TSTP Solution File: SYO463^6 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SYO463^6 : 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.jZERrEVJIR true

% Computer : n015.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 05:51:28 EDT 2023

% Result   : Theorem 1.58s 0.87s
% Output   : Refutation 1.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   74 (  31 unt;  15 typ;   0 def)
%            Number of atoms       :  190 (  24 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  398 (  80   ~;  69   |;   4   &; 241   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   74 (  74   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   5 con; 0-3 aty)
%            Number of variables   :   95 (  45   ^;  50   !;   0   ?;  95   :)

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

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

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

thf(sk__9_type,type,
    sk__9: $i ).

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

thf(sk__10_type,type,
    sk__10: $i ).

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

thf(sk__11_type,type,
    sk__11: $i ).

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

thf(sk__8_type,type,
    sk__8: $i ).

thf(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

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

thf(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

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

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

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

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

thf(mequiv,axiom,
    ( mequiv
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).

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('4',plain,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ),
    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
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ) ).

thf('6',plain,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ),
    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
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    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(mand,axiom,
    ( mand
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).

thf('10',plain,
    ( mand
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand,'5','7']) ).

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

thf('12',plain,
    ( mequiv
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mequiv,'9','11','5','7']) ).

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

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

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ( ~ ! [X6: $i] :
            ( ~ ( ~ ( ~ ( p @ X6 )
                    | ( q @ X6 ) )
                | ~ ( ~ ( q @ X6 )
                    | ( p @ X6 ) ) )
            | ~ ( rel_s5 @ X4 @ X6 ) )
      | ! [X8: $i] :
          ( ~ ( ~ ( ~ ! [X10: $i] :
                        ( ( p @ X10 )
                        | ~ ( rel_s5 @ X8 @ X10 ) )
                  | ! [X12: $i] :
                      ( ( q @ X12 )
                      | ~ ( rel_s5 @ X8 @ X12 ) ) )
              | ~ ( ~ ! [X14: $i] :
                        ( ( q @ X14 )
                        | ~ ( rel_s5 @ X8 @ X14 ) )
                  | ! [X16: $i] :
                      ( ( p @ X16 )
                      | ~ ( rel_s5 @ X8 @ X16 ) ) ) )
          | ~ ( rel_s5 @ X4 @ X8 ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ( ~ ! [X6: $i] :
              ( ~ ( ~ ( ~ ( p @ X6 )
                      | ( q @ X6 ) )
                  | ~ ( ~ ( q @ X6 )
                      | ( p @ X6 ) ) )
              | ~ ( rel_s5 @ X4 @ X6 ) )
        | ! [X8: $i] :
            ( ~ ( ~ ( ~ ! [X10: $i] :
                          ( ( p @ X10 )
                          | ~ ( rel_s5 @ X8 @ X10 ) )
                    | ! [X12: $i] :
                        ( ( q @ X12 )
                        | ~ ( rel_s5 @ X8 @ X12 ) ) )
                | ~ ( ~ ! [X14: $i] :
                          ( ( q @ X14 )
                          | ~ ( rel_s5 @ X8 @ X14 ) )
                    | ! [X16: $i] :
                        ( ( p @ X16 )
                        | ~ ( rel_s5 @ X8 @ X16 ) ) ) )
            | ~ ( rel_s5 @ X4 @ X8 ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl12,plain,
    rel_s5 @ sk__8 @ sk__9,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

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

thf('14',plain,
    ( mtransitive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ T @ U ) )
         => ( R @ S @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mtransitive]) ).

thf('15',plain,
    ( mtransitive
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i,X8: $i] :
          ( ( ( V_1 @ X4 @ X6 )
            & ( V_1 @ X6 @ X8 ) )
         => ( V_1 @ X4 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(a2,axiom,
    mtransitive @ rel_s5 ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ( ( rel_s5 @ X4 @ X6 )
        & ( rel_s5 @ X6 @ X8 ) )
     => ( rel_s5 @ X4 @ X8 ) ) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s5 @ X0 @ X1 )
      | ~ ( rel_s5 @ X1 @ X2 )
      | ( rel_s5 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl24,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ sk__8 @ X0 )
      | ~ ( rel_s5 @ sk__9 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl1]) ).

thf(zip_derived_cl14,plain,
    ! [X2: $i] :
      ( ( p @ X2 )
      | ~ ( q @ X2 )
      | ~ ( rel_s5 @ sk__8 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl122,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ sk__9 @ X0 )
      | ~ ( q @ X0 )
      | ( p @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl14]) ).

thf(zip_derived_cl24_001,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ sk__8 @ X0 )
      | ~ ( rel_s5 @ sk__9 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl1]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i] :
      ( ( q @ X2 )
      | ~ ( p @ X2 )
      | ~ ( rel_s5 @ sk__8 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl123,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ sk__9 @ X0 )
      | ~ ( p @ X0 )
      | ( q @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl13]) ).

