%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 05:29:35 EDT 2022

% Result   : Theorem 0.23s 0.47s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (  11 unt;   0 nHn;  13 RR)
%            Number of literals    :   15 (   0 equ;   6 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    subset(unordered_pair(skc5,skc6),singleton(skc7)),
    file('SET886+1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET886+1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(unordered_pair(skc5,skc6),singleton(skc7)),
    file('SET886+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SET886+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ subset(unordered_pair(u,v),singleton(w))
    | equal(u,w) ),
    file('SET886+1.p',unknown),
    [] ).

cnf(9,plain,
    equal(skc7,skc5),
    inference(res,[status(thm),theory(equality)],[4,8]),
    [iquote('0:Res:4.0,8.0')] ).

cnf(12,plain,
    subset(unordered_pair(skc5,skc6),singleton(skc5)),
    inference(rew,[status(thm),theory(equality)],[9,4]),
    [iquote('0:Rew:9.0,4.0')] ).

cnf(13,plain,
    ~ equal(unordered_pair(skc5,skc6),singleton(skc5)),
    inference(rew,[status(thm),theory(equality)],[9,6]),
    [iquote('0:Rew:9.0,6.0')] ).

cnf(23,plain,
    ( ~ subset(unordered_pair(u,v),singleton(w))
    | equal(v,w) ),
    inference(spl,[status(thm),theory(equality)],[7,8]),
    [iquote('0:SpL:7.0,8.0')] ).

cnf(30,plain,
    equal(skc6,skc5),
    inference(res,[status(thm),theory(equality)],[12,23]),
    [iquote('0:Res:12.0,23.0')] ).

cnf(32,plain,
    ~ equal(unordered_pair(skc5,skc5),singleton(skc5)),
    inference(rew,[status(thm),theory(equality)],[30,13]),
    [iquote('0:Rew:30.0,13.0')] ).

cnf(34,plain,
    ~ equal(singleton(skc5),singleton(skc5)),
    inference(rew,[status(thm),theory(equality)],[5,32]),
    [iquote('0:Rew:5.0,32.0')] ).

cnf(35,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[34]),
    [iquote('0:Obv:34.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.15  % Command  : run_spass %d %s
% 0.15/0.37  % Computer : n010.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Mon Jul 11 08:36:00 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.23/0.47  
% 0.23/0.47  SPASS V 3.9 
% 0.23/0.47  SPASS beiseite: Proof found.
% 0.23/0.47  % SZS status Theorem
% 0.23/0.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.23/0.47  SPASS derived 22 clauses, backtracked 0 clauses, performed 0 splits and kept 15 clauses.
% 0.23/0.47  SPASS allocated 85071 KBytes.
% 0.23/0.47  SPASS spent	0:00:00.08 on the problem.
% 0.23/0.47  		0:00:00.04 for the input.
% 0.23/0.47  		0:00:00.02 for the FLOTTER CNF translation.
% 0.23/0.47  		0:00:00.00 for inferences.
% 0.23/0.47  		0:00:00.00 for the backtracking.
% 0.23/0.47  		0:00:00.00 for the reduction.
% 0.23/0.47  
% 0.23/0.47  
% 0.23/0.47  Here is a proof with depth 2, length 13 :
% 0.23/0.47  % SZS output start Refutation
% See solution above
% 0.23/0.47  Formulae used in the proof : t27_zfmisc_1 t69_enumset1 commutativity_k2_tarski t26_zfmisc_1
% 0.23/0.47  
%------------------------------------------------------------------------------