TSTP Solution File: SYN367^7 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SYN367^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.RsrS0wWNDg true

% Computer : n024.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 04:03:02 EDT 2023

% Result   : Theorem 6.72s 1.46s
% Output   : Refutation 6.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   50
% Syntax   : Number of formulae    :  148 (  64 unt;  24 typ;   0 def)
%            Number of atoms       :  366 (  27 equ;   0 cnn)
%            Maximal formula atoms :   27 (   2 avg)
%            Number of connectives :  982 ( 161   ~; 159   |;   5   &; 643   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   89 (  89   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  23 usr;   8 con; 0-3 aty)
%            Number of variables   :  213 (  51   ^; 161   !;   1   ?; 213   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

thf(sk__14_type,type,
    sk__14: $i ).

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

thf(sk__12_type,type,
    sk__12: mu ).

thf(rel_s4_type,type,
    rel_s4: $i > $i > $o ).

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

thf(mforall_ind_type,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

thf(sk__16_type,type,
    sk__16: $i ).

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

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

thf(sk__13_type,type,
    sk__13: $i ).

thf(sk__type,type,
    sk_: $i > mu ).

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

thf(sk__15_type,type,
    sk__15: mu ).

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

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

thf(big_q_type,type,
    big_q: mu > $i > $o ).

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

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

thf(exists_in_world_type,type,
    exists_in_world: mu > $i > $o ).

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

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

thf(big_r_type,type,
    big_r: mu > $i > $o ).

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

thf(mbox_s4,axiom,
    ( mbox_s4
    = ( ^ [Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( rel_s4 @ W @ V ) ) ) ) ).

thf('0',plain,
    ( mbox_s4
    = ( ^ [Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( rel_s4 @ W @ V ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).

thf('1',plain,
    ( mbox_s4
    = ( ^ [V_1: $i > $o,V_2: $i] :
        ! [X4: $i] :
          ( ( V_1 @ X4 )
          | ~ ( rel_s4 @ 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(mforall_ind,axiom,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] :
          ( ( exists_in_world @ X @ W )
         => ( Phi @ X @ W ) ) ) ) ).

thf('4',plain,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] :
          ( ( exists_in_world @ X @ W )
         => ( Phi @ X @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).

thf('5',plain,
    ( mforall_ind
    = ( ^ [V_1: mu > $i > $o,V_2: $i] :
        ! [X4: mu] :
          ( ( exists_in_world @ X4 @ V_2 )
         => ( V_1 @ X4 @ V_2 ) ) ) ),
    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('6',plain,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mor]) ).

thf('7',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('8',plain,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mnot]) ).

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

thf('10',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'7','9']) ).

