TSTP Solution File: NUM768^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM768^1 : 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.HSVlgQQwXC true

% Computer : n012.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 12:44:03 EDT 2023

% Result   : Theorem 1.50s 1.17s
% Output   : Refutation 1.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   92 (  13 unt;  19 typ;   0 def)
%            Number of atoms       :  230 (  33 equ;  26 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives : 1093 (  40   ~;  23   |;   0   &; 937   @)
%                                         (   0 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   9 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   42 (  42   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  17 usr;   7 con; 0-6 aty)
%                                         (  56  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  131 (  27   ^;  92   !;   0   ?; 131   :)
%                                         (  12  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(frac_type,type,
    frac: $tType ).

thf(ind_type,type,
    ind: ( nat > $o ) > nat ).

thf(some_type,type,
    some: ( nat > $o ) > $o ).

thf(pf_type,type,
    pf: frac > frac > frac ).

thf(pl_type,type,
    pl: nat > nat > nat ).

thf(y_type,type,
    y: frac ).

thf(num_type,type,
    num: frac > nat ).

thf(den_type,type,
    den: frac > nat ).

thf(ts_type,type,
    ts: nat > nat > nat ).

thf(eq_type,type,
    eq: frac > frac > $o ).

thf(x_type,type,
    x: frac ).

thf(fr_type,type,
    fr: nat > nat > frac ).

thf(amone_type,type,
    amone: ( nat > $o ) > $o ).

thf(s_comb_type,type,
    '#S': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).

thf(c_comb_type,type,
    '#C': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).

thf(b_comb_type,type,
    '#B': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).

thf(k_comb_type,type,
    '#K': 
      !>[A: $tType,B: $tType] : ( B > A > B ) ).

thf(i_comb_type,type,
    '#I': 
      !>[A: $tType] : ( A > A ) ).

thf(satz8b,axiom,
    ! [Xx: nat,Xy: nat] :
      ( amone
      @ ^ [Xz: nat] :
          ( Xx
          = ( pl @ Xy @ Xz ) ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: nat] :
        ( !!
        @ ^ [Y1: nat] :
            ( amone
            @ ^ [Y2: nat] :
                ( Y0
                = ( pl @ Y1 @ Y2 ) ) ) ) ),
    inference(cnf,[status(esa)],[satz8b]) ).

thf(zip_derived_cl3,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ amone ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ pl ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl26,plain,
    ! [X2: nat] : ( !! @ ( '#B' @ amone @ ( '#B' @ ( '#B' @ ( nat = X2 ) ) @ pl ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl27,plain,
    ! [X2: nat,X4: nat] : ( amone @ ( '#B' @ ( nat = X2 ) @ ( pl @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).

thf(oneax,axiom,
    ! [Xp: nat > $o] :
      ( ~ ( ( amone @ Xp )
         => ~ ( some @ Xp ) )
     => ( Xp @ ( ind @ Xp ) ) ) ).

thf(zip_derived_cl16,plain,
    ( !!
    @ ^ [Y0: nat > $o] :
        ( ( (~)
          @ ( ( amone @ Y0 )
           => ( (~) @ ( some @ Y0 ) ) ) )
       => ( Y0 @ ( ind @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[oneax]) ).

thf(zip_derived_cl17,plain,
    !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ (~) @ ( '#S' @ ( '#B' @ (=>) @ amone ) @ ( '#B' @ (~) @ some ) ) ) ) @ ( '#S' @ '#I' @ ind ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl30,plain,
    ! [X2: nat > $o] :
      ( ( (~)
        @ ( ( amone @ X2 )
         => ( (~) @ ( some @ X2 ) ) ) )
     => ( X2 @ ( ind @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl31,plain,
    ! [X2: nat > $o] :
      ( ( ( amone @ X2 )
       => ( (~) @ ( some @ X2 ) ) )
      | ( X2 @ ( ind @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl32,plain,
    ! [X2: nat > $o] :
      ( ~ ( amone @ X2 )
      | ~ ( some @ X2 )
      | ( X2 @ ( ind @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl51,plain,
    ! [X0: nat,X1: nat] :
      ( ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) @ ( ind @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) )
      | ~ ( some @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl32]) ).

