TSTP Solution File: GRP166-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP166-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 11:46:00 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 23 RR)
% Number of literals : 23 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(least_upper_bound(b,identity),b),
file('GRP166-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(least_upper_bound(a,multiply(a,b)),multiply(a,b)),
file('GRP166-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP166-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP166-1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP166-1.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP166-1.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP166-1.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP166-1.p',unknown),
[] ).
cnf(14,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP166-1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP166-1.p',unknown),
[] ).
cnf(19,plain,
equal(least_upper_bound(identity,b),b),
inference(rew,[status(thm),theory(equality)],[8,2]),
[iquote('0:Rew:8.0,2.0')] ).
cnf(28,plain,
equal(greatest_lower_bound(identity,b),identity),
inference(spr,[status(thm),theory(equality)],[19,14]),
[iquote('0:SpR:19.0,14.0')] ).
cnf(45,plain,
equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.0,13.0')] ).
cnf(344,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(345,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[4,344]),
[iquote('0:Rew:4.0,344.0')] ).
cnf(348,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[345]),
[iquote('0:SpR:345.0,345.0')] ).
cnf(351,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[5,345]),
[iquote('0:SpR:5.0,345.0')] ).
cnf(353,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[348,351]),
[iquote('0:Rew:348.0,351.0')] ).
cnf(615,plain,
equal(greatest_lower_bound(multiply(u,identity),multiply(u,b)),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[28,16]),
[iquote('0:SpR:28.0,16.0')] ).
cnf(627,plain,
equal(greatest_lower_bound(u,multiply(u,b)),u),
inference(rew,[status(thm),theory(equality)],[353,615]),
[iquote('0:Rew:353.0,615.0')] ).
cnf(660,plain,
equal(least_upper_bound(multiply(u,b),u),multiply(u,b)),
inference(spr,[status(thm),theory(equality)],[627,45]),
[iquote('0:SpR:627.0,45.0')] ).
cnf(674,plain,
equal(least_upper_bound(u,multiply(u,b)),multiply(u,b)),
inference(rew,[status(thm),theory(equality)],[8,660]),
[iquote('0:Rew:8.0,660.0')] ).
cnf(675,plain,
$false,
inference(unc,[status(thm)],[674,3]),
[iquote('0:UnC:674.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP166-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.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 : Tue Jun 14 07:59:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 489 clauses, backtracked 0 clauses, performed 0 splits and kept 131 clauses.
% 0.19/0.45 SPASS allocated 63758 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.03 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.01 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.04 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 3, length 23 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : lat2a_2 prove_lat2a left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub lub_absorbtion glb_absorbtion monotony_glb1
% 0.19/0.45
%------------------------------------------------------------------------------