%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL014+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 20:01:40 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 10 unt; 0 nHn; 12 RR)
% Number of literals : 14 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(composition(u,one),u),
file('REL014+1.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL014+1.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL014+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(composition(skc2,one),skc2)
| ~ equal(composition(one,skc3),skc3) ),
file('REL014+1.p',unknown),
[] ).
cnf(15,plain,
( ~ equal(skc2,skc2)
| ~ equal(composition(one,skc3),skc3) ),
inference(rew,[status(thm),theory(equality)],[1,11]),
[iquote('0:Rew:1.0,11.0')] ).
cnf(16,plain,
~ equal(composition(one,skc3),skc3),
inference(obv,[status(thm),theory(equality)],[15]),
[iquote('0:Obv:15.0')] ).
cnf(29,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(392,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,29]),
[iquote('0:SpR:1.0,29.0')] ).
cnf(395,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,392]),
[iquote('0:Rew:2.0,392.0')] ).
cnf(404,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[395,1]),
[iquote('0:SpR:395.0,1.0')] ).
cnf(414,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[404,395]),
[iquote('0:Rew:404.0,395.0')] ).
cnf(415,plain,
$false,
inference(unc,[status(thm)],[414,16]),
[iquote('0:UnC:414.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL014+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 11:19:51 EDT 2022
% 0.18/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 274 clauses, backtracked 0 clauses, performed 0 splits and kept 132 clauses.
% 0.19/0.47 SPASS allocated 85645 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.03 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 3, length 12 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : composition_identity converse_idempotence converse_multiplicativity goals
% 0.19/0.47
%------------------------------------------------------------------------------