TSTP Solution File: SEU630^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU630^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.JefSlKhtA3 true

% 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  : 300s
% DateTime : Thu Aug 31 19:15:00 EDT 2023

% Result   : Theorem 1.47s 0.87s
% Output   : Refutation 1.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   43 (  16 unt;  14 typ;   0 def)
%            Number of atoms       :  105 (  23 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  635 (  27   ~;  18   |;  16   &; 540   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   9 con; 0-2 aty)
%                                         (   0  !!;   6  ??;   0 @@+;   0 @@-)
%            Number of variables   :   97 (  30   ^;  57   !;  10   ?;  97   :)

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

thf(sk__8_type,type,
    sk__8: $i ).

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

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

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

thf(dsetconstrI_type,type,
    dsetconstrI: $o ).

thf(powerset_type,type,
    powerset: $i > $i ).

thf(binunion_type,type,
    binunion: $i > $i > $i ).

thf(sk__9_type,type,
    sk__9: $i ).

thf(emptyset_type,type,
    emptyset: $i ).

thf(sk__7_type,type,
    sk__7: $i ).

thf(ubforcartprodlem3_type,type,
    ubforcartprodlem3: $o ).

thf(sk__10_type,type,
    sk__10: $i ).

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

thf(ubforcartprodlem3,axiom,
    ( ubforcartprodlem3
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).

thf('0',plain,
    ( ubforcartprodlem3
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ X4 )
         => ! [X10: $i] :
              ( ( in @ X10 @ X6 )
             => ( in @ ( kpair @ X8 @ X10 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(cartprod,axiom,
    ( cartprod
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
          @ ^ [Xx: $i] :
            ? [Xy: $i] :
              ( ? [Xz: $i] :
                  ( ( Xx
                    = ( kpair @ Xy @ Xz ) )
                  & ( in @ Xz @ B ) )
              & ( in @ Xy @ A ) ) ) ) ) ).

thf(kpair,axiom,
    ( kpair
    = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).

thf('1',plain,
    ( kpair
    = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[kpair]) ).

thf('2',plain,
    ( kpair
    = ( ^ [V_1: $i,V_2: $i] : ( setadjoin @ ( setadjoin @ V_1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ V_1 @ ( setadjoin @ V_2 @ emptyset ) ) @ emptyset ) ) ) ),
    define([status(thm)]) ).

thf('3',plain,
    ( cartprod
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
          @ ^ [Xx: $i] :
            ? [Xy: $i] :
              ( ? [Xz: $i] :
                  ( ( Xx
                    = ( kpair @ Xy @ Xz ) )
                  & ( in @ Xz @ B ) )
              & ( in @ Xy @ A ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cartprod,'2']) ).

thf('4',plain,
    ( cartprod
    = ( ^ [V_1: $i,V_2: $i] :
          ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ V_1 @ V_2 ) ) )
          @ ^ [V_3: $i] :
            ? [X4: $i] :
              ( ? [X6: $i] :
                  ( ( V_3
                    = ( kpair @ X4 @ X6 ) )
                  & ( in @ X6 @ V_2 ) )
              & ( in @ X4 @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

thf(dsetconstrI,axiom,
    ( dsetconstrI
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( Xphi @ Xx )
           => ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).

