TSTP Solution File: REL009+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL009+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 22.43s 22.61s
% Output : Refutation 22.43s
% 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+1.p',unknown),
[] ).
cnf(3,axiom,
equal(converse(converse(u)),u),
file('REL009+1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL009+1.p',unknown),
[] ).
cnf(9,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL009+1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL009+1.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+1.p',unknown),
[] ).
cnf(18,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(19,plain,
~ equal(join(composition(skc7,skc4),composition(skc7,skc5)),composition(skc7,skc5)),
inference(obv,[status(thm),theory(equality)],[18]),
[iquote('0:Obv:18.0')] ).
cnf(32,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(36,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(323,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(582,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[32,8]),
[iquote('0:SpR:32.0,8.0')] ).
cnf(603,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
inference(rew,[status(thm),theory(equality)],[582,323]),
[iquote('0:Rew:582.0,323.0')] ).
cnf(660,plain,
equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
inference(spr,[status(thm),theory(equality)],[36,9]),
[iquote('0:SpR:36.0,9.0')] ).
cnf(696,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
inference(rew,[status(thm),theory(equality)],[660,603]),
[iquote('0:Rew:660.0,603.0')] ).
cnf(4526,plain,
equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[3,696]),
[iquote('0:SpR:3.0,696.0')] ).
cnf(61655,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[4526,3]),
[iquote('0:SpR:4526.0,3.0')] ).
cnf(61872,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[3,61655]),
[iquote('0:Rew:3.0,61655.0')] ).
cnf(61875,plain,
~ equal(composition(skc7,join(skc4,skc5)),composition(skc7,skc5)),
inference(rew,[status(thm),theory(equality)],[61872,19]),
[iquote('0:Rew:61872.0,19.0')] ).
cnf(61879,plain,
~ equal(composition(skc7,skc5),composition(skc7,skc5)),
inference(rew,[status(thm),theory(equality)],[1,61875]),
[iquote('0:Rew:1.0,61875.0')] ).
cnf(61880,plain,
$false,
inference(obv,[status(thm),theory(equality)],[61879]),
[iquote('0:Obv:61879.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL009+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 11:09:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 22.43/22.61
% 22.43/22.61 SPASS V 3.9
% 22.43/22.61 SPASS beiseite: Proof found.
% 22.43/22.61 % SZS status Theorem
% 22.43/22.61 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.43/22.61 SPASS derived 36835 clauses, backtracked 0 clauses, performed 0 splits and kept 3977 clauses.
% 22.43/22.61 SPASS allocated 138079 KBytes.
% 22.43/22.61 SPASS spent 0:0:21.24 on the problem.
% 22.43/22.61 0:00:00.04 for the input.
% 22.43/22.61 0:00:00.03 for the FLOTTER CNF translation.
% 22.43/22.61 0:00:00.28 for inferences.
% 22.43/22.61 0:00:00.00 for the backtracking.
% 22.43/22.61 0:0:20.84 for the reduction.
% 22.43/22.61
% 22.43/22.61
% 22.43/22.61 Here is a proof with depth 3, length 21 :
% 22.43/22.61 % SZS output start Refutation
% See solution above
% 22.43/22.61 Formulae used in the proof : goals converse_idempotence converse_additivity converse_multiplicativity composition_distributivity
% 22.43/22.61
%------------------------------------------------------------------------------