%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM190-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 : Mon Jul 18 14:24:34 EDT 2022

% Result   : Unsatisfiable 0.19s 0.54s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (   6 unt;   4 nHn;  16 RR)
%            Number of literals    :   27 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(null_class,omega),
    file('NUM190-1.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('NUM190-1.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ member(u,v)
    | ~ member(u,complement(v)) ),
    file('NUM190-1.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ inductive(u)
    | member(null_class,u) ),
    file('NUM190-1.p',unknown),
    [] ).

cnf(51,axiom,
    inductive(omega),
    file('NUM190-1.p',unknown),
    [] ).

cnf(68,axiom,
    ( equal(u,null_class)
    | equal(intersection(u,regular(u)),null_class) ),
    file('NUM190-1.p',unknown),
    [] ).

cnf(160,plain,
    ( ~ inductive(u)
    | member(omega,u) ),
    inference(rew,[status(thm),theory(equality)],[1,48]),
    [iquote('0:Rew:1.0,48.1')] ).

cnf(164,plain,
    ( equal(u,omega)
    | equal(intersection(u,regular(u)),omega) ),
    inference(rew,[status(thm),theory(equality)],[1,68]),
    [iquote('0:Rew:1.0,68.1,1.0,68.0')] ).

cnf(182,plain,
    member(omega,omega),
    inference(res,[status(thm),theory(equality)],[51,160]),
    [iquote('0:Res:51.0,160.0')] ).

cnf(384,plain,
    ( ~ member(u,omega)
    | equal(v,omega)
    | member(u,v) ),
    inference(spl,[status(thm),theory(equality)],[164,22]),
    [iquote('0:SpL:164.1,22.0')] ).

cnf(738,plain,
    ( equal(u,omega)
    | member(omega,u) ),
    inference(res,[status(thm),theory(equality)],[182,384]),
    [iquote('0:Res:182.0,384.0')] ).

cnf(754,plain,
    ( ~ member(omega,u)
    | equal(complement(u),omega) ),
    inference(res,[status(thm),theory(equality)],[738,25]),
    [iquote('0:Res:738.1,25.1')] ).

cnf(785,plain,
    equal(complement(omega),omega),
    inference(res,[status(thm),theory(equality)],[182,754]),
    [iquote('0:Res:182.0,754.0')] ).

cnf(805,plain,
    ( ~ member(u,omega)
    | ~ member(u,omega) ),
    inference(spl,[status(thm),theory(equality)],[785,25]),
    [iquote('0:SpL:785.0,25.1')] ).

cnf(806,plain,
    ~ member(u,omega),
    inference(obv,[status(thm),theory(equality)],[805]),
    [iquote('0:Obv:805.0')] ).

cnf(807,plain,
    $false,
    inference(unc,[status(thm)],[806,182]),
    [iquote('0:UnC:806.0,182.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM190-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n015.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 : Thu Jul  7 20:43:35 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.54  
% 0.19/0.54  SPASS V 3.9 
% 0.19/0.54  SPASS beiseite: Proof found.
% 0.19/0.54  % SZS status Theorem
% 0.19/0.54  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.54  SPASS derived 563 clauses, backtracked 93 clauses, performed 14 splits and kept 586 clauses.
% 0.19/0.54  SPASS allocated 76437 KBytes.
% 0.19/0.54  SPASS spent	0:00:00.18 on the problem.
% 0.19/0.54  		0:00:00.04 for the input.
% 0.19/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.54  		0:00:00.01 for inferences.
% 0.19/0.54  		0:00:00.01 for the backtracking.
% 0.19/0.54  		0:00:00.09 for the reduction.
% 0.19/0.54  
% 0.19/0.54  
% 0.19/0.54  Here is a proof with depth 5, length 16 :
% 0.19/0.54  % SZS output start Refutation
% See solution above
% 0.19/0.54  Formulae used in the proof : prove_omega_is_not_null_1 intersection1 complement1 inductive1 omega_is_inductive1 regularity2
% 0.19/0.54  
%------------------------------------------------------------------------------