TSTP Solution File: NUM769^4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM769^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HQ3KaDkAEQ true

% Computer : n004.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 151.70s 20.26s
% Output   : Refutation 151.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   76 (  45 unt;  25 typ;   0 def)
%            Number of atoms       :  164 (  52 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  360 (  12   ~;   4   |;   0   &; 324   @)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   60 (  60   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  25 usr;   6 con; 0-3 aty)
%            Number of variables   :   98 (  83   ^;  15   !;   0   ?;  98   :)

% Comments : 
%------------------------------------------------------------------------------
thf(d_29_ii_type,type,
    d_29_ii: $i > $i > $o ).

thf(nat_type,type,
    nat: $i ).

thf(d_367_w_type,type,
    d_367_w: $i > $i > $i ).

thf(is_of_type,type,
    is_of: $i > ( $i > $o ) > $o ).

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

thf(non_type,type,
    non: $i > ( $i > $o ) > $i > $o ).

thf(l_some_type,type,
    l_some: $i > ( $i > $o ) > $o ).

thf(sk__192_type,type,
    sk__192: $i ).

thf(n_pf_type,type,
    n_pf: $i > $i > $i ).

thf(sk__193_type,type,
    sk__193: $i ).

thf(sk__194_type,type,
    sk__194: $i ).

thf(n_is_type,type,
    n_is: $i > $i > $o ).

thf(imp_type,type,
    imp: $o > $o > $o ).

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

thf(n_ts_type,type,
    n_ts: $i > $i > $i ).

thf(n_eq_type,type,
    n_eq: $i > $i > $o ).

thf(all_of_type,type,
    all_of: ( $i > $o ) > ( $i > $o ) > $o ).

thf(diffprop_type,type,
    diffprop: $i > $i > $i > $o ).

thf(num_type,type,
    num: $i > $i ).

thf(n_some_type,type,
    n_some: ( $i > $o ) > $o ).

thf(moref_type,type,
    moref: $i > $i > $o ).

thf(d_not_type,type,
    d_not: $o > $o ).

thf(den_type,type,
    den: $i > $i ).

thf(e_is_type,type,
    e_is: $i > $i > $i > $o ).

thf(n_pl_type,type,
    n_pl: $i > $i > $i ).

thf(def_moref,axiom,
    ( moref
    = ( ^ [X0: $i,X1: $i] : ( d_29_ii @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ) ).

thf(def_d_29_ii,axiom,
    ( d_29_ii
    = ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ) ).

thf(def_diffprop,axiom,
    ( diffprop
    = ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ).

thf(def_n_is,axiom,
    ( n_is
    = ( e_is @ nat ) ) ).

thf(def_e_is,axiom,
    ( e_is
    = ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).

thf('0',plain,
    ( e_is
    = ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).

thf('1',plain,
    ( e_is
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
    define([status(thm)]) ).

thf('2',plain,
    ( n_is
    = ( e_is @ nat ) ),
    inference(simplify_rw_rule,[status(thm)],[def_n_is,'1']) ).

thf('3',plain,
    ( n_is
    = ( e_is @ nat ) ),
    define([status(thm)]) ).

thf('4',plain,
    ( diffprop
    = ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_diffprop,'3','1']) ).

thf('5',plain,
    ( diffprop
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( n_is @ V_1 @ ( n_pl @ V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(def_n_some,axiom,
    ( n_some
    = ( l_some @ nat ) ) ).

thf(def_l_some,axiom,
    ( l_some
    = ( ^ [X0: $i,X1: $i > $o] :
          ( d_not
          @ ( all_of
            @ ^ [X2: $i] : ( in @ X2 @ X0 )
            @ ( non @ X0 @ X1 ) ) ) ) ) ).

thf(def_non,axiom,
    ( non
    = ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ) ).

thf(def_d_not,axiom,
    ( d_not
    = ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).

thf(def_imp,axiom,
    ( imp
    = ( ^ [X0: $o,X1: $o] :
          ( X0
         => X1 ) ) ) ).

thf('6',plain,
    ( imp
    = ( ^ [X0: $o,X1: $o] :
          ( X0
         => X1 ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_imp]) ).

