%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET940+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 05:29:57 EDT 2022

% Result   : Theorem 0.21s 0.45s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    6 (   6 unt;   0 nHn;   6 RR)
%            Number of literals    :    6 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SET940+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(set_union2(u,v),set_union2(v,u)),
    file('SET940+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(union(unordered_pair(u,v)),set_union2(u,v)),
    file('SET940+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(union(unordered_pair(skc5,skc4)),set_union2(skc5,skc4)),
    file('SET940+1.p',unknown),
    [] ).

cnf(10,plain,
    ~ equal(set_union2(skc4,skc5),set_union2(skc4,skc5)),
    inference(rew,[status(thm),theory(equality)],[8,9,6,7]),
    [iquote('0:Rew:8.0,9.0,6.0,9.0,7.0,9.0')] ).

cnf(11,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[10]),
    [iquote('0:Obv:10.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET940+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n017.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sun Jul 10 14:49:33 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.21/0.45  
% 0.21/0.45  SPASS V 3.9 
% 0.21/0.45  SPASS beiseite: Proof found.
% 0.21/0.45  % SZS status Theorem
% 0.21/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.45  SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.21/0.45  SPASS allocated 85067 KBytes.
% 0.21/0.45  SPASS spent	0:00:00.08 on the problem.
% 0.21/0.45  		0:00:00.03 for the input.
% 0.21/0.45  		0:00:00.02 for the FLOTTER CNF translation.
% 0.21/0.45  		0:00:00.00 for inferences.
% 0.21/0.45  		0:00:00.00 for the backtracking.
% 0.21/0.45  		0:00:00.00 for the reduction.
% 0.21/0.45  
% 0.21/0.45  
% 0.21/0.45  Here is a proof with depth 0, length 6 :
% 0.21/0.45  % SZS output start Refutation
% See solution above
% 0.21/0.45  Formulae used in the proof : commutativity_k2_tarski commutativity_k2_xboole_0 l52_zfmisc_1 t93_zfmisc_1
% 0.21/0.45  
%------------------------------------------------------------------------------