%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP170-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 11:46:04 EDT 2022

% Result   : Unsatisfiable 5.79s 5.99s
% Output   : Refutation 5.79s
% 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    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(greatest_lower_bound(a,b),a),
    file('GRP170-2.p',unknown),
    [] ).

cnf(2,axiom,
    equal(greatest_lower_bound(c,d),c),
    file('GRP170-2.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
    file('GRP170-2.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('GRP170-2.p',unknown),
    [] ).

cnf(16,axiom,
    equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
    file('GRP170-2.p',unknown),
    [] ).

cnf(18,axiom,
    equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
    file('GRP170-2.p',unknown),
    [] ).

cnf(338,plain,
    equal(greatest_lower_bound(multiply(a,u),multiply(b,u)),multiply(a,u)),
    inference(spr,[status(thm),theory(equality)],[1,18]),
    [iquote('0:SpR:1.0,18.0')] ).

cnf(539,plain,
    equal(greatest_lower_bound(multiply(u,c),multiply(u,d)),multiply(u,c)),
    inference(spr,[status(thm),theory(equality)],[2,16]),
    [iquote('0:SpR:2.0,16.0')] ).

cnf(1133,plain,
    equal(greatest_lower_bound(multiply(a,u),greatest_lower_bound(multiply(b,u),v)),greatest_lower_bound(multiply(a,u),v)),
    inference(spr,[status(thm),theory(equality)],[338,9]),
    [iquote('0:SpR:338.0,9.0')] ).

cnf(21671,plain,
    equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),greatest_lower_bound(multiply(a,c),multiply(b,c))),
    inference(spr,[status(thm),theory(equality)],[539,1133]),
    [iquote('0:SpR:539.0,1133.0')] ).

cnf(21705,plain,
    equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
    inference(rew,[status(thm),theory(equality)],[338,21671]),
    [iquote('0:Rew:338.0,21671.0')] ).

cnf(21706,plain,
    $false,
    inference(mrr,[status(thm)],[21705,3]),
    [iquote('0:MRR:21705.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP170-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 14 01:15:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 5.79/5.99  
% 5.79/5.99  SPASS V 3.9 
% 5.79/5.99  SPASS beiseite: Proof found.
% 5.79/5.99  % SZS status Theorem
% 5.79/5.99  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 5.79/5.99  SPASS derived 14278 clauses, backtracked 0 clauses, performed 0 splits and kept 2688 clauses.
% 5.79/5.99  SPASS allocated 84635 KBytes.
% 5.79/5.99  SPASS spent	0:00:05.51 on the problem.
% 5.79/5.99  		0:00:00.04 for the input.
% 5.79/5.99  		0:00:00.00 for the FLOTTER CNF translation.
% 5.79/5.99  		0:00:00.10 for inferences.
% 5.79/5.99  		0:00:00.00 for the backtracking.
% 5.79/5.99  		0:00:05.34 for the reduction.
% 5.79/5.99  
% 5.79/5.99  
% 5.79/5.99  Here is a proof with depth 3, length 12 :
% 5.79/5.99  % SZS output start Refutation
% See solution above
% 5.79/5.99  Formulae used in the proof : p03b_1 p03b_2 prove_p03b associativity_of_glb monotony_glb1 monotony_glb2
% 5.79/5.99  
%------------------------------------------------------------------------------