TSTP Solution File: GRP140-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP140-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:45:54 EDT 2022
% Result : Unsatisfiable 1.52s 1.69s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 29 RR)
% Number of literals : 29 ( 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),c),
file('GRP140-1.p',unknown),
[] ).
cnf(2,axiom,
equal(greatest_lower_bound(b,c),c),
file('GRP140-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(least_upper_bound(greatest_lower_bound(a,b),c),greatest_lower_bound(a,b)),
file('GRP140-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP140-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP140-1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP140-1.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP140-1.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP140-1.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('GRP140-1.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP140-1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP140-1.p',unknown),
[] ).
cnf(19,plain,
equal(greatest_lower_bound(c,b),c),
inference(rew,[status(thm),theory(equality)],[7,2]),
[iquote('0:Rew:7.0,2.0')] ).
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(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(254,plain,
equal(greatest_lower_bound(c,greatest_lower_bound(b,u)),greatest_lower_bound(c,u)),
inference(spr,[status(thm),theory(equality)],[19,9]),
[iquote('0:SpR:19.0,9.0')] ).
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(387,plain,
equal(greatest_lower_bound(multiply(a,u),multiply(c,u)),multiply(c,u)),
inference(spr,[status(thm),theory(equality)],[1,18]),
[iquote('0:SpR:1.0,18.0')] ).
cnf(461,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)],[254,46]),
[iquote('0:SpR:254.0,46.0')] ).
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)],[8,461]),
[iquote('0:Rew:8.0,461.0')] ).
cnf(649,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(spr,[status(thm),theory(equality)],[349,346]),
[iquote('0:SpR:349.0,346.0')] ).
cnf(1001,plain,
equal(greatest_lower_bound(multiply(a,multiply(inverse(c),u)),u),u),
inference(spr,[status(thm),theory(equality)],[649,387]),
[iquote('0:SpR:649.0,387.0')] ).
cnf(1014,plain,
equal(greatest_lower_bound(u,multiply(a,multiply(inverse(c),u))),u),
inference(rew,[status(thm),theory(equality)],[7,1001]),
[iquote('0:Rew:7.0,1001.0')] ).
cnf(7598,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)],[1014,476]),
[iquote('0:SpR:1014.0,476.0')] ).
cnf(7654,plain,
equal(least_upper_bound(c,greatest_lower_bound(a,b)),greatest_lower_bound(a,b)),
inference(rew,[status(thm),theory(equality)],[7,7598,354,5]),
[iquote('0:Rew:7.0,7598.0,354.0,7598.0,5.0,7598.0')] ).
cnf(7655,plain,
$false,
inference(mrr,[status(thm)],[7654,20]),
[iquote('0:MRR:7654.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP140-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 : Mon Jun 13 10:16:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.52/1.69
% 1.52/1.69 SPASS V 3.9
% 1.52/1.69 SPASS beiseite: Proof found.
% 1.52/1.69 % SZS status Theorem
% 1.52/1.69 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.52/1.69 SPASS derived 5214 clauses, backtracked 0 clauses, performed 0 splits and kept 1247 clauses.
% 1.52/1.69 SPASS allocated 72630 KBytes.
% 1.52/1.69 SPASS spent 0:00:01.30 on the problem.
% 1.52/1.69 0:00:00.03 for the input.
% 1.52/1.69 0:00:00.00 for the FLOTTER CNF translation.
% 1.52/1.69 0:00:00.04 for inferences.
% 1.52/1.69 0:00:00.00 for the backtracking.
% 1.52/1.69 0:00:01.20 for the reduction.
% 1.52/1.69
% 1.52/1.69
% 1.52/1.69 Here is a proof with depth 5, length 29 :
% 1.52/1.69 % SZS output start Refutation
% See solution above
% 1.52/1.69 Formulae used in the proof : ax_glb1c_1 ax_glb1c_2 prove_ax_glb1c left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub associativity_of_glb lub_absorbtion monotony_glb2
% 1.52/1.69
%------------------------------------------------------------------------------