TSTP Solution File: GRP193-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP193-1 : 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 11:46:16 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% 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; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(least_upper_bound(identity,b),b),
file('GRP193-1.p',unknown),
[] ).
cnf(4,axiom,
equal(greatest_lower_bound(a,b),identity),
file('GRP193-1.p',unknown),
[] ).
cnf(5,axiom,
equal(least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
file('GRP193-1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),
file('GRP193-1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(identity,u),u),
file('GRP193-1.p',unknown),
[] ).
cnf(10,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP193-1.p',unknown),
[] ).
cnf(11,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP193-1.p',unknown),
[] ).
cnf(12,axiom,
equal(greatest_lower_bound(greatest_lower_bound(u,v),w),greatest_lower_bound(u,greatest_lower_bound(v,w))),
file('GRP193-1.p',unknown),
[] ).
cnf(16,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP193-1.p',unknown),
[] ).
cnf(17,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP193-1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP193-1.p',unknown),
[] ).
cnf(21,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP193-1.p',unknown),
[] ).
cnf(22,plain,
equal(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))),greatest_lower_bound(a,c)),
inference(rew,[status(thm),theory(equality)],[11,5,7,19,4]),
[iquote('0:Rew:11.0,5.0,7.0,5.0,7.0,5.0,19.0,5.0,4.0,5.0')] ).
cnf(33,plain,
equal(greatest_lower_bound(identity,b),identity),
inference(spr,[status(thm),theory(equality)],[2,17]),
[iquote('0:SpR:2.0,17.0')] ).
cnf(49,plain,
equal(greatest_lower_bound(u,least_upper_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[11,17]),
[iquote('0:SpR:11.0,17.0')] ).
cnf(72,plain,
equal(greatest_lower_bound(greatest_lower_bound(u,v),u),greatest_lower_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[16,49]),
[iquote('0:SpR:16.0,49.0')] ).
cnf(74,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(u,v)),greatest_lower_bound(u,v)),
inference(rew,[status(thm),theory(equality)],[10,72]),
[iquote('0:Rew:10.0,72.0')] ).
cnf(355,plain,
equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))),
inference(spr,[status(thm),theory(equality)],[22,49]),
[iquote('0:SpR:22.0,49.0')] ).
cnf(359,plain,
equal(greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),greatest_lower_bound(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[74,355,12,10]),
[iquote('0:Rew:74.0,355.0,12.0,355.0,10.0,355.0,12.0,355.0')] ).
cnf(439,plain,
equal(greatest_lower_bound(multiply(identity,u),multiply(b,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[33,21]),
[iquote('0:SpR:33.0,21.0')] ).
cnf(452,plain,
equal(greatest_lower_bound(u,multiply(b,u)),u),
inference(rew,[status(thm),theory(equality)],[7,439]),
[iquote('0:Rew:7.0,439.0')] ).
cnf(453,plain,
equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),
inference(rew,[status(thm),theory(equality)],[452,359]),
[iquote('0:Rew:452.0,359.0')] ).
cnf(454,plain,
$false,
inference(mrr,[status(thm)],[453,6]),
[iquote('0:MRR:453.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 06:16:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 360 clauses, backtracked 0 clauses, performed 0 splits and kept 98 clauses.
% 0.20/0.45 SPASS allocated 63497 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.02 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 2, length 23 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : p8_9a_2 p8_9a_4 p8_9a_5 prove_p8_9a left_identity symmetry_of_glb symmetry_of_lub associativity_of_glb lub_absorbtion glb_absorbtion monotony_glb1 monotony_glb2
% 0.20/0.45
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