TSTP Solution File: LCL874^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : LCL874^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.YlgkMc058Y true

% Computer : n020.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 09:02:29 EDT 2023

% Result   : Theorem 28.43s 4.25s
% Output   : Refutation 28.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   52
% Syntax   : Number of formulae    :  101 (  39 unt;  14 typ;   0 def)
%            Number of atoms       :  270 (  30 equ;  22 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  644 (  61   ~;  61   |;  22   &; 434   @)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  129 ( 129   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  14 usr;   4 con; 0-3 aty)
%                                         (  43  !!;   3  ??;   0 @@+;   0 @@-)
%            Number of variables   :  225 ( 100   ^; 121   !;   4   ?; 225   :)

% Comments : 
%------------------------------------------------------------------------------
thf(meuclidean_type,type,
    meuclidean: ( $i > $i > $o ) > $o ).

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#sk68_type',type,
    '#sk68': $i > $i ).

thf(rk_type,type,
    rk: $i > $i > $o ).

thf(mreflexive_type,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(mimplies_type,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf(rb_type,type,
    rb: $i > $i > $o ).

thf(mserial_type,type,
    mserial: ( $i > $i > $o ) > $o ).

thf('#sk959_type',type,
    '#sk959': $i > ( $i > $o ) > $i ).

thf(mor_type,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ) ).

thf('0',plain,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mvalid]) ).

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

thf(mbox,axiom,
    ( mbox
    = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( R @ W @ V ) ) ) ) ).

thf('2',plain,
    ( mbox
    = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( R @ W @ V ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox]) ).

thf('3',plain,
    ( mbox
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
        ! [X4: $i] :
          ( ( V_2 @ X4 )
          | ~ ( V_1 @ V_3 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(mforall_prop,axiom,
    ( mforall_prop
    = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
        ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).

thf('4',plain,
    ( mforall_prop
    = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
        ! [P: $i > $o] : ( Phi @ P @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_prop]) ).

thf('5',plain,
    ( mforall_prop
    = ( ^ [V_1: ( $i > $o ) > $i > $o,V_2: $i] :
        ! [X4: $i > $o] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).

thf(mor,axiom,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ) ).

thf('6',plain,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mor]) ).

thf('7',plain,
    ( mor
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          | ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ) ).

thf('8',plain,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mnot]) ).

thf('9',plain,
    ( mnot
    = ( ^ [V_1: $i > $o,V_2: $i] :
          ~ ( V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf('10',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'7','9']) ).

thf('11',plain,
    ( mimplies
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
    define([status(thm)]) ).

thf(ax8,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rb @ A ) @ ( mbox @ rb @ ( mbox @ rk @ A ) ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ! [X10: $i] :
          ( ~ ( rb @ X4 @ X10 )
          | ! [X12: $i] :
              ( ~ ( rk @ X10 @ X12 )
              | ( X6 @ X12 ) ) )
      | ~ ! [X8: $i] :
            ( ~ ( rb @ X4 @ X8 )
            | ( X6 @ X8 ) ) ) ).

thf(zip_derived_cl7,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i > $o] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( (~) @ ( rb @ Y0 @ Y2 ) )
                  | ( !!
                    @ ^ [Y3: $i] :
                        ( ( (~) @ ( rk @ Y2 @ Y3 ) )
                        | ( Y1 @ Y3 ) ) ) ) )
            | ( (~)
              @ ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( rb @ Y0 @ Y2 ) )
                    | ( Y1 @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(mserial,axiom,
    ( mserial
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] :
        ? [T: $i] : ( R @ S @ T ) ) ) ).

thf('12',plain,
    ( mserial
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] :
        ? [T: $i] : ( R @ S @ T ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mserial]) ).

thf('13',plain,
    ( mserial
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i] :
        ? [X6: $i] : ( V_1 @ X4 @ X6 ) ) ),
    define([status(thm)]) ).

thf(ax2,axiom,
    mserial @ rb ).

thf(zf_stmt_1,axiom,
    ! [X4: $i] :
    ? [X6: $i] : ( rb @ X4 @ X6 ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ??
        @ ^ [Y1: $i] : ( rb @ Y0 @ Y1 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl41,plain,
    ! [X2: $i] :
      ( ??
      @ ^ [Y0: $i] : ( rb @ X2 @ Y0 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl42,plain,
    ! [X2: $i] : ( rb @ X2 @ ( '#sk68' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).

thf(meuclidean,axiom,
    ( meuclidean
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ S @ U ) )
         => ( R @ T @ U ) ) ) ) ).

thf('14',plain,
    ( meuclidean
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ S @ U ) )
         => ( R @ T @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[meuclidean]) ).

