TSTP Solution File: REL009+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL009+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Mon Jul 18 20:01:34 EDT 2022
% Result : Theorem 56.27s 56.48s
% Output : Refutation 56.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 19 unt; 0 nHn; 21 RR)
% Number of literals : 23 ( 0 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(join(skc4,skc5),skc5),
file('REL009+2.p',unknown),
[] ).
cnf(3,axiom,
equal(converse(converse(u)),u),
file('REL009+2.p',unknown),
[] ).
cnf(8,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL009+2.p',unknown),
[] ).
cnf(9,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL009+2.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL009+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ equal(join(composition(skc4,skc6),composition(skc5,skc6)),composition(skc5,skc6))
| ~ equal(join(composition(skc7,skc4),composition(skc7,skc5)),composition(skc7,skc5)) ),
file('REL009+2.p',unknown),
[] ).
cnf(21,plain,
( ~ equal(composition(skc5,skc6),composition(skc5,skc6))
| ~ equal(join(composition(skc7,skc4),composition(skc7,skc5)),composition(skc7,skc5)) ),
inference(rew,[status(thm),theory(equality)],[1,15,12]),
[iquote('0:Rew:1.0,15.0,12.0,15.0')] ).
cnf(22,plain,
~ equal(join(composition(skc7,skc4),composition(skc7,skc5)),composition(skc7,skc5)),
inference(obv,[status(thm),theory(equality)],[21]),
[iquote('0:Obv:21.0')] ).
cnf(35,plain,
equal(converse(composition(u,converse(v))),composition(v,converse(u))),
inference(spr,[status(thm),theory(equality)],[3,9]),
[iquote('0:SpR:3.0,9.0')] ).
cnf(39,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(328,plain,
equal(join(converse(composition(u,v)),composition(w,converse(u))),composition(join(converse(v),w),converse(u))),
inference(spr,[status(thm),theory(equality)],[9,12]),
[iquote('0:SpR:9.0,12.0')] ).
cnf(744,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[35,8]),
[iquote('0:SpR:35.0,8.0')] ).
cnf(765,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
inference(rew,[status(thm),theory(equality)],[744,328]),
[iquote('0:Rew:744.0,328.0')] ).
cnf(916,plain,
equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
inference(spr,[status(thm),theory(equality)],[39,9]),
[iquote('0:SpR:39.0,9.0')] ).
cnf(950,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
inference(rew,[status(thm),theory(equality)],[916,765]),
[iquote('0:Rew:916.0,765.0')] ).
cnf(5604,plain,
equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[3,950]),
[iquote('0:SpR:3.0,950.0')] ).
cnf(86612,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[5604,3]),
[iquote('0:SpR:5604.0,3.0')] ).
cnf(86861,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[3,86612]),
[iquote('0:Rew:3.0,86612.0')] ).
cnf(86865,plain,
~ equal(composition(skc7,join(skc4,skc5)),composition(skc7,skc5)),
inference(rew,[status(thm),theory(equality)],[86861,22]),
[iquote('0:Rew:86861.0,22.0')] ).
cnf(86891,plain,
~ equal(composition(skc7,skc5),composition(skc7,skc5)),
inference(rew,[status(thm),theory(equality)],[1,86865]),
[iquote('0:Rew:1.0,86865.0')] ).
cnf(86892,plain,
$false,
inference(obv,[status(thm),theory(equality)],[86891]),
[iquote('0:Obv:86891.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL009+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 : Fri Jul 8 11:18:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 56.27/56.48
% 56.27/56.48 SPASS V 3.9
% 56.27/56.48 SPASS beiseite: Proof found.
% 56.27/56.48 % SZS status Theorem
% 56.27/56.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.27/56.48 SPASS derived 52252 clauses, backtracked 0 clauses, performed 0 splits and kept 7241 clauses.
% 56.27/56.48 SPASS allocated 181743 KBytes.
% 56.27/56.48 SPASS spent 0:0:54.28 on the problem.
% 56.27/56.48 0:00:00.03 for the input.
% 56.27/56.48 0:00:00.03 for the FLOTTER CNF translation.
% 56.27/56.48 0:00:00.43 for inferences.
% 56.27/56.48 0:00:00.00 for the backtracking.
% 56.27/56.48 0:0:53.69 for the reduction.
% 56.27/56.48
% 56.27/56.48
% 56.27/56.48 Here is a proof with depth 3, length 21 :
% 56.27/56.48 % SZS output start Refutation
% See solution above
% 56.27/56.48 Formulae used in the proof : goals converse_idempotence converse_additivity converse_multiplicativity composition_distributivity
% 56.27/56.48
%------------------------------------------------------------------------------