%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP170-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 11:46:03 EDT 2022

% Result   : Unsatisfiable 7.41s 7.59s
% Output   : Refutation 7.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            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    :    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(least_upper_bound(a,b),b),
    file('GRP170-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(least_upper_bound(c,d),d),
    file('GRP170-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(least_upper_bound(multiply(a,c),multiply(b,d)),multiply(b,d)),
    file('GRP170-1.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('GRP170-1.p',unknown),
    [] ).

cnf(15,axiom,
    equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
    file('GRP170-1.p',unknown),
    [] ).

cnf(17,axiom,
    equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
    file('GRP170-1.p',unknown),
    [] ).

cnf(438,plain,
    equal(least_upper_bound(multiply(a,u),multiply(b,u)),multiply(b,u)),
    inference(spr,[status(thm),theory(equality)],[1,17]),
    [iquote('0:SpR:1.0,17.0')] ).

cnf(783,plain,
    equal(least_upper_bound(multiply(u,c),multiply(u,d)),multiply(u,d)),
    inference(spr,[status(thm),theory(equality)],[2,15]),
    [iquote('0:SpR:2.0,15.0')] ).

cnf(1131,plain,
    equal(least_upper_bound(multiply(a,u),least_upper_bound(multiply(b,u),v)),least_upper_bound(multiply(b,u),v)),
    inference(spr,[status(thm),theory(equality)],[438,10]),
    [iquote('0:SpR:438.0,10.0')] ).

cnf(25032,plain,
    equal(least_upper_bound(multiply(a,c),multiply(b,d)),multiply(b,d)),
    inference(spr,[status(thm),theory(equality)],[783,1131]),
    [iquote('0:SpR:783.0,1131.0')] ).

cnf(25063,plain,
    $false,
    inference(mrr,[status(thm)],[25032,3]),
    [iquote('0:MRR:25032.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GRP170-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n011.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jun 14 03:52:34 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 7.41/7.59  
% 7.41/7.59  SPASS V 3.9 
% 7.41/7.59  SPASS beiseite: Proof found.
% 7.41/7.59  % SZS status Theorem
% 7.41/7.59  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 7.41/7.59  SPASS derived 16541 clauses, backtracked 0 clauses, performed 0 splits and kept 2866 clauses.
% 7.41/7.59  SPASS allocated 87303 KBytes.
% 7.41/7.59  SPASS spent	0:00:07.07 on the problem.
% 7.41/7.59  		0:00:00.04 for the input.
% 7.41/7.59  		0:00:00.00 for the FLOTTER CNF translation.
% 7.41/7.59  		0:00:00.12 for inferences.
% 7.41/7.59  		0:00:00.00 for the backtracking.
% 7.41/7.59  		0:00:06.87 for the reduction.
% 7.41/7.59  
% 7.41/7.59  
% 7.41/7.59  Here is a proof with depth 3, length 11 :
% 7.41/7.59  % SZS output start Refutation
% See solution above
% 7.41/7.59  Formulae used in the proof : p03a_1 p03a_2 prove_p03a associativity_of_lub monotony_lub1 monotony_lub2
% 7.41/7.59  
%------------------------------------------------------------------------------