%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP036-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   7 unt;   0 nHn;  14 RR)
%            Number of literals    :   25 (   0 equ;  16 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ subgroup_member(u)
    | product(another_identity,u,u) ),
    file('GRP036-3.p',unknown),
    [] ).

cnf(6,axiom,
    subgroup_member(another_identity),
    file('GRP036-3.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(identity,another_identity),
    file('GRP036-3.p',unknown),
    [] ).

cnf(9,axiom,
    product(u,identity,u),
    file('GRP036-3.p',unknown),
    [] ).

cnf(11,axiom,
    product(u,inverse(u),identity),
    file('GRP036-3.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equal(x,w) ),
    file('GRP036-3.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ subgroup_member(u)
    | ~ subgroup_member(v)
    | ~ product(v,inverse(u),w)
    | subgroup_member(w) ),
    file('GRP036-3.p',unknown),
    [] ).

cnf(17,plain,
    ( ~ product(u,v,another_identity)
    | ~ product(u,v,identity) ),
    inference(res,[status(thm),theory(equality)],[13,7]),
    [iquote('0:Res:13.2,7.0')] ).

cnf(20,plain,
    ( ~ subgroup_member(identity)
    | ~ product(another_identity,identity,another_identity) ),
    inference(res,[status(thm),theory(equality)],[1,17]),
    [iquote('0:Res:1.1,17.1')] ).

cnf(25,plain,
    ~ subgroup_member(identity),
    inference(mrr,[status(thm)],[20,9]),
    [iquote('0:MRR:20.1,9.0')] ).

cnf(44,plain,
    ( ~ subgroup_member(u)
    | ~ subgroup_member(u)
    | subgroup_member(identity) ),
    inference(res,[status(thm),theory(equality)],[11,16]),
    [iquote('0:Res:11.0,16.2')] ).

cnf(47,plain,
    ( ~ subgroup_member(u)
    | subgroup_member(identity) ),
    inference(obv,[status(thm),theory(equality)],[44]),
    [iquote('0:Obv:44.0')] ).

cnf(48,plain,
    ~ subgroup_member(u),
    inference(mrr,[status(thm)],[47,25]),
    [iquote('0:MRR:47.1,25.0')] ).

cnf(49,plain,
    $false,
    inference(unc,[status(thm)],[48,6]),
    [iquote('0:UnC:48.0,6.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP036-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n026.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 18:17:36 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 29 clauses, backtracked 0 clauses, performed 0 splits and kept 35 clauses.
% 0.19/0.42  SPASS allocated 75622 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 2, length 14 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : another_left_identity another_identity_in_subgroup prove_identity_equals_another_identity right_identity right_inverse total_function2 closure_of_product_and_inverse
% 0.19/0.42  
%------------------------------------------------------------------------------