thf(zip_derived_cl10,plain,
    ( ~ ( q @ sk__10 )
    | ( rel_s5 @ sk__9 @ sk__11 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl194,plain,
    ( ~ ( p @ sk__10 )
    | ~ ( rel_s5 @ sk__9 @ sk__10 )
    | ( rel_s5 @ sk__9 @ sk__11 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl123,zip_derived_cl10]) ).

thf(zip_derived_cl4,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ sk__9 @ X0 )
      | ( p @ X0 )
      | ( rel_s5 @ sk__9 @ sk__11 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl477,plain,
    ( ( rel_s5 @ sk__9 @ sk__11 )
    | ~ ( rel_s5 @ sk__9 @ sk__10 ) ),
    inference(clc,[status(thm)],[zip_derived_cl194,zip_derived_cl4]) ).

thf(zip_derived_cl7,plain,
    ( ( rel_s5 @ sk__9 @ sk__10 )
    | ( rel_s5 @ sk__9 @ sk__11 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl478,plain,
    rel_s5 @ sk__9 @ sk__11,
    inference(clc,[status(thm)],[zip_derived_cl477,zip_derived_cl7]) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( rel_s5 @ sk__9 @ X0 )
      | ( p @ X0 )
      | ( q @ X1 )
      | ~ ( rel_s5 @ sk__9 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl480,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ sk__9 @ X0 )
      | ( q @ X0 )
      | ( p @ sk__11 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl478,zip_derived_cl3]) ).

thf(zip_derived_cl123_002,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ sk__9 @ X0 )
      | ~ ( p @ X0 )
      | ( q @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl13]) ).

thf(zip_derived_cl11,plain,
    ( ~ ( q @ sk__10 )
    | ~ ( p @ sk__11 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl193,plain,
    ( ~ ( p @ sk__10 )
    | ~ ( rel_s5 @ sk__9 @ sk__10 )
    | ~ ( p @ sk__11 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl123,zip_derived_cl11]) ).

thf(zip_derived_cl5,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ sk__9 @ X0 )
      | ( p @ X0 )
      | ~ ( p @ sk__11 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl227,plain,
    ( ~ ( p @ sk__11 )
    | ~ ( rel_s5 @ sk__9 @ sk__10 ) ),
    inference(clc,[status(thm)],[zip_derived_cl193,zip_derived_cl5]) ).

thf(zip_derived_cl8,plain,
    ( ( rel_s5 @ sk__9 @ sk__10 )
    | ~ ( p @ sk__11 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl228,plain,
    ~ ( p @ sk__11 ),
    inference(clc,[status(thm)],[zip_derived_cl227,zip_derived_cl8]) ).

thf(zip_derived_cl487,plain,
    ! [X0: $i] :
      ( ( q @ X0 )
      | ~ ( rel_s5 @ sk__9 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl480,zip_derived_cl228]) ).

thf(zip_derived_cl491,plain,
    ! [X0: $i] :
      ( ( p @ X0 )
      | ~ ( rel_s5 @ sk__9 @ X0 )
      | ~ ( rel_s5 @ sk__9 @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl122,zip_derived_cl487]) ).

thf(zip_derived_cl496,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ sk__9 @ X0 )
      | ( p @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl491]) ).

thf(zip_derived_cl228_003,plain,
    ~ ( p @ sk__11 ),
    inference(clc,[status(thm)],[zip_derived_cl227,zip_derived_cl8]) ).

thf(zip_derived_cl500,plain,
    ~ ( rel_s5 @ sk__9 @ sk__11 ),
    inference('sup-',[status(thm)],[zip_derived_cl496,zip_derived_cl228]) ).

thf(zip_derived_cl478_004,plain,
    rel_s5 @ sk__9 @ sk__11,
    inference(clc,[status(thm)],[zip_derived_cl477,zip_derived_cl7]) ).

thf(zip_derived_cl502,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl500,zip_derived_cl478]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYO463^6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jZERrEVJIR true
% 0.15/0.35  % Computer : n015.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sat Aug 26 05:25:37 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.15/0.35  % Running portfolio for 300 s
% 0.15/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.35  % Number of cores: 8
% 0.15/0.36  % Python version: Python 3.6.8
% 0.22/0.36  % Running in HO mode
% 0.22/0.68  % Total configuration time : 828
% 0.22/0.68  % Estimated wc time : 1656
% 0.22/0.68  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.78  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.78  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.79  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.79  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.79  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.98/0.79  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.98/0.82  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.98/0.85  % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 1.58/0.87  % Solved by lams/40_c.s.sh.
% 1.58/0.87  % done 213 iterations in 0.094s
% 1.58/0.87  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.58/0.87  % SZS output start Refutation
% See solution above
% 1.58/0.87  
% 1.58/0.87  
% 1.58/0.87  % Terminating...
% 2.02/0.97  % Runner terminated.
% 2.02/0.98  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------