thf('15',plain,
    ( meuclidean
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i,X8: $i] :
          ( ( ( V_1 @ X4 @ X6 )
            & ( V_1 @ X4 @ X8 ) )
         => ( V_1 @ X6 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(ax6,axiom,
    meuclidean @ rb ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ( ( rb @ X4 @ X8 )
        & ( rb @ X4 @ X6 ) )
     => ( rb @ X6 @ X8 ) ) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( rb @ Y0 @ Y2 )
                  & ( rb @ Y0 @ Y1 ) )
               => ( rb @ Y1 @ Y2 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl174,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( ( rb @ X2 @ Y1 )
                & ( rb @ X2 @ Y0 ) )
             => ( rb @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl175,plain,
    ! [X2: $i,X4: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( ( rb @ X2 @ Y0 )
            & ( rb @ X2 @ X4 ) )
         => ( rb @ X4 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl174]) ).

thf(zip_derived_cl176,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( rb @ X2 @ X6 )
        & ( rb @ X2 @ X4 ) )
     => ( rb @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl175]) ).

thf(zip_derived_cl177,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( rb @ X2 @ X6 )
          & ( rb @ X2 @ X4 ) )
      | ( rb @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl176]) ).

thf(zip_derived_cl178,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( rb @ X2 @ X6 )
      | ~ ( rb @ X2 @ X4 )
      | ( rb @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl177]) ).

thf(zip_derived_cl181,plain,
    ! [X0: $i,X1: $i] :
      ( ( rb @ X1 @ ( '#sk68' @ X0 ) )
      | ~ ( rb @ X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl42,zip_derived_cl178]) ).

thf(zip_derived_cl1_001,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ??
        @ ^ [Y1: $i] : ( rb @ Y0 @ Y1 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(mtransitive,axiom,
    ( mtransitive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ T @ U ) )
         => ( R @ S @ U ) ) ) ) ).

thf('16',plain,
    ( mtransitive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ T @ U ) )
         => ( R @ S @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mtransitive]) ).

thf('17',plain,
    ( mtransitive
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i,X8: $i] :
          ( ( ( V_1 @ X4 @ X6 )
            & ( V_1 @ X6 @ X8 ) )
         => ( V_1 @ X4 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(ax4,axiom,
    mtransitive @ rb ).

thf(zf_stmt_3,axiom,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ( ( rb @ X6 @ X8 )
        & ( rb @ X4 @ X6 ) )
     => ( rb @ X4 @ X8 ) ) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( rb @ Y1 @ Y2 )
                  & ( rb @ Y0 @ Y1 ) )
               => ( rb @ Y0 @ Y2 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl42_002,plain,
    ! [X2: $i] : ( rb @ X2 @ ( '#sk68' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).

thf(ax7,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rk @ A ) @ ( mbox @ rb @ A ) ) ) ) ).

thf(zf_stmt_4,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ! [X10: $i] :
          ( ~ ( rb @ X4 @ X10 )
          | ( X6 @ X10 ) )
      | ~ ! [X8: $i] :
            ( ~ ( rk @ X4 @ X8 )
            | ( X6 @ X8 ) ) ) ).

thf(zip_derived_cl6,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i > $o] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( (~) @ ( rb @ Y0 @ Y2 ) )
                  | ( Y1 @ Y2 ) ) )
            | ( (~)
              @ ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( rk @ Y0 @ Y2 ) )
                    | ( Y1 @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl218,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( rb @ X2 @ Y1 ) )
                | ( Y0 @ Y1 ) ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rk @ X2 @ Y1 ) )
                  | ( Y0 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl219,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rb @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rk @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl218]) ).

thf(zip_derived_cl220,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rb @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rk @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl219]) ).

thf(zip_derived_cl221,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( (~) @ ( rb @ X2 @ X6 ) )
      | ( X4 @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rk @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl220]) ).

thf(zip_derived_cl222,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( rb @ X2 @ X6 )
      | ( X4 @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rk @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl221]) ).

thf(zip_derived_cl223,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( ( (~) @ ( rk @ X2 @ ( '#sk959' @ X2 @ X4 ) ) )
          | ( X4 @ ( '#sk959' @ X2 @ X4 ) ) )
      | ( X4 @ X6 )
      | ~ ( rb @ X2 @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl222]) ).

thf(zip_derived_cl224,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( rk @ X2 @ ( '#sk959' @ X2 @ X4 ) )
      | ~ ( rb @ X2 @ X6 )
      | ( X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl223]) ).

thf(zip_derived_cl228,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( X1 @ ( '#sk68' @ X0 ) )
      | ( rk @ X0 @ ( '#sk959' @ X0 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl42,zip_derived_cl224]) ).

thf(zip_derived_cl42_003,plain,
    ! [X2: $i] : ( rb @ X2 @ ( '#sk68' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl225,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( X4 @ ( '#sk959' @ X2 @ X4 ) )
      | ~ ( rb @ X2 @ X6 )
      | ( X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl223]) ).