thf(zip_derived_cl61,plain,
    ! [X0: nat,X1: nat] :
      ( ( X1
        = ( pl @ X0 @ ( ind @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ) )
      | ~ ( some @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ),
    inference('comb-normalize',[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl62,plain,
    ! [X0: nat,X1: nat] :
      ( ( X1
        = ( pl @ X0 @ ( ind @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ) )
      | ~ ( some @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl61]) ).

thf(satz56,axiom,
    ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
      ( ( eq @ Xx @ Xy )
     => ( ( eq @ Xz @ Xu )
       => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).

thf(zip_derived_cl6,plain,
    ( !!
    @ ^ [Y0: frac] :
        ( !!
        @ ^ [Y1: frac] :
            ( !!
            @ ^ [Y2: frac] :
                ( !!
                @ ^ [Y3: frac] :
                    ( ( eq @ Y0 @ Y1 )
                   => ( ( eq @ Y2 @ Y3 )
                     => ( eq @ ( pf @ Y0 @ Y2 ) @ ( pf @ Y1 @ Y3 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[satz56]) ).

thf(zip_derived_cl7,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ eq ) @ pf ) ) ) ) @ pf ) ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl43,plain,
    ! [X2: frac] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( eq @ X2 ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ eq @ ( pf @ X2 ) ) ) ) @ pf ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl44,plain,
    ! [X2: frac,X4: frac] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ ( (=>) @ ( eq @ X2 @ X4 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ eq @ ( pf @ X2 ) ) ) @ ( pf @ X4 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl45,plain,
    ! [X2: frac,X4: frac,X6: frac] : ( !! @ ( '#B' @ ( (=>) @ ( eq @ X2 @ X4 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( eq @ X6 ) ) @ ( '#B' @ ( eq @ ( pf @ X2 @ X6 ) ) @ ( pf @ X4 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl46,plain,
    ! [X2: frac,X4: frac,X6: frac,X8: frac] :
      ( ( eq @ X2 @ X4 )
     => ( ( eq @ X6 @ X8 )
       => ( eq @ ( pf @ X2 @ X6 ) @ ( pf @ X4 @ X8 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl47,plain,
    ! [X2: frac,X4: frac,X6: frac,X8: frac] :
      ( ~ ( eq @ X2 @ X4 )
      | ( ( eq @ X6 @ X8 )
       => ( eq @ ( pf @ X2 @ X6 ) @ ( pf @ X4 @ X8 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl48,plain,
    ! [X2: frac,X4: frac,X6: frac,X8: frac] :
      ( ~ ( eq @ X6 @ X8 )
      | ( eq @ ( pf @ X2 @ X6 ) @ ( pf @ X4 @ X8 ) )
      | ~ ( eq @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).

thf(satz39,axiom,
    ! [Xx: frac,Xy: frac,Xz: frac] :
      ( ( eq @ Xx @ Xy )
     => ( ( eq @ Xy @ Xz )
       => ( eq @ Xx @ Xz ) ) ) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: frac] :
        ( !!
        @ ^ [Y1: frac] :
            ( !!
            @ ^ [Y2: frac] :
                ( ( eq @ Y0 @ Y1 )
               => ( ( eq @ Y1 @ Y2 )
                 => ( eq @ Y0 @ Y2 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[satz39]) ).

