TSTP Solution File: SEU504^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU504^1 : 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.hejpMI7eY6 true

% Computer : n028.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 19:13:22 EDT 2023

% Result   : Theorem 1.99s 0.90s
% Output   : Refutation 1.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   44 (  12 unt;  27 typ;   0 def)
%            Number of atoms       :  136 (  29 equ;   0 cnn)
%            Maximal formula atoms :   25 (   8 avg)
%            Number of connectives :  287 (   2   ~;   0   |;  24   &; 131   @)
%                                         (   6 <=>; 124  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   48 (  48   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  26 usr;  22 con; 0-4 aty)
%            Number of variables   :  108 (  15   ^;  59   !;  34   ?; 108   :)

% Comments : 
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
    setadjoinAx: $o ).

thf(setunionAx_type,type,
    setunionAx: $o ).

thf(omegaSAx_type,type,
    omegaSAx: $o ).

thf(wellorderingAx_type,type,
    wellorderingAx: $o ).

thf(emptysetE_type,type,
    emptysetE: $o ).

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

thf(sk__16_type,type,
    sk__16: $i > $o ).

thf(dsetconstrEL_type,type,
    dsetconstrEL: $o ).

thf(powersetAx_type,type,
    powersetAx: $o ).

thf(notinemptyset_type,type,
    notinemptyset: $o ).

thf(emptysetimpfalse_type,type,
    emptysetimpfalse: $o ).

thf(descr_type,type,
    descr: ( $i > $o ) > $i ).

thf(exuE1_type,type,
    exuE1: $o ).

thf(omega0Ax_type,type,
    omega0Ax: $o ).

thf(prop2setE_type,type,
    prop2setE: $o ).

thf(setextAx_type,type,
    setextAx: $o ).

thf(zip_tseitin_0_type,type,
    zip_tseitin_0: $i > $i > $i > ( $i > $i > $o ) > $o ).

thf(sk__17_type,type,
    sk__17: $i ).

thf(descrp_type,type,
    descrp: $o ).

thf(foundationAx_type,type,
    foundationAx: $o ).

thf(emptysetAx_type,type,
    emptysetAx: $o ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(exu_type,type,
    exu: ( $i > $o ) > $o ).

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

thf(replAx_type,type,
    replAx: $o ).

thf(omegaIndAx_type,type,
    omegaIndAx: $o ).

thf(exuE1,axiom,
    ( exuE1
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ! [Xy: $i] :
                  ( ( Xphi @ Xy )
                 => ( Xx = Xy ) )
              & ( Xphi @ Xx ) ) ) ) ) ).

thf('0',plain,
    ( exuE1
    = ( ! [X4: $i > $o] :
          ( ( exu
            @ ^ [V_1: $i] : ( X4 @ V_1 ) )
         => ? [X6: $i] :
              ( ! [X8: $i] :
                  ( ( X4 @ X8 )
                 => ( X6 = X8 ) )
              & ( X4 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(descrp,axiom,
    ( descrp
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ( Xphi
            @ ( descr
              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).

thf('1',plain,
    ( descrp
    = ( ! [X4: $i > $o] :
          ( ( exu
            @ ^ [V_1: $i] : ( X4 @ V_1 ) )
         => ( X4
            @ ( descr
              @ ^ [V_2: $i] : ( X4 @ V_2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(replAx,axiom,
    ( replAx
    = ( ! [Xphi: $i > $i > $o,A: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( exu
                @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
         => ? [B: $i] :
            ! [Xx: $i] :
              ( ( in @ Xx @ B )
            <=> ? [Xy: $i] :
                  ( ( Xphi @ Xy @ Xx )
                  & ( in @ Xy @ A ) ) ) ) ) ) ).

thf('2',plain,
    ( replAx
    = ( ! [X4: $i > $i > $o,X6: $i] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X6 )
             => ( exu
                @ ^ [V_1: $i] : ( X4 @ X8 @ V_1 ) ) )
         => ? [X10: $i] :
            ! [X12: $i] :
              ( ( in @ X12 @ X10 )
            <=> ? [X14: $i] :
                  ( ( X4 @ X14 @ X12 )
                  & ( in @ X14 @ X6 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(exu,axiom,
    ( exu
    = ( ^ [Xphi: $i > $o] :
        ? [Xx: $i] :
          ( ! [Xy: $i] :
              ( ( Xphi @ Xy )
             => ( Xx = Xy ) )
          & ( Xphi @ Xx ) ) ) ) ).

