TSTP Solution File: SEU667^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU667^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.LcbVoaxHlQ true

% Computer : n014.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  : 300s
% DateTime : Thu Aug 31 19:15:55 EDT 2023

% Result   : Theorem 0.22s 0.76s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   25 (   9 unt;  11 typ;   0 def)
%            Number of atoms       :   59 (  17 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  210 (   2   ~;   0   |;  27   &; 174   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   43 (  43   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   5 con; 0-3 aty)
%                                         (   0  !!;   4  ??;   0 @@+;   0 @@-)
%            Number of variables   :   75 (  37   ^;  24   !;  14   ?;  75   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cartprod_type,type,
    cartprod: $i > $i > $i ).

thf(sk__3_type,type,
    sk__3: $i ).

thf(in_type,type,
    in: $i > $i > $o ).

thf(dpsetconstrSub_type,type,
    dpsetconstrSub: $o ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(dpsetconstr_type,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(sk__5_type,type,
    sk__5: $i > $i > $o ).

thf(breln_type,type,
    breln: $i > $i > $i > $o ).

thf(kpair_type,type,
    kpair: $i > $i > $i ).

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(sk__4_type,type,
    sk__4: $i ).

thf(dpsetconstrSub,axiom,
    ( dpsetconstrSub
    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ A @ B
            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
          @ ( cartprod @ A @ B ) ) ) ) ).

thf('0',plain,
    ( dpsetconstrSub
    = ( ! [X4: $i,X6: $i,X8: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ X4 @ X6
            @ ^ [V_1: $i,V_2: $i] : ( X8 @ V_1 @ V_2 ) )
          @ ( cartprod @ X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(dpsetconstr,axiom,
    ( dpsetconstr
    = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
          ( dsetconstr @ ( cartprod @ A @ B )
          @ ^ [Xu: $i] :
            ? [Xx: $i] :
              ( ? [Xy: $i] :
                  ( ( Xu
                    = ( kpair @ Xx @ Xy ) )
                  & ( Xphi @ Xx @ Xy )
                  & ( in @ Xy @ B ) )
              & ( in @ Xx @ A ) ) ) ) ) ).

thf('1',plain,
    ( dpsetconstr
    = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
          ( dsetconstr @ ( cartprod @ A @ B )
          @ ^ [Xu: $i] :
            ? [Xx: $i] :
              ( ? [Xy: $i] :
                  ( ( Xu
                    = ( kpair @ Xx @ Xy ) )
                  & ( Xphi @ Xx @ Xy )
                  & ( in @ Xy @ B ) )
              & ( in @ Xx @ A ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[dpsetconstr]) ).

thf('2',plain,
    ( dpsetconstr
    = ( ^ [V_1: $i,V_2: $i,V_3: $i > $i > $o] :
          ( dsetconstr @ ( cartprod @ V_1 @ V_2 )
          @ ^ [V_4: $i] :
            ? [X4: $i] :
              ( ? [X6: $i] :
                  ( ( V_4
                    = ( kpair @ X4 @ X6 ) )
                  & ( V_3 @ X4 @ X6 )
                  & ( in @ X6 @ V_2 ) )
              & ( in @ X4 @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

thf(breln,axiom,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).

thf('3',plain,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[breln]) ).

thf('4',plain,
    ( breln
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(setOfPairsIsBReln,conjecture,
    ( dpsetconstrSub
   => ! [A: $i,B: $i,Xphi: $i > $i > $o] :
        ( breln @ A @ B
        @ ( dpsetconstr @ A @ B
          @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i,X8: $i > $i > $o] :
        ( subset
        @ ( dsetconstr @ ( cartprod @ X4 @ X6 )
          @ ^ [V_1: $i] :
            ? [X10: $i] :
              ( ( in @ X10 @ X4 )
              & ? [X12: $i] :
                  ( ( in @ X12 @ X6 )
                  & ( X8 @ X10 @ X12 )
                  & ( V_1
                    = ( kpair @ X10 @ X12 ) ) ) ) )
        @ ( cartprod @ X4 @ X6 ) )
   => ! [X14: $i,X16: $i,X18: $i > $i > $o] :
        ( subset
        @ ( dsetconstr @ ( cartprod @ X14 @ X16 )
          @ ^ [V_2: $i] :
            ? [X20: $i] :
              ( ( in @ X20 @ X14 )
              & ? [X22: $i] :
                  ( ( in @ X22 @ X16 )
                  & ( X18 @ X20 @ X22 )
                  & ( V_2
                    = ( kpair @ X20 @ X22 ) ) ) ) )
        @ ( cartprod @ X14 @ X16 ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i,X8: $i > $i > $o] :
          ( subset
          @ ( dsetconstr @ ( cartprod @ X4 @ X6 )
            @ ^ [V_1: $i] :
              ? [X10: $i] :
                ( ( in @ X10 @ X4 )
                & ? [X12: $i] :
                    ( ( in @ X12 @ X6 )
                    & ( X8 @ X10 @ X12 )
                    & ( V_1
                      = ( kpair @ X10 @ X12 ) ) ) ) )
          @ ( cartprod @ X4 @ X6 ) )
     => ! [X14: $i,X16: $i,X18: $i > $i > $o] :
          ( subset
          @ ( dsetconstr @ ( cartprod @ X14 @ X16 )
            @ ^ [V_2: $i] :
              ? [X20: $i] :
                ( ( in @ X20 @ X14 )
                & ? [X22: $i] :
                    ( ( in @ X22 @ X16 )
                    & ( X18 @ X20 @ X22 )
                    & ( V_2
                      = ( kpair @ X20 @ X22 ) ) ) ) )
          @ ( cartprod @ X14 @ X16 ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ~ ( subset
      @ ( dsetconstr @ ( cartprod @ sk__3 @ sk__4 )
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ sk__3 )
                & ( ??
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ sk__4 )
                      & ( sk__5 @ Y1 @ Y2 )
                      & ( Y0
                        = ( kpair @ Y1 @ Y2 ) ) ) ) ) ) )
      @ ( cartprod @ sk__3 @ sk__4 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i,X2: $i > $i > $o] :
      ( subset
      @ ( dsetconstr @ ( cartprod @ X0 @ X1 )
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ X0 )
                & ( ??
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ X1 )
                      & ( X2 @ Y1 @ Y2 )
                      & ( Y0
                        = ( kpair @ Y1 @ Y2 ) ) ) ) ) ) )
      @ ( cartprod @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl2,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU667^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.LcbVoaxHlQ true
% 0.15/0.35  % Computer : n014.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  : 300
% 0.15/0.35  % DateTime : Wed Aug 23 14:53:19 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.15/0.35  % Running portfolio for 300 s
% 0.15/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36  % Number of cores: 8
% 0.15/0.36  % Python version: Python 3.6.8
% 0.15/0.36  % Running in HO mode
% 0.22/0.66  % Total configuration time : 828
% 0.22/0.66  % Estimated wc time : 1656
% 0.22/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.73  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76  % Solved by lams/40_c.s.sh.
% 0.22/0.76  % done 1 iterations in 0.009s
% 0.22/0.76  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.22/0.76  % SZS output start Refutation
% See solution above
% 0.22/0.76  
% 0.22/0.76  
% 0.22/0.77  % Terminating...
% 0.58/0.87  % Runner terminated.
% 1.62/0.88  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------