TSTP Solution File: GRA010+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRA010+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 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 7 unt; 6 nHn; 17 RR)
% Number of literals : 34 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
path(skc4,skc5,skc3),
file('GRA010+2.p',unknown),
[] ).
cnf(15,axiom,
~ equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)),
file('GRA010+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ path(u,v,w)
| on_path(skf14(w),w)
| equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
file('GRA010+2.p',unknown),
[] ).
cnf(44,axiom,
( ~ path(u,v,w)
| on_path(skf12(w),w)
| equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
file('GRA010+2.p',unknown),
[] ).
cnf(45,axiom,
( ~ path(u,v,w)
| sequential(skf14(w),skf12(w))
| equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
file('GRA010+2.p',unknown),
[] ).
cnf(47,axiom,
( ~ sequential(u,v)
| ~ on_path(v,skc3)
| ~ on_path(u,skc3)
| triangle(u,v,skf10(v,u)) ),
file('GRA010+2.p',unknown),
[] ).
cnf(50,axiom,
( ~ path(u,v,w)
| ~ triangle(skf14(w),skf12(w),x)
| equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
file('GRA010+2.p',unknown),
[] ).
cnf(81,plain,
( sequential(skf14(skc3),skf12(skc3))
| equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)) ),
inference(res,[status(thm),theory(equality)],[2,45]),
[iquote('0:Res:2.0,45.0')] ).
cnf(82,plain,
( on_path(skf14(skc3),skc3)
| equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)) ),
inference(res,[status(thm),theory(equality)],[2,43]),
[iquote('0:Res:2.0,43.0')] ).
cnf(83,plain,
( on_path(skf12(skc3),skc3)
| equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)) ),
inference(res,[status(thm),theory(equality)],[2,44]),
[iquote('0:Res:2.0,44.0')] ).
cnf(100,plain,
( ~ triangle(skf14(skc3),skf12(skc3),u)
| equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)) ),
inference(res,[status(thm),theory(equality)],[2,50]),
[iquote('0:Res:2.0,50.1')] ).
cnf(122,plain,
on_path(skf14(skc3),skc3),
inference(mrr,[status(thm)],[82,15]),
[iquote('0:MRR:82.1,15.0')] ).
cnf(123,plain,
on_path(skf12(skc3),skc3),
inference(mrr,[status(thm)],[83,15]),
[iquote('0:MRR:83.1,15.0')] ).
cnf(124,plain,
sequential(skf14(skc3),skf12(skc3)),
inference(mrr,[status(thm)],[81,15]),
[iquote('0:MRR:81.1,15.0')] ).
cnf(125,plain,
~ triangle(skf14(skc3),skf12(skc3),u),
inference(mrr,[status(thm)],[100,15]),
[iquote('0:MRR:100.1,15.0')] ).
cnf(135,plain,
( ~ on_path(skf14(skc3),skc3)
| ~ sequential(skf14(skc3),skf12(skc3))
| ~ on_path(skf12(skc3),skc3) ),
inference(res,[status(thm),theory(equality)],[47,125]),
[iquote('0:Res:47.3,125.0')] ).
cnf(136,plain,
$false,
inference(mrr,[status(thm)],[135,122,124,123]),
[iquote('0:MRR:135.0,135.1,135.2,122.0,124.0,123.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 23:04:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.47
% 0.18/0.47 SPASS V 3.9
% 0.18/0.47 SPASS beiseite: Proof found.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 35 clauses, backtracked 0 clauses, performed 0 splits and kept 102 clauses.
% 0.18/0.47 SPASS allocated 98304 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.47 0:00:00.03 for the input.
% 0.18/0.47 0:00:00.07 for the FLOTTER CNF translation.
% 0.18/0.47 0:00:00.00 for inferences.
% 0.18/0.47 0:00:00.00 for the backtracking.
% 0.18/0.47 0:00:00.00 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 2, length 17 :
% 0.18/0.47 % SZS output start Refutation
% See solution above
% 0.18/0.47 Formulae used in the proof : complete_means_sequential_pairs_and_triangles sequential_pairs_and_triangles
% 0.18/0.47
%------------------------------------------------------------------------------