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

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

thf(x2118,conjecture,
    ( mvalid
    @ ( mbox_s4
      @ ( mimplies
        @ ( mbox_s4
          @ ( mforall_ind
            @ ^ [X: mu] : ( mor @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_q @ X ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ p ) ) ) @ ( mbox_s4 @ ( big_r @ X ) ) ) ) ) )
        @ ( mor
          @ ( mbox_s4
            @ ( mforall_ind
              @ ^ [X: mu] : ( mbox_s4 @ ( big_q @ X ) ) ) )
          @ ( mbox_s4
            @ ( mforall_ind
              @ ^ [X: mu] : ( mbox_s4 @ ( big_r @ X ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i,X6: $i] :
      ( ~ ! [X8: $i] :
            ( ! [X10: mu] :
                ( ( exists_in_world @ X10 @ X8 )
               => ( ~ ( ~ ! [X12: $i] :
                            ( ( p @ X12 )
                            | ~ ( rel_s4 @ X8 @ X12 ) )
                      | ~ ! [X14: $i] :
                            ( ( big_q @ X10 @ X14 )
                            | ~ ( rel_s4 @ X8 @ X14 ) ) )
                  | ~ ( ~ ! [X16: $i] :
                            ( ~ ! [X18: $i] :
                                  ( ( p @ X18 )
                                  | ~ ( rel_s4 @ X16 @ X18 ) )
                            | ~ ( rel_s4 @ X8 @ X16 ) )
                      | ~ ! [X20: $i] :
                            ( ( big_r @ X10 @ X20 )
                            | ~ ( rel_s4 @ X8 @ X20 ) ) ) ) )
            | ~ ( rel_s4 @ X6 @ X8 ) )
      | ! [X22: $i] :
          ( ! [X24: mu] :
              ( ( exists_in_world @ X24 @ X22 )
             => ! [X26: $i] :
                  ( ( big_q @ X24 @ X26 )
                  | ~ ( rel_s4 @ X22 @ X26 ) ) )
          | ~ ( rel_s4 @ X6 @ X22 ) )
      | ! [X28: $i] :
          ( ! [X30: mu] :
              ( ( exists_in_world @ X30 @ X28 )
             => ! [X32: $i] :
                  ( ( big_r @ X30 @ X32 )
                  | ~ ( rel_s4 @ X28 @ X32 ) ) )
          | ~ ( rel_s4 @ X6 @ X28 ) )
      | ~ ( rel_s4 @ X4 @ X6 ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i,X6: $i] :
        ( ~ ! [X8: $i] :
              ( ! [X10: mu] :
                  ( ( exists_in_world @ X10 @ X8 )
                 => ( ~ ( ~ ! [X12: $i] :
                              ( ( p @ X12 )
                              | ~ ( rel_s4 @ X8 @ X12 ) )
                        | ~ ! [X14: $i] :
                              ( ( big_q @ X10 @ X14 )
                              | ~ ( rel_s4 @ X8 @ X14 ) ) )
                    | ~ ( ~ ! [X16: $i] :
                              ( ~ ! [X18: $i] :
                                    ( ( p @ X18 )
                                    | ~ ( rel_s4 @ X16 @ X18 ) )
                              | ~ ( rel_s4 @ X8 @ X16 ) )
                        | ~ ! [X20: $i] :
                              ( ( big_r @ X10 @ X20 )
                              | ~ ( rel_s4 @ X8 @ X20 ) ) ) ) )
              | ~ ( rel_s4 @ X6 @ X8 ) )
        | ! [X22: $i] :
            ( ! [X24: mu] :
                ( ( exists_in_world @ X24 @ X22 )
               => ! [X26: $i] :
                    ( ( big_q @ X24 @ X26 )
                    | ~ ( rel_s4 @ X22 @ X26 ) ) )
            | ~ ( rel_s4 @ X6 @ X22 ) )
        | ! [X28: $i] :
            ( ! [X30: mu] :
                ( ( exists_in_world @ X30 @ X28 )
               => ! [X32: $i] :
                    ( ( big_r @ X30 @ X32 )
                    | ~ ( rel_s4 @ X28 @ X32 ) ) )
            | ~ ( rel_s4 @ X6 @ X28 ) )
        | ~ ( rel_s4 @ X4 @ X6 ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl8,plain,
    rel_s4 @ sk__9 @ sk__14,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl11,plain,
    rel_s4 @ sk__11 @ sk__13,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl9,plain,
    exists_in_world @ sk__12 @ sk__11,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(cumulative_ax,axiom,
    ! [X: mu,V: $i,W: $i] :
      ( ( ( exists_in_world @ X @ V )
        & ( rel_s4 @ V @ W ) )
     => ( exists_in_world @ X @ W ) ) ).

thf(zip_derived_cl3,plain,
    ! [X0: mu,X1: $i,X2: $i] :
      ( ~ ( exists_in_world @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X2 )
      | ( exists_in_world @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[cumulative_ax]) ).

thf(zip_derived_cl38,plain,
    ! [X0: $i] :
      ( ( exists_in_world @ sk__12 @ X0 )
      | ~ ( rel_s4 @ sk__11 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl3]) ).

thf(zip_derived_cl13,plain,
    ! [X0: mu,X1: $i,X2: $i,X3: $i] :
      ( ~ ( exists_in_world @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X2 )
      | ( big_q @ X0 @ X2 )
      | ~ ( rel_s4 @ X1 @ X3 )
      | ( rel_s4 @ X3 @ ( sk__10 @ X3 ) )
      | ~ ( rel_s4 @ sk__9 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl71,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ sk__11 @ X0 )
      | ~ ( rel_s4 @ sk__9 @ X0 )
      | ( rel_s4 @ X1 @ ( sk__10 @ X1 ) )
      | ~ ( rel_s4 @ X0 @ X1 )
      | ( big_q @ sk__12 @ X2 )
      | ~ ( rel_s4 @ X0 @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl13]) ).

