↑ Up

Zipperpin---2.1.9999.THM-Ref.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU816^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.MIPELysMih true

% Computer : n015.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 Oct  2 04:56:36 PM UTC 2025

% Result   : Theorem 0.60s 0.86s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   51 (  32 unt;   0 typ;   0 def)
%            Number of atoms       :  278 (  38 equ;   0 cnn)
%            Maximal formula atoms :   50 (   5 avg)
%            Number of connectives :  763 (  46   ~;  49   |;  42   &; 524   @)
%                                         (   0 <=>; 102  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   6 con; 0-2 aty)
%            Number of variables   :  122 (  15   ^; 100   !;   7   ?; 122   :)

% Comments : 
%------------------------------------------------------------------------------
thf(stricttotalorderedByIn_type,type,
    stricttotalorderedByIn: $i > $o ).

thf(sk__18_type,type,
    sk__18: $i > $i ).

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

thf(sk__14_type,type,
    sk__14: $i ).

thf(sk__13_type,type,
    sk__13: $i ).

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

thf(binintersect_type,type,
    binintersect: $i > $i > $i ).

thf(wellorderedByIn_type,type,
    wellorderedByIn: $i > $o ).

thf(transitiveset_type,type,
    transitiveset: $i > $o ).

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

thf(sk__12_type,type,
    sk__12: $i ).

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

thf(nonempty_type,type,
    nonempty: $i > $o ).

thf(binintTransitive_type,type,
    binintTransitive: $o ).

thf(ordinal_type,type,
    ordinal: $i > $o ).

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

thf(ordinal,axiom,
    ( ordinal
    = ( ^ [Xx: $i] :
          ( ( transitiveset @ Xx )
          & ( wellorderedByIn @ Xx ) ) ) ) ).

thf(wellorderedByIn,axiom,
    ( wellorderedByIn
    = ( ^ [A: $i] :
          ( ( stricttotalorderedByIn @ A )
          & ! [X: $i] :
              ( ( in @ X @ ( powerset @ A ) )
             => ( ( nonempty @ X )
               => ? [Xx: $i] :
                    ( ! [Y: $i] :
                        ( ( in @ Y @ X )
                       => ( ( Xx = Y )
                          | ( in @ Xx @ Y ) ) )
                    & ( in @ Xx @ X ) ) ) ) ) ) ) ).

thf(stricttotalorderedByIn,axiom,
    ( stricttotalorderedByIn
    = ( ^ [A: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [X: $i] :
                  ( ( in @ X @ A )
                 => ! [Y: $i] :
                      ( ( in @ Y @ A )
                     => ( ( ( in @ Xx @ X )
                          & ( in @ X @ Y ) )
                       => ( in @ Xx @ Y ) ) ) ) )
          & ! [X: $i] :
              ( ( in @ X @ A )
             => ! [Y: $i] :
                  ( ( in @ Y @ A )
                 => ( ( X = Y )
                    | ( in @ X @ Y )
                    | ( in @ Y @ X ) ) ) )
          & ! [X: $i] :
              ( ( in @ X @ A )
             => ~ ( in @ X @ X ) ) ) ) ) ).

thf('0',plain,
    ( stricttotalorderedByIn
    = ( ^ [A: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [X: $i] :
                  ( ( in @ X @ A )
                 => ! [Y: $i] :
                      ( ( in @ Y @ A )
                     => ( ( ( in @ Xx @ X )
                          & ( in @ X @ Y ) )
                       => ( in @ Xx @ Y ) ) ) ) )
          & ! [X: $i] :
              ( ( in @ X @ A )
             => ! [Y: $i] :
                  ( ( in @ Y @ A )
                 => ( ( X = Y )
                    | ( in @ X @ Y )
                    | ( in @ Y @ X ) ) ) )
          & ! [X: $i] :
              ( ( in @ X @ A )
             => ~ ( in @ X @ X ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[stricttotalorderedByIn]) ).

