%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET075-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 05:23:37 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :    8 (   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    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ member(ordered_pair(u,v),cross_product(w,x))
    | member(u,unordered_pair(u,v)) ),
    file('SET075-7.p',unknown),
    [] ).

cnf(12,axiom,
    ~ member(u,null_class),
    file('SET075-7.p',unknown),
    [] ).

cnf(25,axiom,
    member(ordered_pair(x__dfg,y__dfg),cross_product(u__dfg,v__dfg)),
    file('SET075-7.p',unknown),
    [] ).

cnf(26,axiom,
    equal(unordered_pair(x__dfg,y__dfg),null_class),
    file('SET075-7.p',unknown),
    [] ).

cnf(131,plain,
    member(x__dfg,unordered_pair(x__dfg,y__dfg)),
    inference(res,[status(thm),theory(equality)],[25,1]),
    [iquote('0:Res:25.0,1.0')] ).

cnf(138,plain,
    member(x__dfg,null_class),
    inference(rew,[status(thm),theory(equality)],[26,131]),
    [iquote('0:Rew:26.0,131.0')] ).

cnf(139,plain,
    $false,
    inference(mrr,[status(thm)],[138,12]),
    [iquote('0:MRR:138.0,12.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET075-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 19:30:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 119 clauses.
% 0.19/0.42  SPASS allocated 75763 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.01 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 1, length 7 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : corollary_1_to_unordered_pair existence_of_null_class prove_corollary_to_unordered_pair_axiom3_1 prove_corollary_to_unordered_pair_axiom3_2
% 0.19/0.42  
%------------------------------------------------------------------------------