thf('3',plain,
    ( exu
    = ( ^ [Xphi: $i > $o] :
        ? [Xx: $i] :
          ( ! [Xy: $i] :
              ( ( Xphi @ Xy )
             => ( Xx = Xy ) )
          & ( Xphi @ Xx ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[exu]) ).

thf('4',plain,
    ( exu
    = ( ^ [V_1: $i > $o] :
        ? [X4: $i] :
          ( ! [X6: $i] :
              ( ( V_1 @ X6 )
             => ( X4 = X6 ) )
          & ( V_1 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(exuE3e,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ! [Xphi: $i > $o] :
                                              ( ( exu
                                                @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                                             => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( ! [X4: $i > $i > $o,X6: $i] :
                        ( ! [X8: $i] :
                            ( ( in @ X8 @ X6 )
                           => ? [X10: $i] :
                                ( ( X4 @ X8 @ X10 )
                                & ! [X12: $i] :
                                    ( ( X4 @ X8 @ X12 )
                                   => ( X10 = X12 ) ) ) )
                       => ? [X14: $i] :
                          ! [X16: $i] :
                            ( ( in @ X16 @ X14 )
                          <=> ? [X18: $i] :
                                ( ( in @ X18 @ X6 )
                                & ( X4 @ X18 @ X16 ) ) ) )
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( ! [X20: $i > $o] :
                              ( ? [X22: $i] :
                                  ( ( X20 @ X22 )
                                  & ! [X24: $i] :
                                      ( ( X20 @ X24 )
                                     => ( X22 = X24 ) ) )
                             => ( X20
                                @ ( descr
                                  @ ^ [V_1: $i] : ( X20 @ V_1 ) ) ) )
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( ! [X26: $i > $o] :
                                      ( ? [X28: $i] :
                                          ( ( X26 @ X28 )
                                          & ! [X30: $i] :
                                              ( ( X26 @ X30 )
                                             => ( X28 = X30 ) ) )
                                     => ? [X32: $i] :
                                          ( ( X26 @ X32 )
                                          & ! [X34: $i] :
                                              ( ( X26 @ X34 )
                                             => ( X32 = X34 ) ) ) )
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ! [X36: $i > $o] :
                                              ( ? [X38: $i] :
                                                  ( ( X36 @ X38 )
                                                  & ! [X40: $i] :
                                                      ( ( X36 @ X40 )
                                                     => ( X38 = X40 ) ) )
                                             => ? [X42: $i] : ( X36 @ X42 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,type,
    zip_tseitin_0: $i > $i > $i > ( $i > $i > $o ) > $o ).

thf(zf_stmt_2,axiom,
    ! [X18: $i,X16: $i,X6: $i,X4: $i > $i > $o] :
      ( ( zip_tseitin_0 @ X18 @ X16 @ X6 @ X4 )
    <=> ( ( X4 @ X18 @ X16 )
        & ( in @ X18 @ X6 ) ) ) ).

