TSTP Solution File: GRA002+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 0.42s 0.60s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 37 ( 16 unt; 6 nHn; 37 RR)
% Number of literals : 83 ( 0 equ; 44 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
complete,
file('GRA002+3.p',unknown),
[] ).
cnf(2,axiom,
shortest_path(skc4,skc5,skc3),
file('GRA002+3.p',unknown),
[] ).
cnf(12,axiom,
less_or_equal(number_of_in(u,v),number_of_in(u,graph)),
file('GRA002+3.p',unknown),
[] ).
cnf(20,axiom,
~ less_or_equal(minus(length_of(skc3),n1),number_of_in(triangles,graph)),
file('GRA002+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ shortest_path(u,v,w)
| path(u,v,w) ),
file('GRA002+3.p',unknown),
[] ).
cnf(30,axiom,
( ~ on_path(u,v)
| ~ path(w,x,v)
| edge(u) ),
file('GRA002+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ path(u,v,w)
| equal(minus(length_of(w),n1),number_of_in(sequential_pairs,w)) ),
file('GRA002+3.p',unknown),
[] ).
cnf(43,axiom,
( ~ path(u,v,w)
| on_path(skf12(w),w)
| equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
file('GRA002+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ path(u,v,w)
| on_path(skf10(w),w)
| equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
file('GRA002+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ path(u,v,w)
| sequential(skf12(w),skf10(w))
| equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
file('GRA002+3.p',unknown),
[] ).
cnf(49,axiom,
( ~ path(u,v,w)
| ~ triangle(skf12(w),skf10(w),x)
| equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
file('GRA002+3.p',unknown),
[] ).
cnf(54,axiom,
( ~ on_path(u,v)
| ~ on_path(w,v)
| ~ sequential(w,u)
| ~ path(x,y,v)
| precedes(w,u,v) ),
file('GRA002+3.p',unknown),
[] ).
cnf(57,axiom,
( ~ complete
| ~ precedes(u,v,w)
| ~ sequential(u,v)
| ~ shortest_path(x,y,w)
| triangle(u,v,skf13(v,u)) ),
file('GRA002+3.p',unknown),
[] ).
cnf(68,plain,
( ~ sequential(u,v)
| ~ shortest_path(w,x,y)
| ~ precedes(u,v,y)
| triangle(u,v,skf13(v,u)) ),
inference(mrr,[status(thm)],[57,1]),
[iquote('0:MRR:57.0,1.0')] ).
cnf(75,plain,
path(skc4,skc5,skc3),
inference(res,[status(thm),theory(equality)],[2,26]),
[iquote('0:Res:2.0,26.0')] ).
cnf(77,plain,
( ~ sequential(u,v)
| ~ precedes(u,v,skc3)
| triangle(u,v,skf13(v,u)) ),
inference(res,[status(thm),theory(equality)],[2,68]),
[iquote('0:Res:2.0,68.2')] ).
cnf(91,plain,
( ~ on_path(u,skc3)
| edge(u) ),
inference(res,[status(thm),theory(equality)],[75,30]),
[iquote('0:Res:75.0,30.1')] ).
cnf(96,plain,
equal(minus(length_of(skc3),n1),number_of_in(sequential_pairs,skc3)),
inference(res,[status(thm),theory(equality)],[75,33]),
[iquote('0:Res:75.0,33.0')] ).
cnf(97,plain,
~ less_or_equal(number_of_in(sequential_pairs,skc3),number_of_in(triangles,graph)),
inference(rew,[status(thm),theory(equality)],[96,20]),
[iquote('0:Rew:96.0,20.0')] ).
cnf(123,plain,
( on_path(skf10(skc3),skc3)
| equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)) ),
inference(res,[status(thm),theory(equality)],[75,44]),
[iquote('0:Res:75.0,44.0')] ).
cnf(124,plain,
( on_path(skf12(skc3),skc3)
| equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)) ),
inference(res,[status(thm),theory(equality)],[75,43]),
[iquote('0:Res:75.0,43.0')] ).
cnf(125,plain,
( equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3))
| edge(skf10(skc3)) ),
inference(res,[status(thm),theory(equality)],[123,91]),
[iquote('0:Res:123.0,91.0')] ).
cnf(126,plain,
equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)),
inference(spt,[spt(split,[position(s1)])],[125]),
[iquote('1:Spt:125.0')] ).
cnf(127,plain,
less_or_equal(number_of_in(sequential_pairs,skc3),number_of_in(triangles,graph)),
inference(spr,[status(thm),theory(equality)],[126,12]),
[iquote('1:SpR:126.0,12.0')] ).
