%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP176-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 11:46:07 EDT 2022

% Result   : Unsatisfiable 0.21s 0.41s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    5 (   5 unt;   0 nHn;   5 RR)
%            Number of literals    :    5 (   0 equ;   2 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(multiply(c,multiply(least_upper_bound(a,b),d)),least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d)))),
    file('GRP176-1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
    file('GRP176-1.p',unknown),
    [] ).

cnf(15,axiom,
    equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
    file('GRP176-1.p',unknown),
    [] ).

cnf(17,plain,
    ~ equal(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d)))),
    inference(rew,[status(thm),theory(equality)],[13,1,15]),
    [iquote('0:Rew:13.0,1.0,15.0,1.0')] ).

cnf(18,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[17]),
    [iquote('0:Obv:17.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP176-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n028.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jun 13 21:37:23 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.21/0.41  
% 0.21/0.41  SPASS V 3.9 
% 0.21/0.41  SPASS beiseite: Proof found.
% 0.21/0.41  % SZS status Theorem
% 0.21/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.41  SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 16 clauses.
% 0.21/0.41  SPASS allocated 63105 KBytes.
% 0.21/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.21/0.41  		0:00:00.03 for the input.
% 0.21/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.41  		0:00:00.00 for inferences.
% 0.21/0.41  		0:00:00.00 for the backtracking.
% 0.21/0.41  		0:00:00.00 for the reduction.
% 0.21/0.41  
% 0.21/0.41  
% 0.21/0.41  Here is a proof with depth 0, length 5 :
% 0.21/0.41  % SZS output start Refutation
% See solution above
% 0.21/0.41  Formulae used in the proof : prove_p07 monotony_lub1 monotony_lub2
% 0.21/0.41  
%------------------------------------------------------------------------------