thf('1',plain,
    ( stricttotalorderedByIn
    = ( ^ [V_1: $i] :
          ( ! [X4: $i] :
              ( ( in @ X4 @ V_1 )
             => ! [X6: $i] :
                  ( ( in @ X6 @ V_1 )
                 => ! [X8: $i] :
                      ( ( in @ X8 @ V_1 )
                     => ( ( ( in @ X4 @ X6 )
                          & ( in @ X6 @ X8 ) )
                       => ( in @ X4 @ X8 ) ) ) ) )
          & ! [X10: $i] :
              ( ( in @ X10 @ V_1 )
             => ! [X12: $i] :
                  ( ( in @ X12 @ V_1 )
                 => ( ( X10 = X12 )
                    | ( in @ X10 @ X12 )
                    | ( in @ X12 @ X10 ) ) ) )
          & ! [X14: $i] :
              ( ( in @ X14 @ V_1 )
             => ~ ( in @ X14 @ X14 ) ) ) ) ),
    define([status(thm)]) ).

thf(nonempty,axiom,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).

thf('2',plain,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
    inference(simplify_rw_rule,[status(thm)],[nonempty]) ).

thf('3',plain,
    ( nonempty
    = ( ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
    define([status(thm)]) ).

thf('4',plain,
    ( wellorderedByIn
    = ( ^ [A: $i] :
          ( ( stricttotalorderedByIn @ A )
          & ! [X: $i] :
              ( ( in @ X @ ( powerset @ A ) )
             => ( ( nonempty @ X )
               => ? [Xx: $i] :
                    ( ! [Y: $i] :
                        ( ( in @ Y @ X )
                       => ( ( Xx = Y )
                          | ( in @ Xx @ Y ) ) )
                    & ( in @ Xx @ X ) ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[wellorderedByIn,'1','3']) ).

thf('5',plain,
    ( wellorderedByIn
    = ( ^ [V_1: $i] :
          ( ( stricttotalorderedByIn @ V_1 )
          & ! [X4: $i] :
              ( ( in @ X4 @ ( powerset @ V_1 ) )
             => ( ( nonempty @ X4 )
               => ? [X6: $i] :
                    ( ! [X8: $i] :
                        ( ( in @ X8 @ X4 )
                       => ( ( X6 = X8 )
                          | ( in @ X6 @ X8 ) ) )
                    & ( in @ X6 @ X4 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf('6',plain,
    ( ordinal
    = ( ^ [Xx: $i] :
          ( ( transitiveset @ Xx )
          & ( wellorderedByIn @ Xx ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ordinal,'5','1','3']) ).

thf('7',plain,
    ( ordinal
    = ( ^ [V_1: $i] :
          ( ( transitiveset @ V_1 )
          & ( wellorderedByIn @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf(binintTransitive,axiom,
    ( binintTransitive
    = ( ! [X: $i] :
          ( ( transitiveset @ X )
         => ! [Y: $i] :
              ( ( transitiveset @ Y )
             => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).

thf('8',plain,
    ( binintTransitive
    = ( ! [X4: $i] :
          ( ( transitiveset @ X4 )
         => ! [X6: $i] :
              ( ( transitiveset @ X6 )
             => ( transitiveset @ ( binintersect @ X4 @ X6 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(transitiveset,axiom,
    ( transitiveset
    = ( ^ [A: $i] :
        ! [X: $i] :
          ( ( in @ X @ A )
         => ( subset @ X @ A ) ) ) ) ).

thf('9',plain,
    ( transitiveset
    = ( ^ [A: $i] :
        ! [X: $i] :
          ( ( in @ X @ A )
         => ( subset @ X @ A ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[transitiveset]) ).

