%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP172-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 11:46:05 EDT 2022

% Result   : Unsatisfiable 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (  12 unt;   0 nHn;  12 RR)
%            Number of literals    :   12 (   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    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(greatest_lower_bound(identity,a),identity),
    file('GRP172-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(greatest_lower_bound(identity,b),identity),
    file('GRP172-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(greatest_lower_bound(identity,multiply(a,b)),identity),
    file('GRP172-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(identity,u),u),
    file('GRP172-1.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('GRP172-1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
    file('GRP172-1.p',unknown),
    [] ).

cnf(241,plain,
    equal(greatest_lower_bound(identity,greatest_lower_bound(b,u)),greatest_lower_bound(identity,u)),
    inference(spr,[status(thm),theory(equality)],[2,9]),
    [iquote('0:SpR:2.0,9.0')] ).

cnf(386,plain,
    equal(greatest_lower_bound(multiply(identity,u),multiply(a,u)),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[1,18]),
    [iquote('0:SpR:1.0,18.0')] ).

cnf(402,plain,
    equal(greatest_lower_bound(u,multiply(a,u)),u),
    inference(rew,[status(thm),theory(equality)],[4,386]),
    [iquote('0:Rew:4.0,386.0')] ).

cnf(463,plain,
    equal(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(identity,b)),
    inference(spr,[status(thm),theory(equality)],[402,241]),
    [iquote('0:SpR:402.0,241.0')] ).

cnf(469,plain,
    equal(greatest_lower_bound(identity,multiply(a,b)),identity),
    inference(rew,[status(thm),theory(equality)],[2,463]),
    [iquote('0:Rew:2.0,463.0')] ).

cnf(470,plain,
    $false,
    inference(mrr,[status(thm)],[469,3]),
    [iquote('0:MRR:469.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GRP172-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n012.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 : Tue Jun 14 13:42:55 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.20/0.45  
% 0.20/0.45  SPASS V 3.9 
% 0.20/0.45  SPASS beiseite: Proof found.
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.45  SPASS derived 358 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses.
% 0.20/0.45  SPASS allocated 63512 KBytes.
% 0.20/0.45  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.45  		0:00:00.03 for the input.
% 0.20/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45  		0:00:00.00 for inferences.
% 0.20/0.45  		0:00:00.00 for the backtracking.
% 0.20/0.45  		0:00:00.02 for the reduction.
% 0.20/0.45  
% 0.20/0.45  
% 0.20/0.45  Here is a proof with depth 2, length 12 :
% 0.20/0.45  % SZS output start Refutation
% See solution above
% 0.20/0.45  Formulae used in the proof : p04b_1 p04b_2 prove_p04b left_identity associativity_of_glb monotony_glb2
% 0.20/0.45  
%------------------------------------------------------------------------------