%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWW198+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 : Thu Jul 21 01:28:05 EDT 2022

% Result   : Theorem 0.99s 1.16s
% Output   : Refutation 0.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   8 unt;   2 nHn;  10 RR)
%            Number of literals    :   12 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(189,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    file('SWW198+1.p',unknown),
    [] ).

cnf(256,axiom,
    equal(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('SWW198+1.p',unknown),
    [] ).

cnf(371,axiom,
    equal(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('SWW198+1.p',unknown),
    [] ).

cnf(584,axiom,
    ~ equal(c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),u)),v_na____),
    file('SWW198+1.p',unknown),
    [] ).

cnf(755,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,u)
    | equal(c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),skf18(u))),u) ),
    file('SWW198+1.p',unknown),
    [] ).

cnf(1767,plain,
    equal(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(rew,[status(thm),theory(equality)],[256,371]),
    [iquote('0:Rew:256.0,371.0')] ).

cnf(1798,plain,
    ~ equal(c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),u)),v_na____),
    inference(rew,[status(thm),theory(equality)],[1767,584]),
    [iquote('0:Rew:1767.0,584.0')] ).

cnf(1836,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,u)
    | equal(c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),skf18(u))),u) ),
    inference(rew,[status(thm),theory(equality)],[256,755]),
    [iquote('0:Rew:256.0,755.1')] ).

cnf(2024,plain,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(res,[status(thm),theory(equality)],[1836,1798]),
    [iquote('0:Res:1836.1,1798.0')] ).

cnf(2110,plain,
    $false,
    inference(mrr,[status(thm)],[2024,189]),
    [iquote('0:MRR:2024.0,189.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW198+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n021.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 : Sun Jun  5 04:07:04 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.99/1.16  
% 0.99/1.16  SPASS V 3.9 
% 0.99/1.16  SPASS beiseite: Proof found.
% 0.99/1.16  % SZS status Theorem
% 0.99/1.16  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.99/1.16  SPASS derived 44 clauses, backtracked 0 clauses, performed 0 splits and kept 1381 clauses.
% 0.99/1.16  SPASS allocated 104173 KBytes.
% 0.99/1.16  SPASS spent	0:00:00.81 on the problem.
% 0.99/1.16  		0:00:00.06 for the input.
% 0.99/1.16  		0:00:00.35 for the FLOTTER CNF translation.
% 0.99/1.16  		0:00:00.00 for inferences.
% 0.99/1.16  		0:00:00.00 for the backtracking.
% 0.99/1.16  		0:00:00.27 for the reduction.
% 0.99/1.16  
% 0.99/1.16  
% 0.99/1.16  Here is a proof with depth 1, length 10 :
% 0.99/1.16  % SZS output start Refutation
% See solution above
% 0.99/1.16  Formulae used in the proof : fact_o fact_One__nat__def fact_semiring__norm_I115_J conj_0 fact_odd__nat__equiv__def2
% 0.99/1.16  
%------------------------------------------------------------------------------