%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP175-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 11:46:06 EDT 2022

% Result   : Unsatisfiable 0.68s 0.88s
% Output   : Refutation 0.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (  14 unt;   0 nHn;  14 RR)
%            Number of literals    :   14 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(least_upper_bound(identity,b),b),
    file('GRP175-3.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))),identity),
    file('GRP175-3.p',unknown),
    [] ).

cnf(3,axiom,
    equal(multiply(identity,u),u),
    file('GRP175-3.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(inverse(u),u),identity),
    file('GRP175-3.p',unknown),
    [] ).

cnf(13,axiom,
    equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
    file('GRP175-3.p',unknown),
    [] ).

cnf(15,axiom,
    equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
    file('GRP175-3.p',unknown),
    [] ).

cnf(17,axiom,
    equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
    file('GRP175-3.p',unknown),
    [] ).

cnf(24,plain,
    equal(greatest_lower_bound(identity,b),identity),
    inference(spr,[status(thm),theory(equality)],[1,13]),
    [iquote('0:SpR:1.0,13.0')] ).

cnf(330,plain,
    equal(greatest_lower_bound(multiply(identity,u),multiply(b,u)),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[24,17]),
    [iquote('0:SpR:24.0,17.0')] ).

cnf(338,plain,
    equal(greatest_lower_bound(u,multiply(b,u)),u),
    inference(rew,[status(thm),theory(equality)],[3,330]),
    [iquote('0:Rew:3.0,330.0')] ).

cnf(524,plain,
    equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(u,v)),u),multiply(inverse(greatest_lower_bound(u,v)),v)),identity),
    inference(spr,[status(thm),theory(equality)],[15,4]),
    [iquote('0:SpR:15.0,4.0')] ).

cnf(4030,plain,
    equal(greatest_lower_bound(multiply(inverse(u),u),multiply(inverse(u),multiply(b,u))),identity),
    inference(spr,[status(thm),theory(equality)],[338,524]),
    [iquote('0:SpR:338.0,524.0')] ).

cnf(4117,plain,
    equal(greatest_lower_bound(identity,multiply(inverse(u),multiply(b,u))),identity),
    inference(rew,[status(thm),theory(equality)],[4,4030]),
    [iquote('0:Rew:4.0,4030.0')] ).

cnf(4118,plain,
    $false,
    inference(unc,[status(thm)],[4117,2]),
    [iquote('0:UnC:4117.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP175-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n015.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 06:01:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.68/0.88  
% 0.68/0.88  SPASS V 3.9 
% 0.68/0.88  SPASS beiseite: Proof found.
% 0.68/0.88  % SZS status Theorem
% 0.68/0.88  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.68/0.88  SPASS derived 2917 clauses, backtracked 0 clauses, performed 0 splits and kept 533 clauses.
% 0.68/0.88  SPASS allocated 66693 KBytes.
% 0.68/0.88  SPASS spent	0:00:00.51 on the problem.
% 0.68/0.88  		0:00:00.04 for the input.
% 0.68/0.88  		0:00:00.00 for the FLOTTER CNF translation.
% 0.68/0.88  		0:00:00.03 for inferences.
% 0.68/0.88  		0:00:00.00 for the backtracking.
% 0.68/0.88  		0:00:00.42 for the reduction.
% 0.68/0.88  
% 0.68/0.88  
% 0.68/0.88  Here is a proof with depth 3, length 14 :
% 0.68/0.88  % SZS output start Refutation
% See solution above
% 0.68/0.88  Formulae used in the proof : p06c_1 prove_p06c left_identity left_inverse glb_absorbtion monotony_glb1 monotony_glb2
% 0.68/0.88  
%------------------------------------------------------------------------------