thf('10',plain,
    ( transitiveset
    = ( ^ [V_1: $i] :
        ! [X4: $i] :
          ( ( in @ X4 @ V_1 )
         => ( subset @ X4 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf(ordinalMinLem1,conjecture,
    ( binintTransitive
   => ! [X: $i] :
        ( ( ordinal @ X )
       => ! [Y: $i] :
            ( ( ordinal @ Y )
           => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i] :
        ( ! [X6: $i] :
            ( ( in @ X6 @ X4 )
           => ( subset @ X6 @ X4 ) )
       => ! [X8: $i] :
            ( ! [X10: $i] :
                ( ( in @ X10 @ X8 )
               => ( subset @ X10 @ X8 ) )
           => ! [X12: $i] :
                ( ( in @ X12 @ ( binintersect @ X4 @ X8 ) )
               => ( subset @ X12 @ ( binintersect @ X4 @ X8 ) ) ) ) )
   => ! [X14: $i] :
        ( ( ! [X16: $i] :
              ( ( in @ X16 @ X14 )
             => ( subset @ X16 @ X14 ) )
          & ! [X18: $i] :
              ( ( in @ X18 @ X14 )
             => ! [X20: $i] :
                  ( ( in @ X20 @ X14 )
                 => ! [X22: $i] :
                      ( ( in @ X22 @ X14 )
                     => ( ( ( in @ X18 @ X20 )
                          & ( in @ X20 @ X22 ) )
                       => ( in @ X18 @ X22 ) ) ) ) )
          & ! [X24: $i] :
              ( ( in @ X24 @ X14 )
             => ! [X26: $i] :
                  ( ( in @ X26 @ X14 )
                 => ( ( X24 = X26 )
                    | ( in @ X24 @ X26 )
                    | ( in @ X26 @ X24 ) ) ) )
          & ! [X28: $i] :
              ( ( in @ X28 @ X14 )
             => ~ ( in @ X28 @ X28 ) )
          & ! [X30: $i] :
              ( ( in @ X30 @ ( powerset @ X14 ) )
             => ( ( X30 != emptyset )
               => ? [X32: $i] :
                    ( ! [X34: $i] :
                        ( ( in @ X34 @ X30 )
                       => ( ( X32 = X34 )
                          | ( in @ X32 @ X34 ) ) )
                    & ( in @ X32 @ X30 ) ) ) ) )
       => ! [X36: $i] :
            ( ( ! [X38: $i] :
                  ( ( in @ X38 @ X36 )
                 => ( subset @ X38 @ X36 ) )
              & ! [X40: $i] :
                  ( ( in @ X40 @ X36 )
                 => ! [X42: $i] :
                      ( ( in @ X42 @ X36 )
                     => ! [X44: $i] :
                          ( ( in @ X44 @ X36 )
                         => ( ( ( in @ X40 @ X42 )
                              & ( in @ X42 @ X44 ) )
                           => ( in @ X40 @ X44 ) ) ) ) )
              & ! [X46: $i] :
                  ( ( in @ X46 @ X36 )
                 => ! [X48: $i] :
                      ( ( in @ X48 @ X36 )
                     => ( ( X46 = X48 )
                        | ( in @ X46 @ X48 )
                        | ( in @ X48 @ X46 ) ) ) )
              & ! [X50: $i] :
                  ( ( in @ X50 @ X36 )
                 => ~ ( in @ X50 @ X50 ) )
              & ! [X52: $i] :
                  ( ( in @ X52 @ ( powerset @ X36 ) )
                 => ( ( X52 != emptyset )
                   => ? [X54: $i] :
                        ( ! [X56: $i] :
                            ( ( in @ X56 @ X52 )
                           => ( ( X54 = X56 )
                              | ( in @ X54 @ X56 ) ) )
                        & ( in @ X54 @ X52 ) ) ) ) )
           => ! [X58: $i] :
                ( ( in @ X58 @ ( binintersect @ X14 @ X36 ) )
               => ( subset @ X58 @ ( binintersect @ X14 @ X36 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i] :
          ( ! [X6: $i] :
              ( ( in @ X6 @ X4 )
             => ( subset @ X6 @ X4 ) )
         => ! [X8: $i] :
              ( ! [X10: $i] :
                  ( ( in @ X10 @ X8 )
                 => ( subset @ X10 @ X8 ) )
             => ! [X12: $i] :
                  ( ( in @ X12 @ ( binintersect @ X4 @ X8 ) )
                 => ( subset @ X12 @ ( binintersect @ X4 @ X8 ) ) ) ) )
     => ! [X14: $i] :
          ( ( ! [X16: $i] :
                ( ( in @ X16 @ X14 )
               => ( subset @ X16 @ X14 ) )
            & ! [X18: $i] :
                ( ( in @ X18 @ X14 )