thf('7',plain,
    ( imp
    = ( ^ [V_1: $o,V_2: $o] :
          ( V_1
         => V_2 ) ) ),
    define([status(thm)]) ).

thf('8',plain,
    ( d_not
    = ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_d_not,'7']) ).

thf('9',plain,
    ( d_not
    = ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
    define([status(thm)]) ).

thf('10',plain,
    ( non
    = ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_non,'9','7']) ).

thf('11',plain,
    ( non
    = ( ^ [V_1: $i,V_2: $i > $o,V_3: $i] : ( d_not @ ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(def_all_of,axiom,
    ( all_of
    = ( ^ [X0: $i > $o,X1: $i > $o] :
        ! [X2: $i] :
          ( ( is_of @ X2 @ X0 )
         => ( X1 @ X2 ) ) ) ) ).

thf(def_is_of,axiom,
    ( is_of
    = ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ) ).

thf('12',plain,
    ( is_of
    = ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).

thf('13',plain,
    ( is_of
    = ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
    define([status(thm)]) ).

thf('14',plain,
    ( all_of
    = ( ^ [X0: $i > $o,X1: $i > $o] :
        ! [X2: $i] :
          ( ( is_of @ X2 @ X0 )
         => ( X1 @ X2 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_all_of,'13']) ).

thf('15',plain,
    ( all_of
    = ( ^ [V_1: $i > $o,V_2: $i > $o] :
        ! [X4: $i] :
          ( ( is_of @ X4 @ V_1 )
         => ( V_2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf('16',plain,
    ( l_some
    = ( ^ [X0: $i,X1: $i > $o] :
          ( d_not
          @ ( all_of
            @ ^ [X2: $i] : ( in @ X2 @ X0 )
            @ ( non @ X0 @ X1 ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_l_some,'11','9','7','15','13']) ).

thf('17',plain,
    ( l_some
    = ( ^ [V_1: $i,V_2: $i > $o] :
          ( d_not
          @ ( all_of
            @ ^ [V_3: $i] : ( in @ V_3 @ V_1 )
            @ ( non @ V_1 @ V_2 ) ) ) ) ),
    define([status(thm)]) ).

thf('18',plain,
    ( n_some
    = ( l_some @ nat ) ),
    inference(simplify_rw_rule,[status(thm)],[def_n_some,'17','11','9','7','15','13']) ).

thf('19',plain,
    ( n_some
    = ( l_some @ nat ) ),
    define([status(thm)]) ).

thf('20',plain,
    ( d_29_ii
    = ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_d_29_ii,'5','19','3','1','17','11','9','7','15','13']) ).

thf('21',plain,
    ( d_29_ii
    = ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf('22',plain,
    ( moref
    = ( ^ [X0: $i,X1: $i] : ( d_29_ii @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_moref,'21','5','19','3','1','17','11','9','7','15','13']) ).

thf('23',plain,
    ( moref
    = ( ^ [V_1: $i,V_2: $i] : ( d_29_ii @ ( n_ts @ ( num @ V_1 ) @ ( den @ V_2 ) ) @ ( n_ts @ ( num @ V_2 ) @ ( den @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

thf(def_n_eq,axiom,
    ( n_eq
    = ( ^ [X0: $i,X1: $i] : ( n_is @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ) ).

thf('24',plain,
    ( n_eq
    = ( ^ [X0: $i,X1: $i] : ( n_is @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_n_eq,'3','1']) ).

thf('25',plain,
    ( n_eq
    = ( ^ [V_1: $i,V_2: $i] : ( n_is @ ( n_ts @ ( num @ V_1 ) @ ( den @ V_2 ) ) @ ( n_ts @ ( num @ V_2 ) @ ( den @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

