TSTP Solution File: SYN390^4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SYN390^4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.U3PyYnbQ6M true

% Computer : n022.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 : Fri Sep  1 04:03:11 EDT 2023

% Result   : Theorem 1.44s 0.80s
% Output   : Refutation 1.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   47 (  31 unt;  12 typ;   0 def)
%            Number of atoms       :  128 (  30 equ;   2 cnn)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  166 (  11   ~;   9   |;   6   &; 120   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   92 (  92   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  12 usr;   3 con; 0-3 aty)
%                                         (   5  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   81 (  65   ^;  16   !;   0   ?;  81   :)

% Comments : 
%------------------------------------------------------------------------------
thf(iatom_type,type,
    iatom: ( $i > $o ) > $i > $o ).

thf(ivalid_type,type,
    ivalid: ( $i > $o ) > $o ).

thf(irel_type,type,
    irel: $i > $i > $o ).

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

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

thf(mbox_s4_type,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

thf(iimplies_type,type,
    iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(p_type,type,
    p: $i > $o ).

thf(iand_type,type,
    iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

thf(iequiv_type,type,
    iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mand_type,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

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

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

thf(iequiv,axiom,
    ( iequiv
    = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).

thf(iimplies,axiom,
    ( iimplies
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).

thf(mbox_s4,axiom,
    ( mbox_s4
    = ( ^ [P: $i > $o,X: $i] :
        ! [Y: $i] :
          ( ( irel @ X @ Y )
         => ( P @ Y ) ) ) ) ).

thf('2',plain,
    ( mbox_s4
    = ( ^ [P: $i > $o,X: $i] :
        ! [Y: $i] :
          ( ( irel @ X @ Y )
         => ( P @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).

thf('3',plain,
    ( mbox_s4
    = ( ^ [V_1: $i > $o,V_2: $i] :
        ! [X4: $i] :
          ( ( irel @ V_2 @ X4 )
         => ( V_1 @ X4 ) ) ) ),
    define([status(thm)]) ).

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

thf(mor,axiom,
    ( mor
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ) ).

thf('4',plain,
    ( mor
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mor]) ).

thf('5',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
    = ( ^ [X: $i > $o,U: $i] :
          ~ ( X @ U ) ) ) ).

thf('6',plain,
    ( mnot
    = ( ^ [X: $i > $o,U: $i] :
          ~ ( X @ U ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mnot]) ).

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

thf('8',plain,
    ( mimplies
    = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'5','7']) ).

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

thf('10',plain,
    ( iimplies
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[iimplies,'3','9']) ).

thf('11',plain,
    ( iimplies
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mimplies @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(iand,axiom,
    ( iand
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).

thf(mand,axiom,
    ( mand
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ( Y @ U ) ) ) ) ).

thf('12',plain,
    ( mand
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand]) ).

thf('13',plain,
    ( mand
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          & ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf('14',plain,
    ( iand
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
    inference(simplify_rw_rule,[status(thm)],[iand,'13']) ).

thf('15',plain,
    ( iand
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf('16',plain,
    ( iequiv
    = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[iequiv,'11','15','3','9','13','5','7']) ).

thf('17',plain,
    ( iequiv
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( iand @ ( iimplies @ V_1 @ V_2 ) @ ( iimplies @ V_2 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf(iatom,axiom,
    ( iatom
    = ( ^ [P: $i > $o] : P ) ) ).

thf('18',plain,
    ( iatom
    = ( ^ [P: $i > $o] : P ) ),
    inference(simplify_rw_rule,[status(thm)],[iatom]) ).

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

thf(pel11,conjecture,
    ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ p ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ( ( ! [X12: $i] :
            ( ( irel @ X4 @ X12 )
           => ( p @ X12 ) )
        | ~ ! [X10: $i] :
              ( ( irel @ X4 @ X10 )
             => ( p @ X10 ) ) )
      & ( ! [X8: $i] :
            ( ( irel @ X4 @ X8 )
           => ( p @ X8 ) )
        | ~ ! [X6: $i] :
              ( ( irel @ X4 @ X6 )
             => ( p @ X6 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ( ( ! [X12: $i] :
              ( ( irel @ X4 @ X12 )
             => ( p @ X12 ) )
          | ~ ! [X10: $i] :
                ( ( irel @ X4 @ X10 )
               => ( p @ X10 ) ) )
        & ( ! [X8: $i] :
              ( ( irel @ X4 @ X8 )
             => ( p @ X8 ) )
          | ~ ! [X6: $i] :
                ( ( irel @ X4 @ X6 )
               => ( p @ X6 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( p @ Y1 ) ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( p @ Y1 ) ) ) ) )
          & ( ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( p @ Y1 ) ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( p @ Y1 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl17,plain,
    $false,
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl2]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN390^4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.U3PyYnbQ6M true
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 21:45:25 EDT 2023
% 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
% 0.13/0.35  % 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
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.11/0.76  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.11/0.76  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.44/0.78  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.44/0.78  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.44/0.78  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.44/0.78  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.44/0.78  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.44/0.80  % Solved by lams/35_full_unif4.sh.
% 1.44/0.80  % done 2 iterations in 0.015s
% 1.44/0.80  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.44/0.80  % SZS output start Refutation
% See solution above
% 1.44/0.80  
% 1.44/0.80  
% 1.44/0.80  % Terminating...
% 1.87/0.85  % Runner terminated.
% 1.87/0.86  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------