thf(zip_derived_cl12,plain,
    rel_s4 @ sk__9 @ sk__11,
    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_s4 ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ( ( rel_s4 @ X4 @ X6 )
        & ( rel_s4 @ X6 @ X8 ) )
     => ( rel_s4 @ X4 @ X8 ) ) ).

thf(zip_derived_cl2,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X2 )
      | ( rel_s4 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl22,plain,
    ! [X0: $i] :
      ( ( rel_s4 @ sk__9 @ X0 )
      | ~ ( rel_s4 @ sk__11 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl2]) ).

thf(zip_derived_cl439,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ X0 @ X2 )
      | ( big_q @ sk__12 @ X2 )
      | ~ ( rel_s4 @ X0 @ X1 )
      | ( rel_s4 @ X1 @ ( sk__10 @ X1 ) )
      | ~ ( rel_s4 @ sk__11 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl71,zip_derived_cl22]) ).

thf(zip_derived_cl441,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__11 @ sk__11 )
      | ( rel_s4 @ X0 @ ( sk__10 @ X0 ) )
      | ~ ( rel_s4 @ sk__11 @ X0 )
      | ( big_q @ sk__12 @ sk__13 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl439]) ).

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

thf('16',plain,
    ( mreflexive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] : ( R @ S @ S ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).

thf('17',plain,
    ( mreflexive
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i] : ( V_1 @ X4 @ X4 ) ) ),
    define([status(thm)]) ).

thf(a1,axiom,
    mreflexive @ rel_s4 ).

thf(zf_stmt_3,axiom,
    ! [X4: $i] : ( rel_s4 @ X4 @ X4 ) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i] : ( rel_s4 @ X0 @ X0 ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl470,plain,
    ! [X0: $i] :
      ( ( rel_s4 @ X0 @ ( sk__10 @ X0 ) )
      | ~ ( rel_s4 @ sk__11 @ X0 )
      | ( big_q @ sk__12 @ sk__13 ) ),
    inference(demod,[status(thm)],[zip_derived_cl441,zip_derived_cl1]) ).

thf(zip_derived_cl10,plain,
    ~ ( big_q @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl531,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__11 @ X0 )
      | ( rel_s4 @ X0 @ ( sk__10 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl470,zip_derived_cl10]) ).

thf(zip_derived_cl22_001,plain,
    ! [X0: $i] :
      ( ( rel_s4 @ sk__9 @ X0 )
      | ~ ( rel_s4 @ sk__11 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl2]) ).

thf(zip_derived_cl11_002,plain,
    rel_s4 @ sk__11 @ sk__13,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl84,plain,
    rel_s4 @ sk__9 @ sk__13,
    inference('sup+',[status(thm)],[zip_derived_cl22,zip_derived_cl11]) ).

thf(zip_derived_cl2_003,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X2 )
      | ( rel_s4 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl92,plain,
    ! [X0: $i] :
      ( ( rel_s4 @ sk__9 @ X0 )
      | ~ ( rel_s4 @ sk__13 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl84,zip_derived_cl2]) ).

thf(zip_derived_cl531_004,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__11 @ X0 )
      | ( rel_s4 @ X0 @ ( sk__10 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl470,zip_derived_cl10]) ).

thf(zip_derived_cl561,plain,
    ( ( rel_s4 @ sk__9 @ ( sk__10 @ sk__13 ) )
    | ~ ( rel_s4 @ sk__11 @ sk__13 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl92,zip_derived_cl531]) ).

thf(zip_derived_cl11_005,plain,
    rel_s4 @ sk__11 @ sk__13,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl596,plain,
    rel_s4 @ sk__9 @ ( sk__10 @ sk__13 ),
    inference(demod,[status(thm)],[zip_derived_cl561,zip_derived_cl11]) ).

thf(zip_derived_cl2_006,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X2 )
      | ( rel_s4 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl626,plain,
    ! [X0: $i] :
      ( ( rel_s4 @ sk__9 @ X0 )
      | ~ ( rel_s4 @ ( sk__10 @ sk__13 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl596,zip_derived_cl2]) ).

thf(zip_derived_cl1277,plain,
    ( ~ ( rel_s4 @ sk__11 @ ( sk__10 @ sk__13 ) )
    | ( rel_s4 @ sk__9 @ ( sk__10 @ ( sk__10 @ sk__13 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl531,zip_derived_cl626]) ).