thf(satz67d,conjecture,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ frac )
    @ ^ [X0: $i] :
        ( all_of
        @ ^ [X1: $i] : ( in @ X1 @ frac )
        @ ^ [X1: $i] :
            ( ( moref @ X0 @ X1 )
           => ( n_eq @ X0 @ ( n_pf @ X1 @ ( d_367_w @ X0 @ X1 ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ( ( in @ X4 @ frac )
     => ! [X6: $i] :
          ( ( in @ X6 @ frac )
         => ( ~ ! [X8: $i] :
                  ( ( in @ X8 @ nat )
                 => ( ( n_ts @ ( num @ X4 ) @ ( den @ X6 ) )
                   != ( n_pl @ ( n_ts @ ( num @ X6 ) @ ( den @ X4 ) ) @ X8 ) ) )
           => ( ( n_ts @ ( num @ X4 ) @ ( den @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) )
              = ( n_ts @ ( num @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) @ ( den @ X4 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ( ( in @ X4 @ frac )
       => ! [X6: $i] :
            ( ( in @ X6 @ frac )
           => ( ~ ! [X8: $i] :
                    ( ( in @ X8 @ nat )
                   => ( ( n_ts @ ( num @ X4 ) @ ( den @ X6 ) )
                     != ( n_pl @ ( n_ts @ ( num @ X6 ) @ ( den @ X4 ) ) @ X8 ) ) )
             => ( ( n_ts @ ( num @ X4 ) @ ( den @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) )
                = ( n_ts @ ( num @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) @ ( den @ X4 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl759,plain,
    ( ( n_ts @ ( num @ sk__192 ) @ ( den @ ( n_pf @ sk__193 @ ( d_367_w @ sk__192 @ sk__193 ) ) ) )
   != ( n_ts @ ( num @ ( n_pf @ sk__193 @ ( d_367_w @ sk__192 @ sk__193 ) ) ) @ ( den @ sk__192 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl760,plain,
    in @ sk__193 @ frac,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl756,plain,
    in @ sk__192 @ frac,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl757,plain,
    in @ sk__194 @ nat,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl758,plain,
    ( ( n_ts @ ( num @ sk__192 ) @ ( den @ sk__193 ) )
    = ( n_pl @ ( n_ts @ ( num @ sk__193 ) @ ( den @ sk__192 ) ) @ sk__194 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(k_satz67c,axiom,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ frac )
    @ ^ [X0: $i] :
        ( all_of
        @ ^ [X1: $i] : ( in @ X1 @ frac )
        @ ^ [X1: $i] :
            ( ( moref @ X0 @ X1 )
           => ( n_eq @ ( n_pf @ X1 @ ( d_367_w @ X0 @ X1 ) ) @ X0 ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i] :
      ( ( in @ X4 @ frac )
     => ! [X6: $i] :
          ( ( in @ X6 @ frac )
         => ( ~ ! [X8: $i] :
                  ( ( in @ X8 @ nat )
                 => ( ( n_ts @ ( num @ X4 ) @ ( den @ X6 ) )
                   != ( n_pl @ ( n_ts @ ( num @ X6 ) @ ( den @ X4 ) ) @ X8 ) ) )
           => ( ( n_ts @ ( num @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) @ ( den @ X4 ) )
              = ( n_ts @ ( num @ X4 ) @ ( den @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) ) ) ) ) ) ).

thf(zip_derived_cl755,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ frac )
      | ( ( n_ts @ ( num @ ( n_pf @ X0 @ ( d_367_w @ X1 @ X0 ) ) ) @ ( den @ X1 ) )
        = ( n_ts @ ( num @ X1 ) @ ( den @ ( n_pf @ X0 @ ( d_367_w @ X1 @ X0 ) ) ) ) )
      | ( ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) )
       != ( n_pl @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ X2 ) )
      | ~ ( in @ X2 @ nat )
      | ~ ( in @ X1 @ frac ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl26502,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl759,zip_derived_cl760,zip_derived_cl756,zip_derived_cl757,zip_derived_cl758,zip_derived_cl755]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM769^4 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HQ3KaDkAEQ true
% 0.14/0.35  % Computer : n004.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 08:19:38 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
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.22/0.69  % Total configuration time : 828
% 0.22/0.69  % Estimated wc time : 1656
% 0.22/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.79  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.51/0.80  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.51/0.80  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.51/0.80  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.51/0.80  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.51/0.80  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 151.70/20.26  % Solved by lams/40_noforms.sh.
% 151.70/20.26  % done 1407 iterations in 19.433s
% 151.70/20.26  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 151.70/20.26  % SZS output start Refutation
% See solution above
% 151.70/20.26  
% 151.70/20.26  
% 151.70/20.26  % Terminating...
% 152.09/20.33  % Runner terminated.
% 152.09/20.35  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------