%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP044-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 11:44:58 EDT 2022

% Result   : Unsatisfiable 0.18s 0.43s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   6 unt;   0 nHn;  12 RR)
%            Number of literals    :   22 (   0 equ;  12 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;  11 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equalish(a,b),
    file('GRP044-2.p',unknown),
    [] ).

cnf(2,axiom,
    product(a,c,result),
    file('GRP044-2.p',unknown),
    [] ).

cnf(3,axiom,
    ~ product(b,c,result),
    file('GRP044-2.p',unknown),
    [] ).

cnf(4,axiom,
    product(identity,u,u),
    file('GRP044-2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('GRP044-2.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ equalish(u,v)
    | ~ product(w,x,u)
    | product(w,x,v) ),
    file('GRP044-2.p',unknown),
    [] ).

cnf(16,plain,
    ( ~ equalish(u,v)
    | product(identity,u,v) ),
    inference(res,[status(thm),theory(equality)],[4,10]),
    [iquote('0:Res:4.0,10.1')] ).

cnf(30,plain,
    ( ~ product(u,v,w)
    | ~ product(identity,u,x)
    | product(x,v,w) ),
    inference(res,[status(thm),theory(equality)],[4,9]),
    [iquote('0:Res:4.0,9.0')] ).

cnf(134,plain,
    ( ~ product(identity,a,u)
    | product(u,c,result) ),
    inference(res,[status(thm),theory(equality)],[2,30]),
    [iquote('0:Res:2.0,30.0')] ).

cnf(178,plain,
    ( ~ equalish(a,u)
    | product(u,c,result) ),
    inference(res,[status(thm),theory(equality)],[16,134]),
    [iquote('0:Res:16.1,134.0')] ).

cnf(208,plain,
    ~ equalish(a,b),
    inference(res,[status(thm),theory(equality)],[178,3]),
    [iquote('0:Res:178.1,3.0')] ).

cnf(221,plain,
    $false,
    inference(mrr,[status(thm)],[208,1]),
    [iquote('0:MRR:208.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP044-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n011.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 : Tue Jun 14 02:29:49 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.43  
% 0.18/0.43  SPASS V 3.9 
% 0.18/0.43  SPASS beiseite: Proof found.
% 0.18/0.43  % SZS status Theorem
% 0.18/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.43  SPASS derived 210 clauses, backtracked 0 clauses, performed 0 splits and kept 194 clauses.
% 0.18/0.43  SPASS allocated 63290 KBytes.
% 0.18/0.43  SPASS spent	0:00:00.09 on the problem.
% 0.18/0.43  		0:00:00.03 for the input.
% 0.18/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43  		0:00:00.00 for inferences.
% 0.18/0.43  		0:00:00.00 for the backtracking.
% 0.18/0.43  		0:00:00.03 for the reduction.
% 0.18/0.43  
% 0.18/0.43  
% 0.18/0.43  Here is a proof with depth 4, length 12 :
% 0.18/0.43  % SZS output start Refutation
% See solution above
% 0.18/0.43  Formulae used in the proof : a_equals_b product_with_a prove_product_with_b left_identity associativity2 product_substitution3
% 0.18/0.43  
%------------------------------------------------------------------------------