thf(zip_derived_cl11_007,plain,
    rel_s4 @ sk__11 @ sk__13,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl2_008,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X2 )
      | ( rel_s4 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl20,plain,
    ! [X0: $i] :
      ( ( rel_s4 @ sk__11 @ X0 )
      | ~ ( rel_s4 @ sk__13 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl2]) ).

thf(zip_derived_cl531_009,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__11 @ X0 )
      | ( rel_s4 @ X0 @ ( sk__10 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl470,zip_derived_cl10]) ).

thf(zip_derived_cl562,plain,
    ( ( rel_s4 @ sk__11 @ ( sk__10 @ sk__13 ) )
    | ~ ( rel_s4 @ sk__11 @ sk__13 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl20,zip_derived_cl531]) ).

thf(zip_derived_cl11_010,plain,
    rel_s4 @ sk__11 @ sk__13,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl597,plain,
    rel_s4 @ sk__11 @ ( sk__10 @ sk__13 ),
    inference(demod,[status(thm)],[zip_derived_cl562,zip_derived_cl11]) ).

thf(zip_derived_cl1283,plain,
    rel_s4 @ sk__9 @ ( sk__10 @ ( sk__10 @ sk__13 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1277,zip_derived_cl597]) ).

thf(zip_derived_cl1_011,plain,
    ! [X0: $i] : ( rel_s4 @ X0 @ X0 ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(nonempty_ax,axiom,
    ! [V: $i] :
    ? [X: mu] : ( exists_in_world @ X @ V ) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i] : ( exists_in_world @ ( sk_ @ X0 ) @ X0 ),
    inference(cnf,[status(esa)],[nonempty_ax]) ).

thf(zip_derived_cl17,plain,
    ! [X0: mu,X1: $i,X3: $i,X5: $i] :
      ( ~ ( exists_in_world @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X5 )
      | ( p @ X5 )
      | ~ ( rel_s4 @ X1 @ X3 )
      | ~ ( p @ ( sk__10 @ X3 ) )
      | ~ ( rel_s4 @ sk__9 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl213,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ sk__9 @ X0 )
      | ~ ( p @ ( sk__10 @ X1 ) )
      | ~ ( rel_s4 @ X0 @ X1 )
      | ( p @ X2 )
      | ~ ( rel_s4 @ X0 @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl17]) ).

thf(zip_derived_cl477,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( rel_s4 @ sk__9 @ X0 )
      | ( p @ X0 )
      | ~ ( rel_s4 @ sk__9 @ X1 )
      | ~ ( p @ ( sk__10 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl213]) ).

thf(zip_derived_cl1307,plain,
    ! [X0: $i] :
      ( ~ ( p @ ( sk__10 @ X0 ) )
      | ~ ( rel_s4 @ sk__9 @ X0 )
      | ( p @ ( sk__10 @ ( sk__10 @ sk__13 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1283,zip_derived_cl477]) ).

thf(zip_derived_cl597_012,plain,
    rel_s4 @ sk__11 @ ( sk__10 @ sk__13 ),
    inference(demod,[status(thm)],[zip_derived_cl562,zip_derived_cl11]) ).

thf(zip_derived_cl11_013,plain,
    rel_s4 @ sk__11 @ sk__13,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl38_014,plain,
    ! [X0: $i] :
      ( ( exists_in_world @ sk__12 @ X0 )
      | ~ ( rel_s4 @ sk__11 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl3]) ).

thf(zip_derived_cl14,plain,
    ! [X0: mu,X1: $i,X2: $i,X3: $i] :
      ( ~ ( exists_in_world @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X2 )
      | ( big_q @ X0 @ X2 )
      | ~ ( rel_s4 @ X1 @ X3 )
      | ~ ( p @ ( sk__10 @ X3 ) )
      | ~ ( rel_s4 @ sk__9 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl97,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ sk__11 @ X0 )
      | ~ ( rel_s4 @ sk__9 @ X0 )
      | ~ ( p @ ( sk__10 @ X1 ) )
      | ~ ( rel_s4 @ X0 @ X1 )
      | ( big_q @ sk__12 @ X2 )
      | ~ ( rel_s4 @ X0 @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl14]) ).

thf(zip_derived_cl22_015,plain,
    ! [X0: $i] :
      ( ( rel_s4 @ sk__9 @ X0 )
      | ~ ( rel_s4 @ sk__11 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl2]) ).

