%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET113-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 05:24:12 EDT 2022

% Result   : Unsatisfiable 0.19s 0.44s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   6 unt;   3 nHn;   9 RR)
%            Number of literals    :   12 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(63,axiom,
    ( member(ordered_pair(first(u),second(u)),cross_product(universal_class,universal_class))
    | equal(first(u),u) ),
    file('SET113-7.p',unknown),
    [] ).

cnf(65,axiom,
    ( equal(first(u),u)
    | equal(ordered_pair(first(u),second(u)),u) ),
    file('SET113-7.p',unknown),
    [] ).

cnf(69,axiom,
    ~ member(ordered_pair(first(x__dfg),second(x__dfg)),cross_product(universal_class,universal_class)),
    file('SET113-7.p',unknown),
    [] ).

cnf(70,axiom,
    ~ equal(first(x__dfg),x__dfg),
    file('SET113-7.p',unknown),
    [] ).

cnf(166,plain,
    ( member(u,cross_product(universal_class,universal_class))
    | equal(first(u),u) ),
    inference(rew,[status(thm),theory(equality)],[65,63]),
    [iquote('0:Rew:65.0,63.0')] ).

cnf(170,plain,
    member(x__dfg,cross_product(universal_class,universal_class)),
    inference(res,[status(thm),theory(equality)],[166,70]),
    [iquote('0:Res:166.1,70.0')] ).

cnf(171,plain,
    equal(ordered_pair(first(x__dfg),second(x__dfg)),x__dfg),
    inference(res,[status(thm),theory(equality)],[65,70]),
    [iquote('0:Res:65.1,70.0')] ).

cnf(210,plain,
    ~ member(x__dfg,cross_product(universal_class,universal_class)),
    inference(rew,[status(thm),theory(equality)],[171,69]),
    [iquote('0:Rew:171.0,69.0')] ).

cnf(211,plain,
    $false,
    inference(mrr,[status(thm)],[210,170]),
    [iquote('0:MRR:210.0,170.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET113-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.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 : Mon Jul 11 07:55:02 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.44  
% 0.19/0.44  SPASS V 3.9 
% 0.19/0.44  SPASS beiseite: Proof found.
% 0.19/0.44  % SZS status Theorem
% 0.19/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.44  SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 157 clauses.
% 0.19/0.44  SPASS allocated 75823 KBytes.
% 0.19/0.44  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.44  		0:00:00.04 for the input.
% 0.19/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44  		0:00:00.00 for inferences.
% 0.19/0.44  		0:00:00.00 for the backtracking.
% 0.19/0.44  		0:00:00.01 for the reduction.
% 0.19/0.44  
% 0.19/0.44  
% 0.19/0.44  Here is a proof with depth 1, length 9 :
% 0.19/0.44  % SZS output start Refutation
% See solution above
% 0.19/0.44  Formulae used in the proof : existence_of_1st_and_2nd_2 existence_of_1st_and_2nd_4 prove_unique_1st_and_2nd_in_pair_of_non_sets1_1 prove_unique_1st_in_pair_of_non_sets
% 0.19/0.44  
%------------------------------------------------------------------------------