%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 11:44:55 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (   9 unt;   0 nHn;  15 RR)
%            Number of literals    :   22 (   0 equ;  12 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ subgroup_member(u)
    | product(another_identity,u,u) ),
    file('GRP037-3.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ subgroup_member(u)
    | product(another_inverse(u),u,another_identity) ),
    file('GRP037-3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,v,w)
    | equal(u,x) ),
    file('GRP037-3.p',unknown),
    [] ).

cnf(8,axiom,
    subgroup_member(a),
    file('GRP037-3.p',unknown),
    [] ).

cnf(10,axiom,
    ~ equal(inverse(a),another_inverse(a)),
    file('GRP037-3.p',unknown),
    [] ).

cnf(11,axiom,
    product(identity,u,u),
    file('GRP037-3.p',unknown),
    [] ).

cnf(13,axiom,
    product(inverse(u),u,identity),
    file('GRP037-3.p',unknown),
    [] ).

cnf(21,plain,
    ( ~ product(inverse(a),u,v)
    | ~ product(another_inverse(a),u,v) ),
    inference(res,[status(thm),theory(equality)],[7,10]),
    [iquote('0:Res:7.2,10.0')] ).

cnf(28,plain,
    ~ product(another_inverse(a),a,identity),
    inference(res,[status(thm),theory(equality)],[13,21]),
    [iquote('0:Res:13.0,21.0')] ).

cnf(48,plain,
    ( ~ product(u,v,v)
    | equal(identity,u) ),
    inference(res,[status(thm),theory(equality)],[11,7]),
    [iquote('0:Res:11.0,7.0')] ).

cnf(82,plain,
    ( ~ subgroup_member(u)
    | equal(identity,another_identity) ),
    inference(res,[status(thm),theory(equality)],[1,48]),
    [iquote('0:Res:1.1,48.0')] ).

cnf(105,plain,
    equal(identity,another_identity),
    inference(ems,[status(thm)],[82,8]),
    [iquote('0:EmS:82.0,8.0')] ).

cnf(111,plain,
    ~ product(another_inverse(a),a,another_identity),
    inference(rew,[status(thm),theory(equality)],[105,28]),
    [iquote('0:Rew:105.0,28.0')] ).

cnf(165,plain,
    ~ subgroup_member(a),
    inference(res,[status(thm),theory(equality)],[4,111]),
    [iquote('0:Res:4.1,111.0')] ).

cnf(166,plain,
    $false,
    inference(ssi,[status(thm)],[165,8]),
    [iquote('0:SSi:165.0,8.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n022.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 14:12:03 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.43  
% 0.20/0.43  SPASS V 3.9 
% 0.20/0.43  SPASS beiseite: Proof found.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.43  SPASS derived 135 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses.
% 0.20/0.43  SPASS allocated 75704 KBytes.
% 0.20/0.43  SPASS spent	0:00:00.07 on the problem.
% 0.20/0.43  		0:00:00.03 for the input.
% 0.20/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43  		0:00:00.00 for inferences.
% 0.20/0.43  		0:00:00.00 for the backtracking.
% 0.20/0.43  		0:00:00.01 for the reduction.
% 0.20/0.43  
% 0.20/0.43  
% 0.20/0.43  Here is a proof with depth 3, length 15 :
% 0.20/0.43  % SZS output start Refutation
% See solution above
% 0.20/0.43  Formulae used in the proof : another_left_identity another_left_inverse product_left_cancellation a_is_in_subgroup prove_two_inverses_are_equal left_identity left_inverse
% 0.20/0.43  
%------------------------------------------------------------------------------