%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 0.71s 0.90s
% Output   : Refutation 0.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   18 (  18 unt;   0 nHn;  18 RR)
%            Number of literals    :   18 (   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(greatest_lower_bound(identity,b),identity),
    file('GRP175-4.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(least_upper_bound(identity,multiply(inverse(a),multiply(b,a))),multiply(inverse(a),multiply(b,a))),
    file('GRP175-4.p',unknown),
    [] ).

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

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

cnf(6,axiom,
    equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
    file('GRP175-4.p',unknown),
    [] ).

cnf(7,axiom,
    equal(least_upper_bound(u,v),least_upper_bound(v,u)),
    file('GRP175-4.p',unknown),
    [] ).

cnf(12,axiom,
    equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
    file('GRP175-4.p',unknown),
    [] ).

cnf(15,axiom,
    equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
    file('GRP175-4.p',unknown),
    [] ).

cnf(17,axiom,
    equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
    file('GRP175-4.p',unknown),
    [] ).

cnf(39,plain,
    equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[6,12]),
    [iquote('0:SpR:6.0,12.0')] ).

cnf(218,plain,
    equal(greatest_lower_bound(multiply(identity,u),multiply(b,u)),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[1,17]),
    [iquote('0:SpR:1.0,17.0')] ).

cnf(230,plain,
    equal(greatest_lower_bound(u,multiply(b,u)),u),
    inference(rew,[status(thm),theory(equality)],[3,218]),
    [iquote('0:Rew:3.0,218.0')] ).

cnf(379,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(4374,plain,
    equal(greatest_lower_bound(multiply(inverse(u),u),multiply(inverse(u),multiply(b,u))),identity),
    inference(spr,[status(thm),theory(equality)],[230,379]),
    [iquote('0:SpR:230.0,379.0')] ).

cnf(4452,plain,
    equal(greatest_lower_bound(identity,multiply(inverse(u),multiply(b,u))),identity),
    inference(rew,[status(thm),theory(equality)],[4,4374]),
    [iquote('0:Rew:4.0,4374.0')] ).

cnf(4883,plain,
    equal(least_upper_bound(multiply(inverse(u),multiply(b,u)),identity),multiply(inverse(u),multiply(b,u))),
    inference(spr,[status(thm),theory(equality)],[4452,39]),
    [iquote('0:SpR:4452.0,39.0')] ).

cnf(4912,plain,
    equal(least_upper_bound(identity,multiply(inverse(u),multiply(b,u))),multiply(inverse(u),multiply(b,u))),
    inference(rew,[status(thm),theory(equality)],[7,4883]),
    [iquote('0:Rew:7.0,4883.0')] ).

cnf(4913,plain,
    $false,
    inference(unc,[status(thm)],[4912,2]),
    [iquote('0:UnC:4912.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 05:26:36 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.71/0.90  
% 0.71/0.90  SPASS V 3.9 
% 0.71/0.90  SPASS beiseite: Proof found.
% 0.71/0.90  % SZS status Theorem
% 0.71/0.90  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.71/0.90  SPASS derived 3375 clauses, backtracked 0 clauses, performed 0 splits and kept 636 clauses.
% 0.71/0.90  SPASS allocated 67502 KBytes.
% 0.71/0.90  SPASS spent	0:00:00.54 on the problem.
% 0.71/0.90  		0:00:00.03 for the input.
% 0.71/0.90  		0:00:00.00 for the FLOTTER CNF translation.
% 0.71/0.90  		0:00:00.03 for inferences.
% 0.71/0.90  		0:00:00.00 for the backtracking.
% 0.71/0.90  		0:00:00.46 for the reduction.
% 0.71/0.90  
% 0.71/0.90  
% 0.71/0.90  Here is a proof with depth 3, length 18 :
% 0.71/0.90  % SZS output start Refutation
% See solution above
% 0.71/0.90  Formulae used in the proof : p06d_1 prove_p06d left_identity left_inverse symmetry_of_glb symmetry_of_lub lub_absorbtion monotony_glb1 monotony_glb2
% 0.71/0.90  
%------------------------------------------------------------------------------