%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET120-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 05:24:18 EDT 2022

% Result   : Unsatisfiable 0.22s 0.46s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   5 unt;   3 nHn;   9 RR)
%            Number of literals    :   13 (   0 equ;   4 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    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ( ~ member(ordered_pair(u,v),cross_product(w,x))
    | member(u,universal_class) ),
    file('SET120-7.p',unknown),
    [] ).

cnf(70,axiom,
    ( member(ordered_pair(first(u),second(u)),cross_product(universal_class,universal_class))
    | equal(second(u),u) ),
    file('SET120-7.p',unknown),
    [] ).

cnf(72,axiom,
    ( equal(second(u),u)
    | equal(ordered_pair(first(u),second(u)),u) ),
    file('SET120-7.p',unknown),
    [] ).

cnf(75,axiom,
    ~ member(x__dfg,universal_class),
    file('SET120-7.p',unknown),
    [] ).

cnf(76,axiom,
    ~ equal(second(ordered_pair(x__dfg,y__dfg)),ordered_pair(x__dfg,y__dfg)),
    file('SET120-7.p',unknown),
    [] ).

cnf(171,plain,
    ( member(u,cross_product(universal_class,universal_class))
    | equal(second(u),u) ),
    inference(rew,[status(thm),theory(equality)],[72,70]),
    [iquote('0:Rew:72.0,70.0')] ).

cnf(179,plain,
    ~ member(ordered_pair(x__dfg,u),cross_product(v,w)),
    inference(res,[status(thm),theory(equality)],[3,75]),
    [iquote('0:Res:3.1,75.0')] ).

cnf(197,plain,
    member(ordered_pair(x__dfg,y__dfg),cross_product(universal_class,universal_class)),
    inference(res,[status(thm),theory(equality)],[171,76]),
    [iquote('0:Res:171.1,76.0')] ).

cnf(227,plain,
    $false,
    inference(unc,[status(thm)],[179,197]),
    [iquote('0:UnC:179.0,197.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SET120-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.11/0.14  % Command  : run_spass %d %s
% 0.15/0.35  % Computer : n010.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 600
% 0.15/0.35  % DateTime : Mon Jul 11 07:58:15 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.22/0.46  
% 0.22/0.46  SPASS V 3.9 
% 0.22/0.46  SPASS beiseite: Proof found.
% 0.22/0.46  % SZS status Theorem
% 0.22/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.22/0.46  SPASS derived 25 clauses, backtracked 0 clauses, performed 0 splits and kept 165 clauses.
% 0.22/0.46  SPASS allocated 75840 KBytes.
% 0.22/0.46  SPASS spent	0:00:00.08 on the problem.
% 0.22/0.46  		0:00:00.04 for the input.
% 0.22/0.46  		0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.46  		0:00:00.00 for inferences.
% 0.22/0.46  		0:00:00.00 for the backtracking.
% 0.22/0.46  		0:00:00.01 for the reduction.
% 0.22/0.46  
% 0.22/0.46  
% 0.22/0.46  Here is a proof with depth 1, length 9 :
% 0.22/0.46  % SZS output start Refutation
% See solution above
% 0.22/0.46  Formulae used in the proof : corollary_1_to_cartesian_product unique_1st_and_2nd_in_pair_of_non_sets2 unique_1st_and_2nd_in_pair_of_non_sets4 prove_corollary_2_to_OP_determines_components1_1 prove_corollary_2_to_OP_determines_components1_2
% 0.22/0.46  
%------------------------------------------------------------------------------