%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET108-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 05:24:08 EDT 2022

% Result   : Unsatisfiable 0.92s 1.09s
% Output   : Refutation 0.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    6 (   5 unt;   0 nHn;   6 RR)
%            Number of literals    :    7 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(62,axiom,
    member(ordered_pair(y__dfg,z__dfg),cross_product(universal_class,universal_class)),
    file('SET108-7.p',unknown),
    [] ).

cnf(63,axiom,
    ~ member(ordered_pair(first(ordered_pair(y__dfg,z__dfg)),second(ordered_pair(y__dfg,z__dfg))),cross_product(universal_class,universal_class)),
    file('SET108-7.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ member(u,cross_product(v,w))
    | equal(ordered_pair(first(u),second(u)),u) ),
    file('SET108-7.p',unknown),
    [] ).

cnf(4548,plain,
    equal(ordered_pair(first(ordered_pair(y__dfg,z__dfg)),second(ordered_pair(y__dfg,z__dfg))),ordered_pair(y__dfg,z__dfg)),
    inference(res,[status(thm),theory(equality)],[62,80]),
    [iquote('0:Res:62.0,80.0')] ).

cnf(4556,plain,
    ~ member(ordered_pair(y__dfg,z__dfg),cross_product(universal_class,universal_class)),
    inference(rew,[status(thm),theory(equality)],[4548,63]),
    [iquote('0:Rew:4548.0,63.0')] ).

cnf(4559,plain,
    $false,
    inference(mrr,[status(thm)],[4556,62]),
    [iquote('0:MRR:4556.0,62.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET108-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n016.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 14:45:11 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.92/1.09  
% 0.92/1.09  SPASS V 3.9 
% 0.92/1.09  SPASS beiseite: Proof found.
% 0.92/1.09  % SZS status Theorem
% 0.92/1.09  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.92/1.09  SPASS derived 3600 clauses, backtracked 575 clauses, performed 4 splits and kept 1669 clauses.
% 0.92/1.09  SPASS allocated 79089 KBytes.
% 0.92/1.09  SPASS spent	0:00:00.72 on the problem.
% 0.92/1.09  		0:00:00.04 for the input.
% 0.92/1.09  		0:00:00.00 for the FLOTTER CNF translation.
% 0.92/1.09  		0:00:00.05 for inferences.
% 0.92/1.09  		0:00:00.02 for the backtracking.
% 0.92/1.09  		0:00:00.57 for the reduction.
% 0.92/1.09  
% 0.92/1.09  
% 0.92/1.09  Here is a proof with depth 1, length 6 :
% 0.92/1.09  % SZS output start Refutation
% See solution above
% 0.92/1.09  Formulae used in the proof : prove_existence_of_1st_and_2nd_1_1 prove_existence_of_1st_and_2nd_1_2 cartesian_product4
% 0.92/1.09  
%------------------------------------------------------------------------------