
% 0.41/0.58 0:00:00.07 for the FLOTTER CNF translation.
% 0.41/0.58 0:00:00.01 for inferences.
% 0.41/0.58 0:00:00.00 for the backtracking.
% 0.41/0.58 0:00:00.09 for the reduction.
% 0.41/0.58
% 0.41/0.58
% 0.41/0.58 Here is a proof with depth 7, length 58 :
% 0.41/0.58 % SZS output start Refutation
% See solution above
% 0.41/0.58 Formulae used in the proof : back_edge complete_properties shortest_path_defn path_properties edge_ends_are_vertices on_path_properties precedes_properties sequential_defn shortest_path_properties precedes_defn
% 0.41/0.58
%------------------------------------------------------------------------------