TSTP Solution File: NUM801^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM801^1 : 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.Xf9BfrwY5x true

% Computer : n010.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 12:44:17 EDT 2023

% Result   : Theorem 1.35s 0.82s
% Output   : Refutation 1.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   25 (  18 unt;   4 typ;   0 def)
%            Number of atoms       :   26 (  20 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  155 (   6   ~;   0   |;   0   &; 144   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :  138 ( 138   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   2 con; 0-4 aty)
%                                         (   0  !!;   5  ??;   0 @@+;   0 @@-)
%            Number of variables   :   83 (  72   ^;   5   !;   6   ?;  83   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mult_type,type,
    mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(four_type,type,
    four: ( $i > $i ) > $i > $i ).

thf(five_type,type,
    five: ( $i > $i ) > $i > $i ).

thf(plus_type,type,
    plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(mult_ax,axiom,
    ( mult
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ ( N @ X ) @ Y ) ) ) ).

thf('0',plain,
    ( mult
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ ( N @ X ) @ Y ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mult_ax]) ).

thf('1',plain,
    ( mult
    = ( ^ [V_1: ( $i > $i ) > $i > $i,V_2: ( $i > $i ) > $i > $i,V_3: $i > $i,V_4: $i] : ( V_1 @ ( V_2 @ V_3 ) @ V_4 ) ) ),
    define([status(thm)]) ).

thf(plus_ax,axiom,
    ( plus
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ X @ ( N @ X @ Y ) ) ) ) ).

thf('2',plain,
    ( plus
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ X @ ( N @ X @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[plus_ax]) ).

thf('3',plain,
    ( plus
    = ( ^ [V_1: ( $i > $i ) > $i > $i,V_2: ( $i > $i ) > $i > $i,V_3: $i > $i,V_4: $i] : ( V_1 @ V_3 @ ( V_2 @ V_3 @ V_4 ) ) ) ),
    define([status(thm)]) ).

thf(five_ax,axiom,
    ( five
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ).

thf('4',plain,
    ( five
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[five_ax]) ).

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

thf(four_ax,axiom,
    ( four
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ).

thf('6',plain,
    ( four
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[four_ax]) ).

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

thf(thm,conjecture,
    ? [N: ( $i > $i ) > $i > $i,M: ( $i > $i ) > $i > $i] :
      ( ( mult @ N @ four )
      = ( plus @ five @ M ) ) ).

thf(zf_stmt_0,conjecture,
    ? [X4: ( $i > $i ) > $i > $i,X6: ( $i > $i ) > $i > $i] :
      ( ( ^ [V_1: $i > $i,V_2: $i] :
            ( X4
            @ ^ [V_3: $i] : ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ V_3 ) ) ) )
            @ V_2 ) )
      = ( ^ [V_4: $i > $i,V_5: $i] : ( V_4 @ ( V_4 @ ( V_4 @ ( V_4 @ ( V_4 @ ( X6 @ V_4 @ V_5 ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ? [X4: ( $i > $i ) > $i > $i,X6: ( $i > $i ) > $i > $i] :
        ( ( ^ [V_1: $i > $i,V_2: $i] :
              ( X4
              @ ^ [V_3: $i] : ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ V_3 ) ) ) )
              @ V_2 ) )
        = ( ^ [V_4: $i > $i,V_5: $i] : ( V_4 @ ( V_4 @ ( V_4 @ ( V_4 @ ( V_4 @ ( X6 @ V_4 @ V_5 ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ~ ( ??
      @ ^ [Y0: ( $i > $i ) > $i > $i] :
          ( ??
          @ ^ [Y1: ( $i > $i ) > $i > $i] :
              ( ( ^ [Y2: $i > $i,Y3: $i] :
                    ( Y0
                    @ ^ [Y4: $i] : ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ Y4 ) ) ) )
                    @ Y3 ) )
              = ( ^ [Y2: $i > $i,Y3: $i] : ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ~ ( ??
      @ ^ [Y0: ( $i > $i ) > $i > $i] :
          ( ??
          @ ^ [Y1: ( $i > $i ) > $i > $i] :
              ( ( ^ [Y2: $i > $i] :
                    ( Y0
                    @ ^ [Y3: $i] : ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ Y3 ) ) ) ) ) )
              = ( ^ [Y2: $i > $i,Y3: $i] : ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y2 @ ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ! [X2: ( $i > $i ) > $i > $i] :
      ~ ( ??
        @ ^ [Y0: ( $i > $i ) > $i > $i] :
            ( ( ^ [Y1: $i > $i] :
                  ( X2
                  @ ^ [Y2: $i] : ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ Y2 ) ) ) ) ) )
            = ( ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y1 @ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ! [X2: ( $i > $i ) > $i > $i,X4: ( $i > $i ) > $i > $i] :
      ( ( ^ [Y0: $i > $i] :
            ( X2
            @ ^ [Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
     != ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( X4 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ! [X2: ( $i > $i ) > $i > $i,X4: ( $i > $i ) > $i > $i] :
      ( ( ^ [Y0: $i > $i] :
            ( X2
            @ ^ [Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
     != ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( X4 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl7,plain,
    $false,
    inference(eq_res,[status(thm)],[zip_derived_cl4]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM801^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Xf9BfrwY5x true
% 0.14/0.36  % Computer : n010.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri Aug 25 16:20:50 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  % Running portfolio for 300 s
% 0.14/0.36  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37  % Number of cores: 8
% 0.14/0.37  % Python version: Python 3.6.8
% 0.14/0.37  % Running in HO mode
% 0.21/0.66  % Total configuration time : 828
% 0.21/0.66  % Estimated wc time : 1656
% 0.21/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.70  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.79  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.35/0.82  % Solved by lams/30_sp5.sh.
% 1.35/0.82  % done 0 iterations in 0.018s
% 1.35/0.82  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.35/0.82  % SZS output start Refutation
% See solution above
% 1.35/0.82  
% 1.35/0.82  
% 1.35/0.83  % Terminating...
% 1.66/0.88  % Runner terminated.
% 1.66/0.89  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------