%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 : Tue Jul 19 05:22:41 EDT 2022

% Result   : Theorem 0.20s 0.48s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (   7 unt;   0 nHn;  13 RR)
%            Number of literals    :   21 (   0 equ;  12 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 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(3,axiom,
    member(skc5,universal_class),
    file('SET020+1.p',unknown),
    [] ).

cnf(4,axiom,
    member(skc4,universal_class),
    file('SET020+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ equal(first(ordered_pair(skc5,skc4)),skc5)
    | ~ equal(second(ordered_pair(skc5,skc4)),skc4) ),
    file('SET020+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ member(u,universal_class)
    | ~ member(v,universal_class)
    | equal(first(ordered_pair(v,u)),v) ),
    file('SET020+1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ member(u,universal_class)
    | ~ member(v,universal_class)
    | equal(second(ordered_pair(v,u)),u) ),
    file('SET020+1.p',unknown),
    [] ).

cnf(106,plain,
    ( ~ member(u,universal_class)
    | equal(first(ordered_pair(u,skc4)),u) ),
    inference(res,[status(thm),theory(equality)],[4,79]),
    [iquote('0:Res:4.0,79.1')] ).

cnf(107,plain,
    ( ~ member(u,universal_class)
    | equal(second(ordered_pair(u,skc4)),skc4) ),
    inference(res,[status(thm),theory(equality)],[4,80]),
    [iquote('0:Res:4.0,80.1')] ).

cnf(163,plain,
    equal(second(ordered_pair(skc5,skc4)),skc4),
    inference(res,[status(thm),theory(equality)],[3,107]),
    [iquote('0:Res:3.0,107.0')] ).

cnf(164,plain,
    equal(first(ordered_pair(skc5,skc4)),skc5),
    inference(res,[status(thm),theory(equality)],[3,106]),
    [iquote('0:Res:3.0,106.0')] ).

cnf(195,plain,
    ( ~ equal(first(ordered_pair(skc5,skc4)),skc5)
    | ~ equal(skc4,skc4) ),
    inference(rew,[status(thm),theory(equality)],[163,78]),
    [iquote('0:Rew:163.0,78.1')] ).

cnf(196,plain,
    ~ equal(first(ordered_pair(skc5,skc4)),skc5),
    inference(obv,[status(thm),theory(equality)],[195]),
    [iquote('0:Obv:195.1')] ).

cnf(197,plain,
    ~ equal(skc5,skc5),
    inference(rew,[status(thm),theory(equality)],[164,196]),
    [iquote('0:Rew:164.0,196.0')] ).

cnf(198,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[197]),
    [iquote('0:Obv:197.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n025.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 01:32:47 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.48  
% 0.20/0.48  SPASS V 3.9 
% 0.20/0.48  SPASS beiseite: Proof found.
% 0.20/0.48  % SZS status Theorem
% 0.20/0.48  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.48  SPASS derived 103 clauses, backtracked 0 clauses, performed 0 splits and kept 173 clauses.
% 0.20/0.48  SPASS allocated 98319 KBytes.
% 0.20/0.48  SPASS spent	0:00:00.13 on the problem.
% 0.20/0.48  		0:00:00.04 for the input.
% 0.20/0.48  		0:00:00.06 for the FLOTTER CNF translation.
% 0.20/0.48  		0:00:00.00 for inferences.
% 0.20/0.48  		0:00:00.00 for the backtracking.
% 0.20/0.48  		0:00:00.00 for the reduction.
% 0.20/0.48  
% 0.20/0.48  
% 0.20/0.48  Here is a proof with depth 2, length 13 :
% 0.20/0.48  % SZS output start Refutation
% See solution above
% 0.20/0.48  Formulae used in the proof : unique_1st_and_2nd_in_pair_of_sets1 first_second
% 0.20/0.48  
%------------------------------------------------------------------------------