TSTP Solution File: GRP138-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:45:53 EDT 2022
% Result : Unsatisfiable 4.67s 4.83s
% Output : Refutation 4.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(least_upper_bound(a,c),a),
file('GRP138-1.p',unknown),
[] ).
cnf(2,axiom,
equal(least_upper_bound(b,c),b),
file('GRP138-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(least_upper_bound(greatest_lower_bound(a,b),c),greatest_lower_bound(a,b)),
file('GRP138-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP138-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP138-1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP138-1.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP138-1.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP138-1.p',unknown),
[] ).
cnf(9,axiom,
equal(greatest_lower_bound(greatest_lower_bound(u,v),w),greatest_lower_bound(u,greatest_lower_bound(v,w))),
file('GRP138-1.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP138-1.p',unknown),
[] ).
cnf(14,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP138-1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP138-1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP138-1.p',unknown),
[] ).
cnf(19,plain,
equal(least_upper_bound(c,b),b),
inference(rew,[status(thm),theory(equality)],[8,2]),
[iquote('0:Rew:8.0,2.0')] ).
cnf(20,plain,
~ equal(least_upper_bound(c,greatest_lower_bound(a,b)),greatest_lower_bound(a,b)),
inference(rew,[status(thm),theory(equality)],[8,3]),
[iquote('0:Rew:8.0,3.0')] ).
cnf(29,plain,
equal(greatest_lower_bound(c,b),c),
inference(spr,[status(thm),theory(equality)],[19,14]),
[iquote('0:SpR:19.0,14.0')] ).
cnf(46,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(259,plain,
equal(greatest_lower_bound(c,greatest_lower_bound(b,u)),greatest_lower_bound(c,u)),
inference(spr,[status(thm),theory(equality)],[29,9]),
[iquote('0:SpR:29.0,9.0')] ).
cnf(345,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(346,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[4,345]),
[iquote('0:Rew:4.0,345.0')] ).
cnf(349,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[346]),
[iquote('0:SpR:346.0,346.0')] ).
cnf(352,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[5,346]),
[iquote('0:SpR:5.0,346.0')] ).
cnf(354,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[349,352]),
[iquote('0:Rew:349.0,352.0')] ).
cnf(462,plain,
equal(least_upper_bound(greatest_lower_bound(b,u),greatest_lower_bound(c,u)),greatest_lower_bound(b,u)),
inference(spr,[status(thm),theory(equality)],[259,46]),
[iquote('0:SpR:259.0,46.0')] ).
cnf(476,plain,
equal(least_upper_bound(greatest_lower_bound(c,u),greatest_lower_bound(b,u)),greatest_lower_bound(b,u)),
inference(rew,[status(thm),theory(equality)],[8,462]),
[iquote('0:Rew:8.0,462.0')] ).
cnf(515,plain,
equal(least_upper_bound(multiply(a,u),multiply(c,u)),multiply(a,u)),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(645,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[349,5]),
[iquote('0:SpR:349.0,5.0')] ).
cnf(1005,plain,
equal(least_upper_bound(multiply(a,inverse(c)),identity),multiply(a,inverse(c))),
inference(spr,[status(thm),theory(equality)],[645,515]),
[iquote('0:SpR:645.0,515.0')] ).
cnf(1016,plain,
equal(least_upper_bound(identity,multiply(a,inverse(c))),multiply(a,inverse(c))),
inference(rew,[status(thm),theory(equality)],[8,1005]),
[iquote('0:Rew:8.0,1005.0')] ).
cnf(4481,plain,
equal(greatest_lower_bound(identity,multiply(a,inverse(c))),identity),
inference(spr,[status(thm),theory(equality)],[1016,14]),
[iquote('0:SpR:1016.0,14.0')] ).
cnf(4508,plain,
equal(greatest_lower_bound(multiply(identity,u),multiply(multiply(a,inverse(c)),u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[4481,18]),
[iquote('0:SpR:4481.0,18.0')] ).
cnf(4525,plain,
equal(greatest_lower_bound(u,multiply(a,multiply(inverse(c),u))),u),
inference(rew,[status(thm),theory(equality)],[6,4508,4]),
[iquote('0:Rew:6.0,4508.0,4.0,4508.0')] ).
cnf(18925,plain,
equal(least_upper_bound(c,greatest_lower_bound(b,multiply(a,multiply(inverse(c),c)))),greatest_lower_bound(b,multiply(a,multiply(inverse(c),c)))),
inference(spr,[status(thm),theory(equality)],[4525,476]),
[iquote('0:SpR:4525.0,476.0')] ).
cnf(19005,plain,
equal(least_upper_bound(c,greatest_lower_bound(a,b)),greatest_lower_bound(a,b)),
inference(rew,[status(thm),theory(equality)],[7,18925,354,5]),
[iquote('0:Rew:7.0,18925.0,354.0,18925.0,5.0,18925.0')] ).
cnf(19006,plain,
$false,
inference(mrr,[status(thm)],[19005,20]),
[iquote('0:MRR:19005.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 21:05:21 EDT 2022
% 0.14/0.35 % CPUTime :
% 4.67/4.83
% 4.67/4.83 SPASS V 3.9
% 4.67/4.83 SPASS beiseite: Proof found.
% 4.67/4.83 % SZS status Theorem
% 4.67/4.83 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.67/4.83 SPASS derived 12465 clauses, backtracked 0 clauses, performed 0 splits and kept 2472 clauses.
% 4.67/4.83 SPASS allocated 82340 KBytes.
% 4.67/4.83 SPASS spent 0:00:04.37 on the problem.
% 4.67/4.83 0:00:00.04 for the input.
% 4.67/4.83 0:00:00.00 for the FLOTTER CNF translation.
% 4.67/4.83 0:00:00.08 for inferences.
% 4.67/4.83 0:00:00.00 for the backtracking.
% 4.67/4.83 0:00:04.22 for the reduction.
% 4.67/4.83
% 4.67/4.83
% 4.67/4.83 Here is a proof with depth 7, length 35 :
% 4.67/4.83 % SZS output start Refutation
% See solution above
% 4.67/4.83 Formulae used in the proof : ax_glb1a_1 ax_glb1a_2 prove_ax_glb1a left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub associativity_of_glb lub_absorbtion glb_absorbtion monotony_lub2 monotony_glb2
% 4.67/4.83
%------------------------------------------------------------------------------