%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET074-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 05:23:36 EDT 2022

% Result   : Unsatisfiable 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   8 unt;   0 nHn;   9 RR)
%            Number of literals    :   10 (   0 equ;   2 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    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(12,axiom,
    ~ member(u,null_class),
    file('SET074-7.p',unknown),
    [] ).

cnf(17,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SET074-7.p',unknown),
    [] ).

cnf(25,axiom,
    member(y__dfg,universal_class),
    file('SET074-7.p',unknown),
    [] ).

cnf(26,axiom,
    equal(unordered_pair(x__dfg,y__dfg),null_class),
    file('SET074-7.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ member(u,universal_class)
    | member(u,unordered_pair(u,v)) ),
    file('SET074-7.p',unknown),
    [] ).

cnf(118,plain,
    equal(unordered_pair(y__dfg,x__dfg),null_class),
    inference(rew,[status(thm),theory(equality)],[17,26]),
    [iquote('0:Rew:17.0,26.0')] ).

cnf(127,plain,
    member(y__dfg,unordered_pair(y__dfg,u)),
    inference(res,[status(thm),theory(equality)],[25,35]),
    [iquote('0:Res:25.0,35.0')] ).

cnf(172,plain,
    member(y__dfg,null_class),
    inference(spr,[status(thm),theory(equality)],[118,127]),
    [iquote('0:SpR:118.0,127.0')] ).

cnf(174,plain,
    $false,
    inference(mrr,[status(thm)],[172,12]),
    [iquote('0:MRR:172.0,12.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET074-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n009.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 : Sun Jul 10 11:41:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 45 clauses, backtracked 19 clauses, performed 1 splits and kept 170 clauses.
% 0.20/0.44  SPASS allocated 75804 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.44  		0:00:00.04 for the input.
% 0.20/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.02 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 2, length 9 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : existence_of_null_class commutativity_of_unordered_pair prove_corollary_to_unordered_pair_axiom2_1 prove_corollary_to_unordered_pair_axiom2_2 unordered_pair2
% 0.20/0.44  
%------------------------------------------------------------------------------