TSTP Solution File: GRP138-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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  
%------------------------------------------------------------------------------