cnf(129,plain,
$false,
inference(mrr,[status(thm)],[127,97]),
[iquote('1:MRR:127.0,97.0')] ).
cnf(130,plain,
~ equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)),
inference(spt,[spt(split,[position(sa)])],[129,126]),
[iquote('1:Spt:129.0,125.0,126.0')] ).
cnf(131,plain,
edge(skf10(skc3)),
inference(spt,[spt(split,[position(s2)])],[125]),
[iquote('1:Spt:129.0,125.1')] ).
cnf(132,plain,
on_path(skf10(skc3),skc3),
inference(mrr,[status(thm)],[123,130]),
[iquote('1:MRR:123.1,130.0')] ).
cnf(133,plain,
on_path(skf12(skc3),skc3),
inference(mrr,[status(thm)],[124,130]),
[iquote('1:MRR:124.1,130.0')] ).
cnf(179,plain,
( ~ sequential(skf12(u),skf10(u))
| ~ precedes(skf12(u),skf10(u),skc3)
| ~ path(v,w,u)
| equal(number_of_in(triangles,u),number_of_in(sequential_pairs,u)) ),
inference(res,[status(thm),theory(equality)],[77,49]),
[iquote('0:Res:77.2,49.1')] ).
cnf(181,plain,
( ~ precedes(skf12(u),skf10(u),skc3)
| ~ path(v,w,u)
| equal(number_of_in(triangles,u),number_of_in(sequential_pairs,u)) ),
inference(mrr,[status(thm)],[179,45]),
[iquote('0:MRR:179.0,45.1')] ).
cnf(322,plain,
( ~ on_path(u,skc3)
| ~ on_path(v,skc3)
| ~ sequential(v,u)
| precedes(v,u,skc3) ),
inference(res,[status(thm),theory(equality)],[75,54]),
[iquote('0:Res:75.0,54.3')] ).
cnf(345,plain,
( ~ on_path(skf10(u),skc3)
| ~ on_path(skf12(u),skc3)
| ~ sequential(skf12(u),skf10(u))
| ~ path(v,w,u)
| equal(number_of_in(triangles,u),number_of_in(sequential_pairs,u)) ),
inference(res,[status(thm),theory(equality)],[322,181]),
[iquote('0:Res:322.3,181.0')] ).
cnf(357,plain,
( ~ on_path(skf10(u),skc3)
| ~ on_path(skf12(u),skc3)
| ~ path(v,w,u)
| equal(number_of_in(triangles,u),number_of_in(sequential_pairs,u)) ),
inference(mrr,[status(thm)],[345,45]),
[iquote('0:MRR:345.2,45.1')] ).
cnf(592,plain,
( ~ on_path(skf12(skc3),skc3)
| ~ path(u,v,skc3)
| equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)) ),
inference(res,[status(thm),theory(equality)],[132,357]),
[iquote('1:Res:132.0,357.0')] ).
cnf(593,plain,
~ path(u,v,skc3),
inference(mrr,[status(thm)],[592,133,130]),
[iquote('1:MRR:592.0,592.2,133.0,130.0')] ).
cnf(594,plain,
$false,
inference(unc,[status(thm)],[593,75]),
[iquote('1:UnC:593.0,75.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.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 02:50:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.42/0.60
% 0.42/0.60 SPASS V 3.9
% 0.42/0.60 SPASS beiseite: Proof found.
% 0.42/0.60 % SZS status Theorem
% 0.42/0.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/0.60 SPASS derived 397 clauses, backtracked 4 clauses, performed 1 splits and kept 306 clauses.
% 0.42/0.60 SPASS allocated 98288 KBytes.
% 0.42/0.60 SPASS spent 0:00:00.25 on the problem.
% 0.42/0.60 0:00:00.04 for the input.
% 0.42/0.60 0:00:00.08 for the FLOTTER CNF translation.
% 0.42/0.60 0:00:00.01 for inferences.
% 0.42/0.60 0:00:00.00 for the backtracking.
% 0.42/0.60 0:00:00.09 for the reduction.
% 0.42/0.60
% 0.42/0.60
% 0.42/0.60 Here is a proof with depth 5, length 37 :
% 0.42/0.60 % SZS output start Refutation
% See solution above
% 0.42/0.60 Formulae used in the proof : maximal_path_length graph_has_them_all shortest_path_defn on_path_properties path_length_sequential_pairs sequential_pairs_and_triangles precedes_defn sequential_is_triangle
% 0.42/0.60
%------------------------------------------------------------------------------