%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP159-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 11:45:58 EDT 2022

% Result   : Unsatisfiable 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (  11 unt;   0 nHn;  11 RR)
%            Number of literals    :   11 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(greatest_lower_bound(a,b),a),
    file('GRP159-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(least_upper_bound(multiply(c,a),multiply(c,b)),multiply(c,b)),
    file('GRP159-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
    file('GRP159-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(least_upper_bound(u,v),least_upper_bound(v,u)),
    file('GRP159-1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
    file('GRP159-1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
    file('GRP159-1.p',unknown),
    [] ).

cnf(39,plain,
    equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[6,12]),
    [iquote('0:SpR:6.0,12.0')] ).

cnf(75,plain,
    equal(least_upper_bound(b,a),b),
    inference(spr,[status(thm),theory(equality)],[1,39]),
    [iquote('0:SpR:1.0,39.0')] ).

cnf(81,plain,
    equal(least_upper_bound(a,b),b),
    inference(rew,[status(thm),theory(equality)],[7,75]),
    [iquote('0:Rew:7.0,75.0')] ).

cnf(771,plain,
    equal(least_upper_bound(multiply(u,a),multiply(u,b)),multiply(u,b)),
    inference(spr,[status(thm),theory(equality)],[81,14]),
    [iquote('0:SpR:81.0,14.0')] ).

cnf(779,plain,
    $false,
    inference(unc,[status(thm)],[771,2]),
    [iquote('0:UnC:771.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP159-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n009.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 22:12:08 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.47  
% 0.19/0.47  SPASS V 3.9 
% 0.19/0.47  SPASS beiseite: Proof found.
% 0.19/0.47  % SZS status Theorem
% 0.19/0.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.47  SPASS derived 580 clauses, backtracked 0 clauses, performed 0 splits and kept 145 clauses.
% 0.19/0.47  SPASS allocated 63869 KBytes.
% 0.19/0.47  SPASS spent	0:00:00.12 on the problem.
% 0.19/0.47  		0:00:00.03 for the input.
% 0.19/0.47  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47  		0:00:00.01 for inferences.
% 0.19/0.47  		0:00:00.00 for the backtracking.
% 0.19/0.47  		0:00:00.05 for the reduction.
% 0.19/0.47  
% 0.19/0.47  
% 0.19/0.47  Here is a proof with depth 3, length 11 :
% 0.19/0.47  % SZS output start Refutation
% See solution above
% 0.19/0.47  Formulae used in the proof : ax_mono2c_1 prove_ax_mono2c symmetry_of_glb symmetry_of_lub lub_absorbtion monotony_lub1
% 0.19/0.47  
%------------------------------------------------------------------------------