               => ! [X20: $i] :
                    ( ( in @ X20 @ X14 )
                   => ! [X22: $i] :
                        ( ( in @ X22 @ X14 )
                       => ( ( ( in @ X18 @ X20 )
                            & ( in @ X20 @ X22 ) )
                         => ( in @ X18 @ X22 ) ) ) ) )
            & ! [X24: $i] :
                ( ( in @ X24 @ X14 )
               => ! [X26: $i] :
                    ( ( in @ X26 @ X14 )
                   => ( ( X24 = X26 )
                      | ( in @ X24 @ X26 )
                      | ( in @ X26 @ X24 ) ) ) )
            & ! [X28: $i] :
                ( ( in @ X28 @ X14 )
               => ~ ( in @ X28 @ X28 ) )
            & ! [X30: $i] :
                ( ( in @ X30 @ ( powerset @ X14 ) )
               => ( ( X30 != emptyset )
                 => ? [X32: $i] :
                      ( ! [X34: $i] :
                          ( ( in @ X34 @ X30 )
                         => ( ( X32 = X34 )
                            | ( in @ X32 @ X34 ) ) )
                      & ( in @ X32 @ X30 ) ) ) ) )
         => ! [X36: $i] :
              ( ( ! [X38: $i] :
                    ( ( in @ X38 @ X36 )
                   => ( subset @ X38 @ X36 ) )
                & ! [X40: $i] :
                    ( ( in @ X40 @ X36 )
                   => ! [X42: $i] :
                        ( ( in @ X42 @ X36 )
                       => ! [X44: $i] :
                            ( ( in @ X44 @ X36 )
                           => ( ( ( in @ X40 @ X42 )
                                & ( in @ X42 @ X44 ) )
                             => ( in @ X40 @ X44 ) ) ) ) )
                & ! [X46: $i] :
                    ( ( in @ X46 @ X36 )
                   => ! [X48: $i] :
                        ( ( in @ X48 @ X36 )
                       => ( ( X46 = X48 )
                          | ( in @ X46 @ X48 )
                          | ( in @ X48 @ X46 ) ) ) )
                & ! [X50: $i] :
                    ( ( in @ X50 @ X36 )
                   => ~ ( in @ X50 @ X50 ) )
                & ! [X52: $i] :
                    ( ( in @ X52 @ ( powerset @ X36 ) )
                   => ( ( X52 != emptyset )
                     => ? [X54: $i] :
                          ( ! [X56: $i] :
                              ( ( in @ X56 @ X52 )
                             => ( ( X54 = X56 )
                                | ( in @ X54 @ X56 ) ) )
                          & ( in @ X54 @ X52 ) ) ) ) )
             => ! [X58: $i] :
                  ( ( in @ X58 @ ( binintersect @ X14 @ X36 ) )
                 => ( subset @ X58 @ ( binintersect @ X14 @ X36 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl17,plain,
    ! [X20: $i] :
      ( ( subset @ X20 @ sk__12 )
      | ~ ( in @ X20 @ sk__12 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl11,plain,
    in @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl2,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ ( sk__17 @ X0 ) @ X0 )
      | ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
      | ~ ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
      | ~ ( subset @ ( sk__18 @ X2 ) @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl128,plain,
    ( ~ ( subset @ ( sk__18 @ sk__12 ) @ sk__12 )
    | ( subset @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) )
    | ( in @ ( sk__17 @ sk__13 ) @ sk__13 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ! [X3: $i] :
      ( ( subset @ X3 @ sk__13 )
      | ~ ( in @ X3 @ sk__13 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl11_001,plain,
    in @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( subset @ ( sk__17 @ X0 ) @ X0 )
      | ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
      | ~ ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
      | ( in @ ( sk__18 @ X2 ) @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl122,plain,
    ( ( in @ ( sk__18 @ sk__12 ) @ sk__12 )
    | ( subset @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) )
    | ~ ( subset @ ( sk__17 @ sk__13 ) @ sk__13 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).