thf('5',plain,
    ( dsetconstrI
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8 @ X4 )
         => ( ( X6 @ X8 )
           => ( in @ X8
              @ ( dsetconstr @ X4
                @ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(cartprodpairin,conjecture,
    ( dsetconstrI
   => ( ubforcartprodlem3
     => ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i > $o,X8: $i] :
        ( ( in @ X8 @ X4 )
       => ( ( X6 @ X8 )
         => ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) )
   => ( ! [X10: $i,X12: $i,X14: $i] :
          ( ( in @ X14 @ X10 )
         => ! [X16: $i] :
              ( ( in @ X16 @ X12 )
             => ( in @ ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X16 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X10 @ X12 ) ) ) ) ) )
     => ! [X18: $i,X20: $i,X22: $i] :
          ( ( in @ X22 @ X18 )
         => ! [X24: $i] :
              ( ( in @ X24 @ X20 )
             => ( in @ ( setadjoin @ ( setadjoin @ X22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X22 @ ( setadjoin @ X24 @ emptyset ) ) @ emptyset ) )
                @ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X18 @ X20 ) ) )
                  @ ^ [V_2: $i] :
                    ? [X26: $i] :
                      ( ( in @ X26 @ X18 )
                      & ? [X28: $i] :
                          ( ( in @ X28 @ X20 )
                          & ( V_2
                            = ( setadjoin @ ( setadjoin @ X26 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X26 @ ( setadjoin @ X28 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8 @ X4 )
         => ( ( X6 @ X8 )
           => ( in @ X8
              @ ( dsetconstr @ X4
                @ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) )
     => ( ! [X10: $i,X12: $i,X14: $i] :
            ( ( in @ X14 @ X10 )
           => ! [X16: $i] :
                ( ( in @ X16 @ X12 )
               => ( in @ ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X16 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X10 @ X12 ) ) ) ) ) )
       => ! [X18: $i,X20: $i,X22: $i] :
            ( ( in @ X22 @ X18 )
           => ! [X24: $i] :
                ( ( in @ X24 @ X20 )
               => ( in @ ( setadjoin @ ( setadjoin @ X22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X22 @ ( setadjoin @ X24 @ emptyset ) ) @ emptyset ) )
                  @ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X18 @ X20 ) ) )
                    @ ^ [V_2: $i] :
                      ? [X26: $i] :
                        ( ( in @ X26 @ X18 )
                        & ? [X28: $i] :
                            ( ( in @ X28 @ X20 )
                            & ( V_2
                              = ( setadjoin @ ( setadjoin @ X26 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X26 @ ( setadjoin @ X28 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3,plain,
    in @ sk__9 @ sk__7,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    in @ sk__10 @ sk__8,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4,plain,
    ! [X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ~ ( in @ X3 @ X4 )
      | ( in @ ( setadjoin @ ( setadjoin @ X5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X5 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X6 @ X4 ) ) ) )
      | ~ ( in @ X5 @ X6 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ~ ( X0 @ X1 )
      | ( in @ X1
        @ ( dsetconstr @ X2
          @ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
      | ~ ( in @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl5,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ~ ( X0 @ X1 )
      | ( in @ X1 @ ( dsetconstr @ X2 @ X0 ) )
      | ~ ( in @ X1 @ X2 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ~ ( in @ ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) )
      @ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sk__7 @ sk__8 ) ) )
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ sk__7 )
                & ( ??
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ sk__8 )
                      & ( Y0
                        = ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl57,plain,
    ( ~ ( in @ ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sk__7 @ sk__8 ) ) ) )
    | ~ ( ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ sk__7 )
                & ( ??
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ sk__8 )
                      & ( Y0
                        = ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
        @ ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl2]) ).

thf(zip_derived_cl58,plain,
    ( ~ ( in @ ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sk__7 @ sk__8 ) ) ) )
    | ~ ( ??
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ sk__7 )
            & ( ??
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ sk__8 )
                  & ( ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) )
                    = ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl85,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ sk__7 )
      | ( ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
      | ~ ( in @ X1 @ sk__8 )
      | ~ ( in @ ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ sk__7 @ sk__8 ) ) ) ) ),
    inference(cnf_otf,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl86,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ sk__9 @ sk__7 )
      | ~ ( in @ sk__10 @ sk__8 )
      | ~ ( in @ X0 @ sk__8 )
      | ( ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
      | ~ ( in @ X1 @ sk__7 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl85]) ).

thf(zip_derived_cl3_001,plain,
    in @ sk__9 @ sk__7,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1_002,plain,
    in @ sk__10 @ sk__8,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl88,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ sk__8 )
      | ( ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
      | ~ ( in @ X1 @ sk__7 ) ),
    inference(demod,[status(thm)],[zip_derived_cl86,zip_derived_cl3,zip_derived_cl1]) ).

thf(zip_derived_cl90,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ sk__7 )
      | ( ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl88]) ).

thf(zip_derived_cl92,plain,
    ( ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) )
   != ( setadjoin @ ( setadjoin @ sk__9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk__9 @ ( setadjoin @ sk__10 @ emptyset ) ) @ emptyset ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl90]) ).

thf(zip_derived_cl94,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl92]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU630^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.JefSlKhtA3 true
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Aug 23 15:19:52 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.36  % Running in HO mode
% 0.20/0.67  % Total configuration time : 828
% 0.20/0.67  % Estimated wc time : 1656
% 0.20/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.73  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.77  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.77  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.78  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.78  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.80  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.47/0.87  % Solved by lams/40_c_ic.sh.
% 1.47/0.87  % done 19 iterations in 0.074s
% 1.47/0.87  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.47/0.87  % SZS output start Refutation
% See solution above
% 1.47/0.87  
% 1.47/0.87  
% 1.47/0.87  % Terminating...
% 1.82/0.97  % Runner terminated.
% 1.82/0.98  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------