%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP010-1 : 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 11:44:44 EDT 2022

% Result   : Unsatisfiable 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   9 unt;   0 nHn;  14 RR)
%            Number of literals    :   23 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   9 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    product(a,b,identity),
    file('GRP010-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ product(b,a,identity),
    file('GRP010-1.p',unknown),
    [] ).

cnf(3,axiom,
    product(identity,u,u),
    file('GRP010-1.p',unknown),
    [] ).

cnf(4,axiom,
    product(u,identity,u),
    file('GRP010-1.p',unknown),
    [] ).

cnf(5,axiom,
    product(inverse(u),u,identity),
    file('GRP010-1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equal(x,w) ),
    file('GRP010-1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('GRP010-1.p',unknown),
    [] ).

cnf(16,plain,
    ( ~ product(identity,u,v)
    | equal(v,u) ),
    inference(res,[status(thm),theory(equality)],[3,8]),
    [iquote('0:Res:3.0,8.0')] ).

cnf(25,plain,
    ( ~ product(u,v,identity)
    | ~ product(w,u,x)
    | product(x,v,w) ),
    inference(res,[status(thm),theory(equality)],[4,10]),
    [iquote('0:Res:4.0,10.0')] ).

cnf(128,plain,
    ( ~ product(u,a,v)
    | product(v,b,u) ),
    inference(res,[status(thm),theory(equality)],[1,25]),
    [iquote('0:Res:1.0,25.0')] ).

cnf(146,plain,
    product(identity,b,inverse(a)),
    inference(res,[status(thm),theory(equality)],[5,128]),
    [iquote('0:Res:5.0,128.0')] ).

cnf(156,plain,
    equal(inverse(a),b),
    inference(res,[status(thm),theory(equality)],[146,16]),
    [iquote('0:Res:146.0,16.0')] ).

cnf(174,plain,
    product(b,a,identity),
    inference(spr,[status(thm),theory(equality)],[156,5]),
    [iquote('0:SpR:156.0,5.0')] ).

cnf(181,plain,
    $false,
    inference(mrr,[status(thm)],[174,2]),
    [iquote('0:MRR:174.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP010-1 : 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 : Tue Jun 14 10:49:06 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.43  
% 0.19/0.43  SPASS V 3.9 
% 0.19/0.43  SPASS beiseite: Proof found.
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.43  SPASS derived 147 clauses, backtracked 0 clauses, performed 0 splits and kept 80 clauses.
% 0.19/0.43  SPASS allocated 63213 KBytes.
% 0.19/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.43  		0:00:00.04 for the input.
% 0.19/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43  		0:00:00.00 for inferences.
% 0.19/0.43  		0:00:00.00 for the backtracking.
% 0.19/0.43  		0:00:00.01 for the reduction.
% 0.19/0.43  
% 0.19/0.43  
% 0.19/0.43  Here is a proof with depth 5, length 14 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : a_multiply_b_is_identity prove_b_multiply_a_is_identity left_identity right_identity left_inverse total_function2 associativity2
% 0.19/0.43  
%------------------------------------------------------------------------------