thf(zip_derived_cl17_002,plain,
    ! [X20: $i] :
      ( ( subset @ X20 @ sk__12 )
      | ~ ( in @ X20 @ sk__12 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( subset @ ( sk__17 @ X0 ) @ X0 )
      | ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
      | ~ ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
      | ~ ( subset @ ( sk__18 @ X2 ) @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl10,plain,
    ~ ( subset @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl27,plain,
    ( ~ ( subset @ ( sk__18 @ sk__12 ) @ sk__12 )
    | ~ ( in @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) )
    | ~ ( subset @ ( sk__17 @ sk__13 ) @ sk__13 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl10]) ).

thf(zip_derived_cl11_003,plain,
    in @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl56,plain,
    ( ~ ( subset @ ( sk__18 @ sk__12 ) @ sk__12 )
    | ~ ( subset @ ( sk__17 @ sk__13 ) @ sk__13 ) ),
    inference(demod,[status(thm)],[zip_derived_cl27,zip_derived_cl11]) ).

thf(zip_derived_cl68,plain,
    ( ~ ( in @ ( sk__18 @ sk__12 ) @ sk__12 )
    | ~ ( subset @ ( sk__17 @ sk__13 ) @ sk__13 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl56]) ).

thf(zip_derived_cl124,plain,
    ( ~ ( subset @ ( sk__17 @ sk__13 ) @ sk__13 )
    | ( subset @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl122,zip_derived_cl68]) ).

thf(zip_derived_cl10_004,plain,
    ~ ( subset @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl125,plain,
    ~ ( subset @ ( sk__17 @ sk__13 ) @ sk__13 ),
    inference(clc,[status(thm)],[zip_derived_cl124,zip_derived_cl10]) ).

thf(zip_derived_cl126,plain,
    ~ ( in @ ( sk__17 @ sk__13 ) @ sk__13 ),
    inference('sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl125]) ).

thf(zip_derived_cl137,plain,
    ( ~ ( subset @ ( sk__18 @ sk__12 ) @ sk__12 )
    | ( subset @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl128,zip_derived_cl126]) ).

thf(zip_derived_cl10_005,plain,
    ~ ( subset @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl138,plain,
    ~ ( subset @ ( sk__18 @ sk__12 ) @ sk__12 ),
    inference(clc,[status(thm)],[zip_derived_cl137,zip_derived_cl10]) ).

thf(zip_derived_cl139,plain,
    ~ ( in @ ( sk__18 @ sk__12 ) @ sk__12 ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl138]) ).

thf(zip_derived_cl11_006,plain,
    in @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ ( sk__17 @ X0 ) @ X0 )
      | ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
      | ~ ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
      | ( in @ ( sk__18 @ X2 ) @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl80,plain,
    ( ( in @ ( sk__18 @ sk__12 ) @ sk__12 )
    | ( subset @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) )
    | ( in @ ( sk__17 @ sk__13 ) @ sk__13 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl3]) ).

thf(zip_derived_cl10_007,plain,
    ~ ( subset @ sk__14 @ ( binintersect @ sk__12 @ sk__13 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl82,plain,
    ( ( in @ ( sk__17 @ sk__13 ) @ sk__13 )
    | ( in @ ( sk__18 @ sk__12 ) @ sk__12 ) ),
    inference(clc,[status(thm)],[zip_derived_cl80,zip_derived_cl10]) ).

thf(zip_derived_cl126_008,plain,
    ~ ( in @ ( sk__17 @ sk__13 ) @ sk__13 ),
    inference('sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl125]) ).

thf(zip_derived_cl132,plain,
    in @ ( sk__18 @ sk__12 ) @ sk__12,
    inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl126]) ).

thf(zip_derived_cl141,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl139,zip_derived_cl132]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU816^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.MIPELysMih true
% 0.13/0.35  % Computer : n015.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 Oct  1 16:09:38 EDT 2025
% 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
% 0.57/0.69  % Total configuration time : 828
% 0.57/0.69  % Estimated wc time : 1656
% 0.57/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/0.75  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.58/0.76  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.58/0.80  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.82  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.60/0.86  % Solved by lams/40_c.s.sh.
% 0.60/0.86  % done 35 iterations in 0.085s
% 0.60/0.86  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.60/0.86  % SZS output start Refutation
% See solution above
% 0.60/0.86  
% 0.60/0.86  
% 0.60/0.86  % Terminating...
% 1.75/0.89  % Runner terminated.
% 1.75/0.91  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------