TSTP Solution File: GRP147-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP147-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:45:55 EDT 2022
% Result : Unsatisfiable 4.38s 4.61s
% Output : Refutation 4.38s
% 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(greatest_lower_bound(a,c),a),
file('GRP147-1.p',unknown),
[] ).
cnf(2,axiom,
equal(greatest_lower_bound(b,c),b),
file('GRP147-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(greatest_lower_bound(least_upper_bound(a,b),c),least_upper_bound(a,b)),
file('GRP147-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP147-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP147-1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP147-1.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP147-1.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP147-1.p',unknown),
[] ).
cnf(10,axiom,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
file('GRP147-1.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP147-1.p',unknown),
[] ).
cnf(14,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP147-1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP147-1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP147-1.p',unknown),
[] ).
cnf(19,plain,
equal(greatest_lower_bound(c,b),b),
inference(rew,[status(thm),theory(equality)],[7,2]),
[iquote('0:Rew:7.0,2.0')] ).
cnf(20,plain,
~ equal(greatest_lower_bound(c,least_upper_bound(a,b)),least_upper_bound(a,b)),
inference(rew,[status(thm),theory(equality)],[7,3]),
[iquote('0:Rew:7.0,3.0')] ).
cnf(32,plain,
equal(least_upper_bound(c,b),c),
inference(spr,[status(thm),theory(equality)],[19,13]),
[iquote('0:SpR:19.0,13.0')] ).
cnf(38,plain,
equal(greatest_lower_bound(u,least_upper_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[8,14]),
[iquote('0:SpR:8.0,14.0')] ).
cnf(156,plain,
equal(least_upper_bound(c,least_upper_bound(b,u)),least_upper_bound(c,u)),
inference(spr,[status(thm),theory(equality)],[32,10]),
[iquote('0:SpR:32.0,10.0')] ).
cnf(175,plain,
equal(greatest_lower_bound(least_upper_bound(b,u),least_upper_bound(c,u)),least_upper_bound(b,u)),
inference(spr,[status(thm),theory(equality)],[156,38]),
[iquote('0:SpR:156.0,38.0')] ).
cnf(187,plain,
equal(greatest_lower_bound(least_upper_bound(c,u),least_upper_bound(b,u)),least_upper_bound(b,u)),
inference(rew,[status(thm),theory(equality)],[7,175]),
[iquote('0:Rew:7.0,175.0')] ).
cnf(347,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(348,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[4,347]),
[iquote('0:Rew:4.0,347.0')] ).
cnf(351,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[348]),
[iquote('0:SpR:348.0,348.0')] ).
cnf(354,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[5,348]),
[iquote('0:SpR:5.0,348.0')] ).
cnf(356,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[351,354]),
[iquote('0:Rew:351.0,354.0')] ).
cnf(389,plain,
equal(greatest_lower_bound(multiply(a,u),multiply(c,u)),multiply(a,u)),
inference(spr,[status(thm),theory(equality)],[1,18]),
[iquote('0:SpR:1.0,18.0')] ).
cnf(645,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[351,5]),
[iquote('0:SpR:351.0,5.0')] ).
cnf(1001,plain,
equal(greatest_lower_bound(multiply(a,inverse(c)),identity),multiply(a,inverse(c))),
inference(spr,[status(thm),theory(equality)],[645,389]),
[iquote('0:SpR:645.0,389.0')] ).
cnf(1012,plain,
equal(greatest_lower_bound(identity,multiply(a,inverse(c))),multiply(a,inverse(c))),
inference(rew,[status(thm),theory(equality)],[7,1001]),
[iquote('0:Rew:7.0,1001.0')] ).
cnf(4408,plain,
equal(least_upper_bound(identity,multiply(a,inverse(c))),identity),
inference(spr,[status(thm),theory(equality)],[1012,13]),
[iquote('0:SpR:1012.0,13.0')] ).
cnf(4431,plain,
equal(least_upper_bound(multiply(identity,u),multiply(multiply(a,inverse(c)),u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[4408,17]),
[iquote('0:SpR:4408.0,17.0')] ).
cnf(4452,plain,
equal(least_upper_bound(u,multiply(a,multiply(inverse(c),u))),u),
inference(rew,[status(thm),theory(equality)],[6,4431,4]),
[iquote('0:Rew:6.0,4431.0,4.0,4431.0')] ).
cnf(17383,plain,
equal(greatest_lower_bound(c,least_upper_bound(b,multiply(a,multiply(inverse(c),c)))),least_upper_bound(b,multiply(a,multiply(inverse(c),c)))),
inference(spr,[status(thm),theory(equality)],[4452,187]),
[iquote('0:SpR:4452.0,187.0')] ).
cnf(17468,plain,
equal(greatest_lower_bound(c,least_upper_bound(a,b)),least_upper_bound(a,b)),
inference(rew,[status(thm),theory(equality)],[8,17383,356,5]),
[iquote('0:Rew:8.0,17383.0,356.0,17383.0,5.0,17383.0')] ).
cnf(17469,plain,
$false,
inference(mrr,[status(thm)],[17468,20]),
[iquote('0:MRR:17468.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP147-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n022.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 16:39:48 EDT 2022
% 0.14/0.35 % CPUTime :
% 4.38/4.61
% 4.38/4.61 SPASS V 3.9
% 4.38/4.61 SPASS beiseite: Proof found.
% 4.38/4.61 % SZS status Theorem
% 4.38/4.61 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.38/4.61 SPASS derived 11455 clauses, backtracked 0 clauses, performed 0 splits and kept 2256 clauses.
% 4.38/4.61 SPASS allocated 80879 KBytes.
% 4.38/4.61 SPASS spent 0:00:04.14 on the problem.
% 4.38/4.61 0:00:00.03 for the input.
% 4.38/4.61 0:00:00.00 for the FLOTTER CNF translation.
% 4.38/4.61 0:00:00.09 for inferences.
% 4.38/4.61 0:00:00.00 for the backtracking.
% 4.38/4.61 0:00:03.99 for the reduction.
% 4.38/4.61
% 4.38/4.61
% 4.38/4.61 Here is a proof with depth 7, length 35 :
% 4.38/4.61 % SZS output start Refutation
% See solution above
% 4.38/4.61 Formulae used in the proof : ax_lub1b_1 ax_lub1b_2 prove_ax_lub1b left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub associativity_of_lub lub_absorbtion glb_absorbtion monotony_lub2 monotony_glb2
% 4.38/4.61
%------------------------------------------------------------------------------