%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP162-1 : 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 11:45:59 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   7 unt;   0 nHn;   7 RR)
%            Number of literals    :    7 (   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    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(least_upper_bound(a,b),b),
    file('GRP162-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(least_upper_bound(b,c),c),
    file('GRP162-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(least_upper_bound(a,c),c),
    file('GRP162-1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
    file('GRP162-1.p',unknown),
    [] ).

cnf(72,plain,
    equal(least_upper_bound(a,least_upper_bound(b,u)),least_upper_bound(b,u)),
    inference(spr,[status(thm),theory(equality)],[1,10]),
    [iquote('0:SpR:1.0,10.0')] ).

cnf(157,plain,
    equal(least_upper_bound(a,c),c),
    inference(spr,[status(thm),theory(equality)],[2,72]),
    [iquote('0:SpR:2.0,72.0')] ).

cnf(164,plain,
    $false,
    inference(mrr,[status(thm)],[157,3]),
    [iquote('0:MRR:157.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP162-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 13 05:22:32 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.42  
% 0.20/0.42  SPASS V 3.9 
% 0.20/0.42  SPASS beiseite: Proof found.
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.42  SPASS derived 128 clauses, backtracked 0 clauses, performed 0 splits and kept 57 clauses.
% 0.20/0.42  SPASS allocated 63244 KBytes.
% 0.20/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.20/0.42  		0:00:00.04 for the input.
% 0.20/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42  		0:00:00.00 for inferences.
% 0.20/0.42  		0:00:00.00 for the backtracking.
% 0.20/0.42  		0:00:00.01 for the reduction.
% 0.20/0.42  
% 0.20/0.42  
% 0.20/0.42  Here is a proof with depth 2, length 7 :
% 0.20/0.42  % SZS output start Refutation
% See solution above
% 0.20/0.42  Formulae used in the proof : ax_transa_1 ax_transa_2 prove_ax_transa associativity_of_lub
% 0.20/0.42  
%------------------------------------------------------------------------------