TSTP Solution File: GRP166-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP166-1 : 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 11:46:00 EDT 2022

% Result   : Unsatisfiable 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% 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;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(least_upper_bound(b,identity),b),
    file('GRP166-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(least_upper_bound(a,multiply(a,b)),multiply(a,b)),
    file('GRP166-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(identity,u),u),
    file('GRP166-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(multiply(inverse(u),u),identity),
    file('GRP166-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
    file('GRP166-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
    file('GRP166-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(least_upper_bound(u,v),least_upper_bound(v,u)),
    file('GRP166-1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
    file('GRP166-1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
    file('GRP166-1.p',unknown),
    [] ).

cnf(16,axiom,
    equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
    file('GRP166-1.p',unknown),
    [] ).

cnf(19,plain,
    equal(least_upper_bound(identity,b),b),
    inference(rew,[status(thm),theory(equality)],[8,2]),
    [iquote('0:Rew:8.0,2.0')] ).

cnf(28,plain,
    equal(greatest_lower_bound(identity,b),identity),
    inference(spr,[status(thm),theory(equality)],[19,14]),
    [iquote('0:SpR:19.0,14.0')] ).

cnf(45,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(344,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(345,plain,
    equal(multiply(inverse(u),multiply(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[4,344]),
    [iquote('0:Rew:4.0,344.0')] ).

cnf(348,plain,
    equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
    inference(spr,[status(thm),theory(equality)],[345]),
    [iquote('0:SpR:345.0,345.0')] ).

cnf(351,plain,
    equal(multiply(inverse(inverse(u)),identity),u),
    inference(spr,[status(thm),theory(equality)],[5,345]),
    [iquote('0:SpR:5.0,345.0')] ).

cnf(353,plain,
    equal(multiply(u,identity),u),
    inference(rew,[status(thm),theory(equality)],[348,351]),
    [iquote('0:Rew:348.0,351.0')] ).

cnf(615,plain,
    equal(greatest_lower_bound(multiply(u,identity),multiply(u,b)),multiply(u,identity)),
    inference(spr,[status(thm),theory(equality)],[28,16]),
    [iquote('0:SpR:28.0,16.0')] ).

cnf(627,plain,
    equal(greatest_lower_bound(u,multiply(u,b)),u),
    inference(rew,[status(thm),theory(equality)],[353,615]),
    [iquote('0:Rew:353.0,615.0')] ).

cnf(660,plain,
    equal(least_upper_bound(multiply(u,b),u),multiply(u,b)),
    inference(spr,[status(thm),theory(equality)],[627,45]),
    [iquote('0:SpR:627.0,45.0')] ).

cnf(674,plain,
    equal(least_upper_bound(u,multiply(u,b)),multiply(u,b)),
    inference(rew,[status(thm),theory(equality)],[8,660]),
    [iquote('0:Rew:8.0,660.0')] ).

cnf(675,plain,
    $false,
    inference(unc,[status(thm)],[674,3]),
    [iquote('0:UnC:674.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP166-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n027.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 : Tue Jun 14 07:59:18 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.45  
% 0.19/0.45  SPASS V 3.9 
% 0.19/0.45  SPASS beiseite: Proof found.
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 489 clauses, backtracked 0 clauses, performed 0 splits and kept 131 clauses.
% 0.19/0.45  SPASS allocated 63758 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.10 on the problem.
% 0.19/0.45  		0:00:00.03 for the input.
% 0.19/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45  		0:00:00.01 for inferences.
% 0.19/0.45  		0:00:00.00 for the backtracking.
% 0.19/0.45  		0:00:00.04 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 3, length 23 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : lat2a_2 prove_lat2a left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub lub_absorbtion glb_absorbtion monotony_glb1
% 0.19/0.45  
%------------------------------------------------------------------------------