TSTP Solution File: SYO457^6 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SYO457^6 : 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.Wy48hHkshn true

% Computer : n014.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 05:51:22 EDT 2023

% Result   : Theorem 0.23s 0.82s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   66 (  30 unt;  13 typ;   0 def)
%            Number of atoms       :  190 (  24 equ;  29 cnn)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  346 (  63   ~;  42   |;   0   &; 218   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   67 (  67   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  13 usr;   5 con; 0-3 aty)
%                                         (  16  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   93 (  55   ^;  38   !;   0   ?;  93   :)

% Comments : 
%------------------------------------------------------------------------------
thf(q_type,type,
    q: $i > $o ).

thf(rel_s5_type,type,
    rel_s5: $i > $i > $o ).

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

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

thf('#sk1_type',type,
    '#sk1': $i ).

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

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

thf(mdia_s5_type,type,
    mdia_s5: ( $i > $o ) > $i > $o ).

thf('#sk2_type',type,
    '#sk2': $i ).

thf(mbox_s5_type,type,
    mbox_s5: ( $i > $o ) > $i > $o ).

thf(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

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

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

thf(mdia_s5,axiom,
    ( mdia_s5
    = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) ) ) ).

thf(mbox_s5,axiom,
    ( mbox_s5
    = ( ^ [Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( rel_s5 @ W @ V ) ) ) ) ).

thf('0',plain,
    ( mbox_s5
    = ( ^ [Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( rel_s5 @ W @ V ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox_s5]) ).

thf('1',plain,
    ( mbox_s5
    = ( ^ [V_1: $i > $o,V_2: $i] :
        ! [X4: $i] :
          ( ( V_1 @ X4 )
          | ~ ( rel_s5 @ V_2 @ X4 ) ) ) ),
    define([status(thm)]) ).

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

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

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

thf('4',plain,
    ( mdia_s5
    = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mdia_s5,'1','3']) ).

thf('5',plain,
    ( mdia_s5
    = ( ^ [V_1: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

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

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

thf('7',plain,
    ( mvalid
    = ( ^ [V_1: $i > $o] :
        ! [X4: $i] : ( V_1 @ X4 ) ) ),
    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('8',plain,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mor]) ).

thf('9',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('10',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'9','3']) ).

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

thf(prove,conjecture,
    mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mdia_s5 @ ( mimplies @ q @ p ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ( ~ ! [X10: $i] :
            ( ~ ( rel_s5 @ X4 @ X10 )
            | ~ ( ( p @ X10 )
                | ~ ( q @ X10 ) ) )
      | ! [X6: $i] :
          ( ~ ( rel_s5 @ X4 @ X6 )
          | ~ ! [X8: $i] :
                ( ~ ( rel_s5 @ X6 @ X8 )
                | ( p @ X8 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ( ~ ! [X10: $i] :
              ( ~ ( rel_s5 @ X4 @ X10 )
              | ~ ( ( p @ X10 )
                  | ~ ( q @ X10 ) ) )
        | ! [X6: $i] :
            ( ~ ( rel_s5 @ X4 @ X6 )
            | ~ ! [X8: $i] :
                  ( ~ ( rel_s5 @ X6 @ X8 )
                  | ( p @ X8 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~)
                    @ ( ( p @ Y1 )
                      | ( (~) @ ( q @ Y1 ) ) ) ) ) ) )
          | ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y2: $i] :
                        ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                        | ( p @ Y2 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl25,plain,
    ~ ( ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~)
                @ ( ( p @ Y0 )
                  | ( (~) @ ( q @ Y0 ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( p @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl27,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( p @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl29,plain,
    ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
              | ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl31,plain,
    rel_s5 @ '#sk1' @ '#sk2',
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).

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

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

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

thf(a3,axiom,
    msymmetric @ rel_s5 ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: $i] :
      ( ( rel_s5 @ X4 @ X6 )
     => ( rel_s5 @ X6 @ X4 ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( rel_s5 @ Y0 @ Y1 )
           => ( rel_s5 @ Y1 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl5,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( rel_s5 @ X2 @ Y0 )
         => ( rel_s5 @ Y0 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl6,plain,
    ! [X2: $i,X4: $i] :
      ( ( rel_s5 @ X2 @ X4 )
     => ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl38,plain,
    rel_s5 @ '#sk2' @ '#sk1',
    inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl7]) ).

thf(zip_derived_cl32,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
        | ( p @ Y0 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl35,plain,
    ! [X2: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk2' @ X2 ) )
      | ( p @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl36,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk2' @ X2 )
      | ( p @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl26,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
        | ( (~)
          @ ( ( p @ Y0 )
            | ( (~) @ ( q @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl28,plain,
    ! [X2: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
      | ( (~)
        @ ( ( p @ X2 )
          | ( (~) @ ( q @ X2 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( ( p @ X2 )
          | ( (~) @ ( q @ X2 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl33,plain,
    ! [X2: $i] :
      ( ~ ( p @ X2 )
      | ~ ( rel_s5 @ '#sk1' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl45,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ '#sk2' @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl33]) ).

thf(zip_derived_cl49,plain,
    ~ ( rel_s5 @ '#sk1' @ '#sk1' ),
    inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl45]) ).

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

thf('14',plain,
    ( mreflexive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] : ( R @ S @ S ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).

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

thf(a1,axiom,
    mreflexive @ rel_s5 ).

thf(zf_stmt_3,axiom,
    ! [X4: $i] : ( rel_s5 @ X4 @ X4 ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl4,plain,
    ! [X2: $i] : ( rel_s5 @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl53,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl49,zip_derived_cl4]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem  : SYO457^6 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Wy48hHkshn true
% 0.14/0.36  % Computer : n014.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 : Sat Aug 26 04:12:47 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
% 0.14/0.36  % Number of cores: 8
% 0.22/0.37  % Python version: Python 3.6.8
% 0.22/0.37  % 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
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.23/0.78  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.23/0.78  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.23/0.80  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.23/0.82  % Solved by lams/35_full_unif4.sh.
% 0.23/0.82  % done 13 iterations in 0.025s
% 0.23/0.82  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.23/0.82  % SZS output start Refutation
% See solution above
% 0.23/0.82  
% 0.23/0.82  
% 0.23/0.82  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.23/0.82  % Terminating...
% 1.55/0.88  % Runner terminated.
% 1.95/0.89  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------