TSTP Solution File: GRP193-2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP193-2 : 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 11:46:16 EDT 2022

% Result   : Unsatisfiable 0.21s 0.46s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   21 (  21 unt;   0 nHn;  21 RR)
%            Number of literals    :   21 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   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(greatest_lower_bound(identity,b),identity),
    file('GRP193-2.p',unknown),
    [] ).

cnf(4,axiom,
    equal(greatest_lower_bound(a,b),identity),
    file('GRP193-2.p',unknown),
    [] ).

cnf(5,axiom,
    equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),greatest_lower_bound(a,multiply(b,c))),
    file('GRP193-2.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),
    file('GRP193-2.p',unknown),
    [] ).

cnf(7,axiom,
    equal(multiply(identity,u),u),
    file('GRP193-2.p',unknown),
    [] ).

cnf(10,axiom,
    equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
    file('GRP193-2.p',unknown),
    [] ).

cnf(11,axiom,
    equal(least_upper_bound(u,v),least_upper_bound(v,u)),
    file('GRP193-2.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('GRP193-2.p',unknown),
    [] ).

cnf(16,axiom,
    equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
    file('GRP193-2.p',unknown),
    [] ).

cnf(17,axiom,
    equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
    file('GRP193-2.p',unknown),
    [] ).

cnf(19,axiom,
    equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
    file('GRP193-2.p',unknown),
    [] ).

cnf(21,axiom,
    equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
    file('GRP193-2.p',unknown),
    [] ).

cnf(22,plain,
    equal(greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))),greatest_lower_bound(a,multiply(b,c))),
    inference(rew,[status(thm),theory(equality)],[12,5,10,7,19,4]),
    [iquote('0:Rew:12.0,5.0,10.0,5.0,12.0,5.0,7.0,5.0,7.0,5.0,19.0,5.0,4.0,5.0')] ).

cnf(45,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(65,plain,
    equal(greatest_lower_bound(greatest_lower_bound(u,v),u),greatest_lower_bound(u,v)),
    inference(spr,[status(thm),theory(equality)],[16,45]),
    [iquote('0:SpR:16.0,45.0')] ).

cnf(68,plain,
    equal(greatest_lower_bound(u,greatest_lower_bound(u,v)),greatest_lower_bound(u,v)),
    inference(rew,[status(thm),theory(equality)],[10,65]),
    [iquote('0:Rew:10.0,65.0')] ).

cnf(69,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)],[68,22]),
    [iquote('0:Rew:68.0,22.0')] ).

cnf(384,plain,
    equal(greatest_lower_bound(multiply(identity,u),multiply(b,u)),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[2,21]),
    [iquote('0:SpR:2.0,21.0')] ).

cnf(403,plain,
    equal(greatest_lower_bound(u,multiply(b,u)),u),
    inference(rew,[status(thm),theory(equality)],[7,384]),
    [iquote('0:Rew:7.0,384.0')] ).

cnf(404,plain,
    equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),
    inference(rew,[status(thm),theory(equality)],[403,69]),
    [iquote('0:Rew:403.0,69.0')] ).

cnf(406,plain,
    $false,
    inference(mrr,[status(thm)],[404,6]),
    [iquote('0:MRR:404.0,6.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GRP193-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n022.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Tue Jun 14 09:11:33 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.21/0.46  
% 0.21/0.46  SPASS V 3.9 
% 0.21/0.46  SPASS beiseite: Proof found.
% 0.21/0.46  % SZS status Theorem
% 0.21/0.46  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.46  SPASS derived 326 clauses, backtracked 0 clauses, performed 0 splits and kept 108 clauses.
% 0.21/0.46  SPASS allocated 63500 KBytes.
% 0.21/0.46  SPASS spent	0:00:00.08 on the problem.
% 0.21/0.46  		0:00:00.04 for the input.
% 0.21/0.46  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.46  		0:00:00.00 for inferences.
% 0.21/0.46  		0:00:00.00 for the backtracking.
% 0.21/0.46  		0:00:00.02 for the reduction.
% 0.21/0.46  
% 0.21/0.46  
% 0.21/0.46  Here is a proof with depth 2, length 21 :
% 0.21/0.46  % SZS output start Refutation
% See solution above
% 0.21/0.46  Formulae used in the proof : p8_9b_2 p8_9b_4 p8_9b_5 prove_p8_9b left_identity symmetry_of_glb symmetry_of_lub associativity_of_glb lub_absorbtion glb_absorbtion monotony_glb1 monotony_glb2
% 0.21/0.46  
%------------------------------------------------------------------------------