thf(zip_derived_cl5,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) @ eq ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl35,plain,
    ! [X2: frac] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( eq @ X2 ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) @ ( eq @ X2 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl36,plain,
    ! [X2: frac,X4: frac] : ( !! @ ( '#B' @ ( (=>) @ ( eq @ X2 @ X4 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( eq @ X4 ) ) @ ( eq @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl37,plain,
    ! [X2: frac,X4: frac,X6: frac] :
      ( ( eq @ X2 @ X4 )
     => ( ( eq @ X4 @ X6 )
       => ( eq @ X2 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl38,plain,
    ! [X2: frac,X4: frac,X6: frac] :
      ( ~ ( eq @ X2 @ X4 )
      | ( ( eq @ X4 @ X6 )
       => ( eq @ X2 @ X6 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl39,plain,
    ! [X2: frac,X4: frac,X6: frac] :
      ( ~ ( eq @ X4 @ X6 )
      | ( eq @ X2 @ X6 )
      | ~ ( eq @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(satz67c,conjecture,
    ( eq
    @ ( pf @ y
      @ ( fr
        @ ( ind
          @ ^ [Xt: nat] :
              ( ( ts @ ( num @ x ) @ ( den @ y ) )
              = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
        @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
    @ x ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( eq
      @ ( pf @ y
        @ ( fr
          @ ( ind
            @ ^ [Xt: nat] :
                ( ( ts @ ( num @ x ) @ ( den @ y ) )
                = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
          @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
      @ x ),
    inference('cnf.neg',[status(esa)],[satz67c]) ).

thf(zip_derived_cl20,plain,
    ~ ( eq
      @ ( pf @ y
        @ ( fr
          @ ( ind
            @ ^ [Y0: nat] :
                ( ( ts @ ( num @ x ) @ ( den @ y ) )
                = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
          @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
      @ x ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl21,plain,
    ~ ( eq
      @ ( pf @ y
        @ ( fr
          @ ( ind
            @ ( '#B'
              @ ( nat
                = ( ts @ ( num @ x ) @ ( den @ y ) ) )
              @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
          @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
      @ x ),
    inference(lams2combs,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl148,plain,
    ! [X0: frac] :
      ( ~ ( eq
          @ ( pf @ y
            @ ( fr
              @ ( ind
                @ ( '#B'
                  @ ( nat
                    = ( ts @ ( num @ x ) @ ( den @ y ) ) )
                  @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
              @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
          @ X0 )
      | ~ ( eq @ X0 @ x ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl21]) ).

thf(zip_derived_cl215,plain,
    ! [X0: frac,X1: frac] :
      ( ~ ( eq @ y @ X1 )
      | ~ ( eq
          @ ( fr
            @ ( ind
              @ ( '#B'
                @ ( nat
                  = ( ts @ ( num @ x ) @ ( den @ y ) ) )
                @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
            @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
          @ X0 )
      | ~ ( eq @ ( pf @ X1 @ X0 ) @ x ) ),
    inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl148]) ).

thf(satz37,axiom,
    ! [Xx: frac] : ( eq @ Xx @ Xx ) ).

thf(zip_derived_cl10,plain,
    ( !!
    @ ^ [Y0: frac] : ( eq @ Y0 @ Y0 ) ),
    inference(cnf,[status(esa)],[satz37]) ).

thf(zip_derived_cl11,plain,
    !! @ ( '#S' @ eq @ '#I' ),
    inference(lams2combs,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl22,plain,
    ! [X2: frac] : ( eq @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl369,plain,
    ! [X0: frac] :
      ( ~ ( eq
          @ ( pf @ X0
            @ ( fr
              @ ( ind
                @ ( '#B'
                  @ ( nat
                    = ( ts @ ( num @ x ) @ ( den @ y ) ) )
                  @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
              @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
          @ x )
      | ~ ( eq @ y @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl215,zip_derived_cl22]) ).

