%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 11:44:39 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (  16 unt;   0 nHn;  16 RR)
%            Number of literals    :   16 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(multiply(u,identity),u),
    file('GRP001-2.p',unknown),
    [] ).

cnf(3,axiom,
    equal(multiply(u,u),identity),
    file('GRP001-2.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(a,b),c),
    file('GRP001-2.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(b,a),c),
    file('GRP001-2.p',unknown),
    [] ).

cnf(6,axiom,
    equal(multiply(identity,u),u),
    file('GRP001-2.p',unknown),
    [] ).

cnf(8,axiom,
    equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
    file('GRP001-2.p',unknown),
    [] ).

cnf(24,plain,
    equal(multiply(u,multiply(v,multiply(u,v))),identity),
    inference(spr,[status(thm),theory(equality)],[8,3]),
    [iquote('0:SpR:8.0,3.0')] ).

cnf(28,plain,
    equal(multiply(a,multiply(b,u)),multiply(c,u)),
    inference(spr,[status(thm),theory(equality)],[4,8]),
    [iquote('0:SpR:4.0,8.0')] ).

cnf(32,plain,
    equal(multiply(u,multiply(u,v)),multiply(identity,v)),
    inference(spr,[status(thm),theory(equality)],[3,8]),
    [iquote('0:SpR:3.0,8.0')] ).

cnf(36,plain,
    equal(multiply(u,multiply(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[6,32]),
    [iquote('0:Rew:6.0,32.0')] ).

cnf(70,plain,
    equal(multiply(c,b),multiply(a,identity)),
    inference(spr,[status(thm),theory(equality)],[3,28]),
    [iquote('0:SpR:3.0,28.0')] ).

cnf(73,plain,
    equal(multiply(c,b),a),
    inference(rew,[status(thm),theory(equality)],[1,70]),
    [iquote('0:Rew:1.0,70.0')] ).

cnf(84,plain,
    equal(multiply(u,multiply(v,u)),multiply(v,identity)),
    inference(spr,[status(thm),theory(equality)],[24,36]),
    [iquote('0:SpR:24.0,36.0')] ).

cnf(108,plain,
    equal(multiply(u,multiply(v,u)),v),
    inference(rew,[status(thm),theory(equality)],[1,84]),
    [iquote('0:Rew:1.0,84.0')] ).

cnf(140,plain,
    equal(multiply(b,a),c),
    inference(spr,[status(thm),theory(equality)],[73,108]),
    [iquote('0:SpR:73.0,108.0')] ).

cnf(142,plain,
    $false,
    inference(mrr,[status(thm)],[140,5]),
    [iquote('0:MRR:140.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n021.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 : Mon Jun 13 18:31:12 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.42  
% 0.20/0.42  SPASS V 3.9 
% 0.20/0.42  SPASS beiseite: Proof found.
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.42  SPASS derived 106 clauses, backtracked 0 clauses, performed 0 splits and kept 33 clauses.
% 0.20/0.42  SPASS allocated 63203 KBytes.
% 0.20/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.42  		0:00:00.03 for the input.
% 0.20/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42  		0:00:00.00 for inferences.
% 0.20/0.42  		0:00:00.00 for the backtracking.
% 0.20/0.42  		0:00:00.00 for the reduction.
% 0.20/0.42  
% 0.20/0.42  
% 0.20/0.42  Here is a proof with depth 3, length 16 :
% 0.20/0.42  % SZS output start Refutation
% See solution above
% 0.20/0.42  Formulae used in the proof : right_identity squareness a_times_b_is_c prove_b_times_a_is_c left_identity associativity
% 0.20/0.42  
%------------------------------------------------------------------------------