TSTP Solution File: REL008+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL008+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 20:01:32 EDT 2022
% Result : Theorem 111.25s 111.43s
% Output : Refutation 111.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 18 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 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(2,axiom,
equal(converse(converse(u)),u),
file('REL008+3.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL008+3.p',unknown),
[] ).
cnf(7,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL008+3.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL008+3.p',unknown),
[] ).
cnf(11,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL008+3.p',unknown),
[] ).
cnf(13,axiom,
~ equal(join(composition(skc5,skc4),composition(skc5,skc3)),composition(skc5,join(skc4,skc3))),
file('REL008+3.p',unknown),
[] ).
cnf(20,plain,
~ equal(join(composition(skc5,skc3),composition(skc5,skc4)),composition(skc5,join(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[5,13]),
[iquote('0:Rew:5.0,13.0,5.0,13.0')] ).
cnf(32,plain,
equal(converse(composition(u,converse(v))),composition(v,converse(u))),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(36,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(266,plain,
equal(join(converse(composition(u,v)),composition(w,converse(u))),composition(join(converse(v),w),converse(u))),
inference(spr,[status(thm),theory(equality)],[8,11]),
[iquote('0:SpR:8.0,11.0')] ).
cnf(926,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[32,7]),
[iquote('0:SpR:32.0,7.0')] ).
cnf(949,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
inference(rew,[status(thm),theory(equality)],[926,266]),
[iquote('0:Rew:926.0,266.0')] ).
cnf(1014,plain,
equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
inference(spr,[status(thm),theory(equality)],[36,8]),
[iquote('0:SpR:36.0,8.0')] ).
cnf(1054,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
inference(rew,[status(thm),theory(equality)],[1014,949]),
[iquote('0:Rew:1014.0,949.0')] ).
cnf(5915,plain,
equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[2,1054]),
[iquote('0:SpR:2.0,1054.0')] ).
cnf(116010,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[5915,2]),
[iquote('0:SpR:5915.0,2.0')] ).
cnf(116288,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[2,116010]),
[iquote('0:Rew:2.0,116010.0')] ).
cnf(116289,plain,
$false,
inference(unc,[status(thm)],[116288,20]),
[iquote('0:UnC:116288.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL008+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.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 13:40:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 111.25/111.43
% 111.25/111.43 SPASS V 3.9
% 111.25/111.43 SPASS beiseite: Proof found.
% 111.25/111.43 % SZS status Theorem
% 111.25/111.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 111.25/111.43 SPASS derived 70200 clauses, backtracked 0 clauses, performed 0 splits and kept 9069 clauses.
% 111.25/111.43 SPASS allocated 203748 KBytes.
% 111.25/111.43 SPASS spent 0:1:47.57 on the problem.
% 111.25/111.43 0:00:00.04 for the input.
% 111.25/111.43 0:00:00.03 for the FLOTTER CNF translation.
% 111.25/111.43 0:00:00.58 for inferences.
% 111.25/111.43 0:00:00.00 for the backtracking.
% 111.25/111.43 0:1:46.74 for the reduction.
% 111.25/111.43
% 111.25/111.43
% 111.25/111.43 Here is a proof with depth 3, length 18 :
% 111.25/111.43 % SZS output start Refutation
% See solution above
% 111.25/111.43 Formulae used in the proof : converse_idempotence maddux1_join_commutativity converse_additivity converse_multiplicativity composition_distributivity goals
% 111.25/111.43
%------------------------------------------------------------------------------