thf(zip_derived_cl39_001,plain,
    ! [X2: frac,X4: frac,X6: frac] :
      ( ~ ( eq @ X4 @ X6 )
      | ( eq @ X2 @ X6 )
      | ~ ( eq @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl387,plain,
    ! [X0: frac,X1: frac] :
      ( ~ ( eq @ y @ X0 )
      | ~ ( eq
          @ ( pf @ X0
            @ ( fr
              @ ( ind
                @ ( '#B'
                  @ ( nat
                    = ( ts @ ( num @ x ) @ ( den @ y ) ) )
                  @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
              @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
          @ X1 )
      | ~ ( eq @ X1 @ x ) ),
    inference('sup+',[status(thm)],[zip_derived_cl369,zip_derived_cl39]) ).

thf(satz57,axiom,
    ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) ).

thf(zip_derived_cl14,plain,
    ( !!
    @ ^ [Y0: nat] :
        ( !!
        @ ^ [Y1: nat] :
            ( !!
            @ ^ [Y2: nat] : ( eq @ ( pf @ ( fr @ Y0 @ Y2 ) @ ( fr @ Y1 @ Y2 ) ) @ ( fr @ ( pl @ Y0 @ Y1 ) @ Y2 ) ) ) ) ),
    inference(cnf,[status(esa)],[satz57]) ).

thf(zip_derived_cl15,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ eq ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ pf ) @ fr ) ) ) @ fr ) ) ) ) @ ( '#B' @ ( '#B' @ fr ) @ pl ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl40,plain,
    ! [X2: nat] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ eq ) @ ( '#B' @ ( '#S' @ ( '#B' @ pf @ ( fr @ X2 ) ) ) @ fr ) ) ) @ ( '#B' @ fr @ ( pl @ X2 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl41,plain,
    ! [X2: nat,X4: nat] : ( !! @ ( '#S' @ ( '#B' @ eq @ ( '#S' @ ( '#B' @ pf @ ( fr @ X2 ) ) @ ( fr @ X4 ) ) ) @ ( fr @ ( pl @ X2 @ X4 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl42,plain,
    ! [X2: nat,X4: nat,X6: nat] : ( eq @ ( pf @ ( fr @ X2 @ X6 ) @ ( fr @ X4 @ X6 ) ) @ ( fr @ ( pl @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl421,plain,
    ! [X0: nat] :
      ( ~ ( eq
          @ ( fr
            @ ( pl @ X0
              @ ( ind
                @ ( '#B'
                  @ ( nat
                    = ( ts @ ( num @ x ) @ ( den @ y ) ) )
                  @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) ) )
            @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
          @ x )
      | ~ ( eq @ y @ ( fr @ X0 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl387,zip_derived_cl42]) ).

thf(zip_derived_cl561,plain,
    ( ~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ x )
    | ~ ( some
        @ ( '#B'
          @ ( nat
            = ( ts @ ( num @ x ) @ ( den @ y ) ) )
          @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
    | ~ ( eq @ y @ ( fr @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl421]) ).

thf(satz40a,axiom,
    ! [Xx: frac,Xn: nat] : ( eq @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) @ Xx ) ).

thf(zip_derived_cl18,plain,
    ( !!
    @ ^ [Y0: frac] :
        ( !!
        @ ^ [Y1: nat] : ( eq @ ( fr @ ( ts @ ( num @ Y0 ) @ Y1 ) @ ( ts @ ( den @ Y0 ) @ Y1 ) ) @ Y0 ) ) ),
    inference(cnf,[status(esa)],[satz40a]) ).

thf(zip_derived_cl19,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ eq ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ fr ) @ ( '#B' @ ts @ num ) ) ) @ ( '#B' @ ts @ den ) ) ) ) @ '#I' ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl33,plain,
    ! [X2: frac] : ( !! @ ( '#C' @ ( '#B' @ eq @ ( '#S' @ ( '#B' @ fr @ ( ts @ ( num @ X2 ) ) ) @ ( ts @ ( den @ X2 ) ) ) ) @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl34,plain,
    ! [X2: frac,X4: nat] : ( eq @ ( fr @ ( ts @ ( num @ X2 ) @ X4 ) @ ( ts @ ( den @ X2 ) @ X4 ) ) @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(m,axiom,
    ( some
    @ ^ [Xu: nat] :
        ( ( ts @ ( num @ x ) @ ( den @ y ) )
        = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xu ) ) ) ).

