TSTP Solution File: GRP010-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 : Sat Jul 16 11:44:44 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP010-4.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(identity,u),u),
file('GRP010-4.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP010-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(c,b),identity),
file('GRP010-4.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,c),identity),
file('GRP010-4.p',unknown),
[] ).
cnf(11,plain,
equal(multiply(c,multiply(b,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(13,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(14,plain,
equal(multiply(c,multiply(b,u)),u),
inference(rew,[status(thm),theory(equality)],[2,11]),
[iquote('0:Rew:2.0,11.0')] ).
cnf(15,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[2,13]),
[iquote('0:Rew:2.0,13.0')] ).
cnf(24,plain,
equal(multiply(inverse(c),u),multiply(b,u)),
inference(spr,[status(thm),theory(equality)],[14,15]),
[iquote('0:SpR:14.0,15.0')] ).
cnf(45,plain,
equal(multiply(b,c),identity),
inference(spr,[status(thm),theory(equality)],[24,3]),
[iquote('0:SpR:24.0,3.0')] ).
cnf(51,plain,
$false,
inference(mrr,[status(thm)],[45,5]),
[iquote('0:MRR:45.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n015.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 : Mon Jun 13 06:44:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 38 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.20/0.41 SPASS allocated 63132 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.03 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.00 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 3, length 12 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : associativity left_identity left_inverse c_times_b_is_e prove_b_times_c_is_e
% 0.20/0.41
%------------------------------------------------------------------------------