%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU150+1 : TPTP v8.1.0. Released v3.3.0.
% 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 14:34:23 EDT 2022

% Result   : Theorem 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   8 unt;   0 nHn;   9 RR)
%            Number of literals    :   10 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 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(1,axiom,
    ~ equal(skc4,skc3),
    file('SEU150+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(unordered_pair(skc3,skc4),singleton(skc5)),
    file('SEU150+1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SEU150+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ equal(singleton(u),unordered_pair(v,w))
    | equal(u,v) ),
    file('SEU150+1.p',unknown),
    [] ).

cnf(6,plain,
    ~ equal(unordered_pair(skc4,u),singleton(skc3)),
    inference(res,[status(thm),theory(equality)],[4,1]),
    [iquote('0:Res:4.1,1.0')] ).

cnf(7,plain,
    equal(skc5,skc3),
    inference(res,[status(thm),theory(equality)],[2,4]),
    [iquote('0:Res:2.0,4.0')] ).

cnf(8,plain,
    equal(unordered_pair(skc3,skc4),singleton(skc3)),
    inference(rew,[status(thm),theory(equality)],[7,2]),
    [iquote('0:Rew:7.0,2.0')] ).

cnf(15,plain,
    ~ equal(unordered_pair(u,skc4),singleton(skc3)),
    inference(spl,[status(thm),theory(equality)],[3,6]),
    [iquote('0:SpL:3.0,6.0')] ).

cnf(17,plain,
    $false,
    inference(unc,[status(thm)],[15,8]),
    [iquote('0:UnC:15.0,8.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU150+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jun 19 11:39:37 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.45  
% 0.20/0.45  SPASS V 3.9 
% 0.20/0.45  SPASS beiseite: Proof found.
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.45  SPASS derived 12 clauses, backtracked 0 clauses, performed 0 splits and kept 10 clauses.
% 0.20/0.45  SPASS allocated 85060 KBytes.
% 0.20/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.20/0.45  		0:00:00.04 for the input.
% 0.20/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.45  		0:00:00.00 for inferences.
% 0.20/0.45  		0:00:00.00 for the backtracking.
% 0.20/0.45  		0:00:00.00 for the reduction.
% 0.20/0.45  
% 0.20/0.45  
% 0.20/0.45  Here is a proof with depth 2, length 9 :
% 0.20/0.45  % SZS output start Refutation
% See solution above
% 0.20/0.45  Formulae used in the proof : t9_zfmisc_1 commutativity_k2_tarski t8_zfmisc_1
% 0.20/0.45  
%------------------------------------------------------------------------------