thf(zip_derived_cl0,plain,
    ( some
    @ ^ [Y0: nat] :
        ( ( ts @ ( num @ x ) @ ( den @ y ) )
        = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) ),
    inference(cnf,[status(esa)],[m]) ).

thf(zip_derived_cl1,plain,
    ( some
    @ ( '#B'
      @ ( nat
        = ( ts @ ( num @ x ) @ ( den @ y ) ) )
      @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl0]) ).

thf(satz29,axiom,
    ! [Xx: nat,Xy: nat] :
      ( ( ts @ Xx @ Xy )
      = ( ts @ Xy @ Xx ) ) ).

thf(zip_derived_cl12,plain,
    ( !!
    @ ^ [Y0: nat] :
        ( !!
        @ ^ [Y1: nat] :
            ( ( ts @ Y0 @ Y1 )
            = ( ts @ Y1 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[satz29]) ).

thf(zip_derived_cl13,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ts ) ) @ ( '#C' @ ts ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl23,plain,
    ! [X2: nat] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( ts @ X2 ) ) @ ( '#C' @ ts @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl24,plain,
    ! [X2: nat,X4: nat] :
      ( ( ts @ X2 @ X4 )
      = ( ts @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl25,plain,
    ! [X2: nat,X4: nat] :
      ( ( ts @ X2 @ X4 )
      = ( ts @ X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl24]) ).

thf(satz40,axiom,
    ! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) ) ).

thf(zip_derived_cl8,plain,
    ( !!
    @ ^ [Y0: frac] :
        ( !!
        @ ^ [Y1: nat] : ( eq @ Y0 @ ( fr @ ( ts @ ( num @ Y0 ) @ Y1 ) @ ( ts @ ( den @ Y0 ) @ Y1 ) ) ) ) ),
    inference(cnf,[status(esa)],[satz40]) ).

thf(zip_derived_cl9,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#B' @ eq ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ fr ) @ ( '#B' @ ts @ num ) ) ) @ ( '#B' @ ts @ den ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl28,plain,
    ! [X2: frac] : ( !! @ ( '#B' @ ( eq @ X2 ) @ ( '#S' @ ( '#B' @ fr @ ( ts @ ( num @ X2 ) ) ) @ ( ts @ ( den @ X2 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl29,plain,
    ! [X2: frac,X4: nat] : ( eq @ X2 @ ( fr @ ( ts @ ( num @ X2 ) @ X4 ) @ ( ts @ ( den @ X2 ) @ X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl129,plain,
    ! [X0: frac,X1: nat] : ( eq @ X0 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ X1 @ ( den @ X0 ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl25,zip_derived_cl29]) ).

thf(zip_derived_cl565,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl561,zip_derived_cl34,zip_derived_cl1,zip_derived_cl129]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUM768^1 : TPTP v8.1.2. Released v3.7.0.
% 0.15/0.15  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HSVlgQQwXC true
% 0.15/0.37  % Computer : n012.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Fri Aug 25 08:39:26 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  % Running portfolio for 300 s
% 0.15/0.37  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37  % Number of cores: 8
% 0.15/0.37  % Python version: Python 3.6.8
% 0.15/0.37  % Running in HO mode
% 0.23/0.69  % Total configuration time : 828
% 0.23/0.69  % Estimated wc time : 1656
% 0.23/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.78  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.78  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.23/0.80  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.87/0.82  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.87/0.83  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.50/1.17  % Solved by lams/40_b.comb.sh.
% 1.50/1.17  % done 74 iterations in 0.349s
% 1.50/1.17  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.50/1.17  % SZS output start Refutation
% See solution above
% 1.50/1.17  
% 1.50/1.17  
% 1.50/1.18  % Terminating...
% 1.89/1.30  % Runner terminated.
% 1.89/1.31  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------