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 : n014.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 : Unsatisfiable 61.08s 61.28s
% Output : Refutation 61.08s
% 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(join(sk1,sk2),sk2),
file('REL009-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(join(composition(sk1,sk3),composition(sk2,sk3)),composition(sk2,sk3))
| ~ equal(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2)) ),
file('REL009-2.p',unknown),
[] ).
cnf(9,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL009-2.p',unknown),
[] ).
cnf(10,axiom,
equal(converse(converse(u)),u),
file('REL009-2.p',unknown),
[] ).
cnf(11,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL009-2.p',unknown),
[] ).
cnf(12,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL009-2.p',unknown),
[] ).
cnf(21,plain,
( ~ equal(composition(sk2,sk3),composition(sk2,sk3))
| ~ equal(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2)) ),
inference(rew,[status(thm),theory(equality)],[1,2,9]),
[iquote('0:Rew:1.0,2.0,9.0,2.0')] ).
cnf(22,plain,
~ equal(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2)),
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)],[10,12]),
[iquote('0:SpR:10.0,12.0')] ).
cnf(39,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpR:10.0,11.0')] ).
cnf(329,plain,
equal(join(converse(composition(u,v)),composition(w,converse(u))),composition(join(converse(v),w),converse(u))),
inference(spr,[status(thm),theory(equality)],[12,9]),
[iquote('0:SpR:12.0,9.0')] ).
cnf(762,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[35,11]),
[iquote('0:SpR:35.0,11.0')] ).
cnf(785,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
inference(rew,[status(thm),theory(equality)],[762,329]),
[iquote('0:Rew:762.0,329.0')] ).
cnf(935,plain,
equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
inference(spr,[status(thm),theory(equality)],[39,12]),
[iquote('0:SpR:39.0,12.0')] ).
cnf(969,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
inference(rew,[status(thm),theory(equality)],[935,785]),
[iquote('0:Rew:935.0,785.0')] ).
cnf(5668,plain,
equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[10,969]),
[iquote('0:SpR:10.0,969.0')] ).
cnf(86671,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[5668,10]),
[iquote('0:SpR:5668.0,10.0')] ).
cnf(86920,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[10,86671]),
[iquote('0:Rew:10.0,86671.0')] ).
cnf(86924,plain,
~ equal(composition(sk3,join(sk1,sk2)),composition(sk3,sk2)),
inference(rew,[status(thm),theory(equality)],[86920,22]),
[iquote('0:Rew:86920.0,22.0')] ).
cnf(86950,plain,
~ equal(composition(sk3,sk2),composition(sk3,sk2)),
inference(rew,[status(thm),theory(equality)],[1,86924]),
[iquote('0:Rew:1.0,86924.0')] ).
cnf(86951,plain,
$false,
inference(obv,[status(thm),theory(equality)],[86950]),
[iquote('0:Obv:86950.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : REL009-2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.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 07:55:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 61.08/61.28
% 61.08/61.28 SPASS V 3.9
% 61.08/61.28 SPASS beiseite: Proof found.
% 61.08/61.28 % SZS status Theorem
% 61.08/61.28 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.08/61.28 SPASS derived 52295 clauses, backtracked 0 clauses, performed 0 splits and kept 7255 clauses.
% 61.08/61.28 SPASS allocated 159739 KBytes.
% 61.08/61.28 SPASS spent 0:0:59.02 on the problem.
% 61.08/61.28 0:00:00.04 for the input.
% 61.08/61.28 0:00:00.00 for the FLOTTER CNF translation.
% 61.08/61.28 0:00:00.46 for inferences.
% 61.08/61.28 0:00:00.00 for the backtracking.
% 61.08/61.28 0:0:58.39 for the reduction.
% 61.08/61.28
% 61.08/61.28
% 61.08/61.28 Here is a proof with depth 3, length 21 :
% 61.08/61.28 % SZS output start Refutation
% See solution above
% 61.08/61.28 Formulae used in the proof : goals_17 goals_18 composition_distributivity_7 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10
% 61.08/61.28
%------------------------------------------------------------------------------