%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP042-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   6 unt;   0 nHn;  10 RR)
%            Number of literals    :   16 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   7 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equalish(a,b),
    file('GRP042-2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equalish(b,a),
    file('GRP042-2.p',unknown),
    [] ).

cnf(3,axiom,
    product(identity,u,u),
    file('GRP042-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equalish(x,w) ),
    file('GRP042-2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ equalish(u,v)
    | ~ product(w,x,u)
    | product(w,x,v) ),
    file('GRP042-2.p',unknown),
    [] ).

cnf(10,plain,
    ( ~ product(u,v,a)
    | ~ product(u,v,b) ),
    inference(res,[status(thm),theory(equality)],[6,2]),
    [iquote('0:Res:6.2,2.0')] ).

cnf(11,plain,
    ~ product(identity,a,b),
    inference(res,[status(thm),theory(equality)],[3,10]),
    [iquote('0:Res:3.0,10.0')] ).

cnf(12,plain,
    ( ~ equalish(u,v)
    | product(identity,u,v) ),
    inference(res,[status(thm),theory(equality)],[3,9]),
    [iquote('0:Res:3.0,9.1')] ).

cnf(16,plain,
    ~ equalish(a,b),
    inference(res,[status(thm),theory(equality)],[12,11]),
    [iquote('0:Res:12.1,11.0')] ).

cnf(18,plain,
    $false,
    inference(mrr,[status(thm)],[16,1]),
    [iquote('0:MRR:16.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP042-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n010.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 12:20:54 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.41  
% 0.20/0.41  SPASS V 3.9 
% 0.20/0.41  SPASS beiseite: Proof found.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.41  SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 17 clauses.
% 0.20/0.41  SPASS allocated 63092 KBytes.
% 0.20/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.41  		0:00:00.03 for the input.
% 0.20/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41  		0:00:00.00 for inferences.
% 0.20/0.41  		0:00:00.00 for the backtracking.
% 0.20/0.41  		0:00:00.00 for the reduction.
% 0.20/0.41  
% 0.20/0.41  
% 0.20/0.41  Here is a proof with depth 3, length 10 :
% 0.20/0.41  % SZS output start Refutation
% See solution above
% 0.20/0.41  Formulae used in the proof : a_equals_b prove_symmetry left_identity total_function2 product_substitution3
% 0.20/0.41  
%------------------------------------------------------------------------------