thf(zip_derived_cl2023,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( X1 @ ( '#sk68' @ X0 ) )
      | ~ ( X1 @ ( '#sk959' @ X0 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl42,zip_derived_cl225]) ).

thf(ax3,axiom,
    mtransitive @ rk ).

thf(zf_stmt_5,axiom,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ( ( rk @ X6 @ X8 )
        & ( rk @ X4 @ X6 ) )
     => ( rk @ X4 @ X8 ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( rk @ Y1 @ Y2 )
                  & ( rk @ Y0 @ Y1 ) )
               => ( rk @ Y0 @ Y2 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_5]) ).

thf(conj,conjecture,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rb @ A ) @ ( mbox @ rk @ A ) ) ) ) ).

thf(zf_stmt_6,conjecture,
    ! [X4: $i,X6: $i > $o] :
      ( ! [X10: $i] :
          ( ~ ( rk @ X4 @ X10 )
          | ( X6 @ X10 ) )
      | ~ ! [X8: $i] :
            ( ~ ( rb @ X4 @ X8 )
            | ( X6 @ X8 ) ) ) ).

thf(zf_stmt_7,negated_conjecture,
    ~ ! [X4: $i,X6: $i > $o] :
        ( ! [X10: $i] :
            ( ~ ( rk @ X4 @ X10 )
            | ( X6 @ X10 ) )
        | ~ ! [X8: $i] :
              ( ~ ( rb @ X4 @ X8 )
              | ( X6 @ X8 ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_6]) ).

thf(zip_derived_cl8,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( rk @ Y0 @ Y2 ) )
                    | ( Y1 @ Y2 ) ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( rb @ Y0 @ Y2 ) )
                      | ( Y1 @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(mreflexive,axiom,
    ( mreflexive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] : ( R @ S @ S ) ) ) ).

thf('18',plain,
    ( mreflexive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] : ( R @ S @ S ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).

thf('19',plain,
    ( mreflexive
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i] : ( V_1 @ X4 @ X4 ) ) ),
    define([status(thm)]) ).

thf(ax1,axiom,
    mreflexive @ rk ).

thf(zf_stmt_8,axiom,
    ! [X4: $i] : ( rk @ X4 @ X4 ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: $i] : ( rk @ Y0 @ Y0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_8]) ).

thf(zip_derived_cl20,plain,
    ! [X2: $i] : ( rk @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(ax5,axiom,
    meuclidean @ rk ).

thf(zf_stmt_9,axiom,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ( ( rk @ X4 @ X8 )
        & ( rk @ X4 @ X6 ) )
     => ( rk @ X6 @ X8 ) ) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( rk @ Y0 @ Y2 )
                  & ( rk @ Y0 @ Y1 ) )
               => ( rk @ Y1 @ Y2 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl117,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( ( rk @ X2 @ Y1 )
                & ( rk @ X2 @ Y0 ) )
             => ( rk @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl118,plain,
    ! [X2: $i,X4: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( ( rk @ X2 @ Y0 )
            & ( rk @ X2 @ X4 ) )
         => ( rk @ X4 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl117]) ).

thf(zip_derived_cl119,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( rk @ X2 @ X6 )
        & ( rk @ X2 @ X4 ) )
     => ( rk @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl118]) ).

thf(zip_derived_cl120,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( rk @ X2 @ X6 )
          & ( rk @ X2 @ X4 ) )
      | ( rk @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl119]) ).

thf(zip_derived_cl121,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( rk @ X2 @ X6 )
      | ~ ( rk @ X2 @ X4 )
      | ( rk @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl120]) ).

thf(zip_derived_cl123,plain,
    ! [X0: $i,X1: $i] :
      ( ( rk @ X1 @ X0 )
      | ~ ( rk @ X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl121]) ).

thf(zip_derived_cl4302,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl7,zip_derived_cl181,zip_derived_cl1,zip_derived_cl3,zip_derived_cl228,zip_derived_cl2023,zip_derived_cl2,zip_derived_cl8,zip_derived_cl123]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL874^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.YlgkMc058Y true
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri Aug 25 00:45:00 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.22/0.65  % Total configuration time : 828
% 0.22/0.65  % Estimated wc time : 1656
% 0.22/0.65  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.70  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.56/0.84  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 28.43/4.25  % Solved by lams/15_e_short1.sh.
% 28.43/4.25  % done 330 iterations in 3.463s
% 28.43/4.25  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 28.43/4.25  % SZS output start Refutation
% See solution above
% 28.43/4.25  
% 28.43/4.25  
% 28.43/4.26  % Terminating...
% 29.19/4.37  % Runner terminated.
% 29.19/4.38  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------