thf(zf_stmt_3,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( ! [X4: $i > $i > $o,X6: $i] :
                        ( ! [X8: $i] :
                            ( ( in @ X8 @ X6 )
                           => ? [X10: $i] :
                                ( ! [X12: $i] :
                                    ( ( X4 @ X8 @ X12 )
                                   => ( X10 = X12 ) )
                                & ( X4 @ X8 @ X10 ) ) )
                       => ? [X14: $i] :
                          ! [X16: $i] :
                            ( ( in @ X16 @ X14 )
                          <=> ? [X18: $i] : ( zip_tseitin_0 @ X18 @ X16 @ X6 @ X4 ) ) )
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( ! [X20: $i > $o] :
                              ( ? [X22: $i] :
                                  ( ! [X24: $i] :
                                      ( ( X20 @ X24 )
                                     => ( X22 = X24 ) )
                                  & ( X20 @ X22 ) )
                             => ( X20
                                @ ( descr
                                  @ ^ [V_1: $i] : ( X20 @ V_1 ) ) ) )
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( ! [X26: $i > $o] :
                                      ( ? [X28: $i] :
                                          ( ! [X30: $i] :
                                              ( ( X26 @ X30 )
                                             => ( X28 = X30 ) )
                                          & ( X26 @ X28 ) )
                                     => ? [X32: $i] :
                                          ( ! [X34: $i] :
                                              ( ( X26 @ X34 )
                                             => ( X32 = X34 ) )
                                          & ( X26 @ X32 ) ) )
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ! [X36: $i > $o] :
                                              ( ? [X38: $i] :
                                                  ( ! [X40: $i] :
                                                      ( ( X36 @ X40 )
                                                     => ( X38 = X40 ) )
                                                  & ( X36 @ X38 ) )
                                             => ? [X42: $i] : ( X36 @ X42 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_4,negated_conjecture,
    ~ ( setextAx
     => ( emptysetAx
       => ( setadjoinAx
         => ( powersetAx
           => ( setunionAx
             => ( omega0Ax
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( ! [X4: $i > $i > $o,X6: $i] :
                          ( ! [X8: $i] :
                              ( ( in @ X8 @ X6 )
                             => ? [X10: $i] :
                                  ( ! [X12: $i] :
                                      ( ( X4 @ X8 @ X12 )
                                     => ( X10 = X12 ) )
                                  & ( X4 @ X8 @ X10 ) ) )
                         => ? [X14: $i] :
                            ! [X16: $i] :
                              ( ( in @ X16 @ X14 )
                            <=> ? [X18: $i] : ( zip_tseitin_0 @ X18 @ X16 @ X6 @ X4 ) ) )
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( ! [X20: $i > $o] :
                                ( ? [X22: $i] :
                                    ( ! [X24: $i] :
                                        ( ( X20 @ X24 )
                                       => ( X22 = X24 ) )
                                    & ( X20 @ X22 ) )
                               => ( X20
                                  @ ( descr
                                    @ ^ [V_1: $i] : ( X20 @ V_1 ) ) ) )
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( ! [X26: $i > $o] :
                                        ( ? [X28: $i] :
                                            ( ! [X30: $i] :
                                                ( ( X26 @ X30 )
                                               => ( X28 = X30 ) )
                                            & ( X26 @ X28 ) )
                                       => ? [X32: $i] :
                                            ( ! [X34: $i] :
                                                ( ( X26 @ X34 )
                                               => ( X32 = X34 ) )
                                            & ( X26 @ X32 ) ) )
                                   => ( prop2setE
                                     => ( emptysetE
                                       => ( emptysetimpfalse
                                         => ( notinemptyset
                                           => ! [X36: $i > $o] :
                                                ( ? [X38: $i] :
                                                    ( ! [X40: $i] :
                                                        ( ( X36 @ X40 )
                                                       => ( X38 = X40 ) )
                                                    & ( X36 @ X38 ) )
                                               => ? [X42: $i] : ( X36 @ X42 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl19,plain,
    sk__16 @ sk__17,
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl18,plain,
    ! [X6: $i] :
      ~ ( sk__16 @ X6 ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl107,plain,
    $false,
    inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl18]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU504^1 : 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.hejpMI7eY6 true
% 0.13/0.34  % Computer : n028.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  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 15:58:03 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34  % Number of cores: 8
% 0.13/0.34  % Python version: Python 3.6.8
% 0.13/0.34  % Running in HO mode
% 0.19/0.62  % Total configuration time : 828
% 0.19/0.62  % Estimated wc time : 1656
% 0.19/0.62  % Estimated cpu time (8 cpus) : 207.0
% 0.19/0.73  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.19/0.73  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.19/0.73  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.19/0.73  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.19/0.74  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.19/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.19/0.74  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.19/0.75  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.99/0.90  % Solved by lams/40_c_ic.sh.
% 1.99/0.90  % done 23 iterations in 0.113s
% 1.99/0.90  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.99/0.90  % SZS output start Refutation
% See solution above
% 1.99/0.90  
% 1.99/0.90  
% 1.99/0.90  % Terminating...
% 2.04/0.93  % Runner terminated.
% 2.04/0.95  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------