TSTP Solution File: REL009-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% 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 : n011.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 20:01:33 EDT 2022
% Result : Unsatisfiable 33.79s 34.00s
% Output : Refutation 33.79s
% 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('REL009-1.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('REL009-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL009-1.p',unknown),
[] ).
cnf(10,axiom,
equal(converse(converse(u)),u),
file('REL009-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL009-1.p',unknown),
[] ).
cnf(12,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL009-1.p',unknown),
[] ).
cnf(18,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(19,plain,
~ equal(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2)),
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)],[10,12]),
[iquote('0:SpR:10.0,12.0')] ).
cnf(36,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(324,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(614,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[32,11]),
[iquote('0:SpR:32.0,11.0')] ).
cnf(635,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
inference(rew,[status(thm),theory(equality)],[614,324]),
[iquote('0:Rew:614.0,324.0')] ).
cnf(693,plain,
equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
inference(spr,[status(thm),theory(equality)],[36,12]),
[iquote('0:SpR:36.0,12.0')] ).
cnf(729,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
inference(rew,[status(thm),theory(equality)],[693,635]),
[iquote('0:Rew:693.0,635.0')] ).
cnf(4561,plain,
equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[10,729]),
[iquote('0:SpR:10.0,729.0')] ).
cnf(61691,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[4561,10]),
[iquote('0:SpR:4561.0,10.0')] ).
cnf(61908,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[10,61691]),
[iquote('0:Rew:10.0,61691.0')] ).
cnf(61911,plain,
~ equal(composition(sk3,join(sk1,sk2)),composition(sk3,sk2)),
inference(rew,[status(thm),theory(equality)],[61908,19]),
[iquote('0:Rew:61908.0,19.0')] ).
cnf(61915,plain,
~ equal(composition(sk3,sk2),composition(sk3,sk2)),
inference(rew,[status(thm),theory(equality)],[1,61911]),
[iquote('0:Rew:1.0,61911.0')] ).
cnf(61916,plain,
$false,
inference(obv,[status(thm),theory(equality)],[61915]),
[iquote('0:Obv:61915.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : REL009-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Fri Jul 8 09:29:54 EDT 2022
% 0.12/0.32 % CPUTime :
% 33.79/34.00
% 33.79/34.00 SPASS V 3.9
% 33.79/34.00 SPASS beiseite: Proof found.
% 33.79/34.00 % SZS status Theorem
% 33.79/34.00 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.79/34.00 SPASS derived 36860 clauses, backtracked 0 clauses, performed 0 splits and kept 3975 clauses.
% 33.79/34.00 SPASS allocated 116080 KBytes.
% 33.79/34.00 SPASS spent 0:0:32.71 on the problem.
% 33.79/34.00 0:00:00.04 for the input.
% 33.79/34.00 0:00:00.00 for the FLOTTER CNF translation.
% 33.79/34.00 0:00:00.37 for inferences.
% 33.79/34.00 0:00:00.00 for the backtracking.
% 33.79/34.00 0:0:32.22 for the reduction.
% 33.79/34.00
% 33.79/34.00
% 33.79/34.00 Here is a proof with depth 3, length 21 :
% 33.79/34.00 % SZS output start Refutation
% See solution above
% 33.79/34.00 Formulae used in the proof : goals_14 goals_15 composition_distributivity_7 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10
% 33.79/34.00
%------------------------------------------------------------------------------