TSTP Solution File: GRP175-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP175-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 11:46:06 EDT 2022
% Result : Unsatisfiable 0.69s 0.89s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% 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 : 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(greatest_lower_bound(identity,b),identity),
file('GRP175-2.p',unknown),
[] ).
cnf(2,axiom,
~ equal(greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))),identity),
file('GRP175-2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(identity,u),u),
file('GRP175-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP175-2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP175-2.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP175-2.p',unknown),
[] ).
cnf(290,plain,
equal(greatest_lower_bound(multiply(identity,u),multiply(b,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(305,plain,
equal(greatest_lower_bound(u,multiply(b,u)),u),
inference(rew,[status(thm),theory(equality)],[3,290]),
[iquote('0:Rew:3.0,290.0')] ).
cnf(443,plain,
equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(u,v)),u),multiply(inverse(greatest_lower_bound(u,v)),v)),identity),
inference(spr,[status(thm),theory(equality)],[15,4]),
[iquote('0:SpR:15.0,4.0')] ).
cnf(4217,plain,
equal(greatest_lower_bound(multiply(inverse(u),u),multiply(inverse(u),multiply(b,u))),identity),
inference(spr,[status(thm),theory(equality)],[305,443]),
[iquote('0:SpR:305.0,443.0')] ).
cnf(4295,plain,
equal(greatest_lower_bound(identity,multiply(inverse(u),multiply(b,u))),identity),
inference(rew,[status(thm),theory(equality)],[4,4217]),
[iquote('0:Rew:4.0,4217.0')] ).
cnf(4296,plain,
$false,
inference(unc,[status(thm)],[4295,2]),
[iquote('0:UnC:4295.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP175-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 14:27:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.69/0.89
% 0.69/0.89 SPASS V 3.9
% 0.69/0.89 SPASS beiseite: Proof found.
% 0.69/0.89 % SZS status Theorem
% 0.69/0.89 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.69/0.89 SPASS derived 3076 clauses, backtracked 0 clauses, performed 0 splits and kept 540 clauses.
% 0.69/0.89 SPASS allocated 66748 KBytes.
% 0.69/0.89 SPASS spent 0:00:00.52 on the problem.
% 0.69/0.89 0:00:00.03 for the input.
% 0.69/0.89 0:00:00.00 for the FLOTTER CNF translation.
% 0.69/0.89 0:00:00.03 for inferences.
% 0.69/0.89 0:00:00.00 for the backtracking.
% 0.69/0.89 0:00:00.43 for the reduction.
% 0.69/0.89
% 0.69/0.89
% 0.69/0.89 Here is a proof with depth 2, length 12 :
% 0.69/0.89 % SZS output start Refutation
% See solution above
% 0.69/0.89 Formulae used in the proof : p06b_1 prove_p06b left_identity left_inverse monotony_glb1 monotony_glb2
% 0.69/0.89
%------------------------------------------------------------------------------