thf(zip_derived_cl1140,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ X0 @ X2 )
      | ( big_q @ sk__12 @ X2 )
      | ~ ( rel_s4 @ X0 @ X1 )
      | ~ ( p @ ( sk__10 @ X1 ) )
      | ~ ( rel_s4 @ sk__11 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl97,zip_derived_cl22]) ).

thf(zip_derived_cl1144,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__11 @ sk__11 )
      | ~ ( p @ ( sk__10 @ X0 ) )
      | ~ ( rel_s4 @ sk__11 @ X0 )
      | ( big_q @ sk__12 @ sk__13 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl1140]) ).

thf(zip_derived_cl1_016,plain,
    ! [X0: $i] : ( rel_s4 @ X0 @ X0 ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl1191,plain,
    ! [X0: $i] :
      ( ~ ( p @ ( sk__10 @ X0 ) )
      | ~ ( rel_s4 @ sk__11 @ X0 )
      | ( big_q @ sk__12 @ sk__13 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1144,zip_derived_cl1]) ).

thf(zip_derived_cl10_017,plain,
    ~ ( big_q @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1288,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__11 @ X0 )
      | ~ ( p @ ( sk__10 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1191,zip_derived_cl10]) ).

thf(zip_derived_cl1290,plain,
    ~ ( p @ ( sk__10 @ ( sk__10 @ sk__13 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl597,zip_derived_cl1288]) ).

thf(zip_derived_cl1784,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__9 @ X0 )
      | ~ ( p @ ( sk__10 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1307,zip_derived_cl1290]) ).

thf(zip_derived_cl1786,plain,
    ~ ( p @ ( sk__10 @ sk__14 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl1784]) ).

thf(zip_derived_cl7,plain,
    rel_s4 @ sk__14 @ sk__16,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl5,plain,
    exists_in_world @ sk__15 @ sk__14,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl18,plain,
    ! [X0: mu,X1: $i,X4: $i,X5: $i] :
      ( ~ ( exists_in_world @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X5 )
      | ( p @ X5 )
      | ~ ( rel_s4 @ X1 @ X4 )
      | ( big_r @ X0 @ X4 )
      | ~ ( rel_s4 @ sk__9 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl234,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( rel_s4 @ sk__9 @ sk__14 )
      | ( big_r @ sk__15 @ X0 )
      | ~ ( rel_s4 @ sk__14 @ X0 )
      | ( p @ X1 )
      | ~ ( rel_s4 @ sk__14 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl18]) ).

thf(zip_derived_cl8_018,plain,
    rel_s4 @ sk__9 @ sk__14,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl250,plain,
    ! [X0: $i,X1: $i] :
      ( ( big_r @ sk__15 @ X0 )
      | ~ ( rel_s4 @ sk__14 @ X0 )
      | ( p @ X1 )
      | ~ ( rel_s4 @ sk__14 @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl234,zip_derived_cl8]) ).

thf(zip_derived_cl256,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__14 @ X0 )
      | ( p @ X0 )
      | ( big_r @ sk__15 @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl250]) ).

thf(zip_derived_cl6,plain,
    ~ ( big_r @ sk__15 @ sk__16 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl260,plain,
    ! [X0: $i] :
      ( ( p @ X0 )
      | ~ ( rel_s4 @ sk__14 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl256,zip_derived_cl6]) ).

thf(zip_derived_cl22_019,plain,
    ! [X0: $i] :
      ( ( rel_s4 @ sk__9 @ X0 )
      | ~ ( rel_s4 @ sk__11 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl2]) ).

thf(zip_derived_cl531_020,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__11 @ X0 )
      | ( rel_s4 @ X0 @ ( sk__10 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl470,zip_derived_cl10]) ).

thf(zip_derived_cl563,plain,
    ( ( rel_s4 @ sk__9 @ ( sk__10 @ sk__11 ) )
    | ~ ( rel_s4 @ sk__11 @ sk__11 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl22,zip_derived_cl531]) ).

thf(zip_derived_cl1_021,plain,
    ! [X0: $i] : ( rel_s4 @ X0 @ X0 ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl598,plain,
    rel_s4 @ sk__9 @ ( sk__10 @ sk__11 ),
    inference(demod,[status(thm)],[zip_derived_cl563,zip_derived_cl1]) ).

thf(zip_derived_cl0_022,plain,
    ! [X0: $i] : ( exists_in_world @ ( sk_ @ X0 ) @ X0 ),
    inference(cnf,[status(esa)],[nonempty_ax]) ).

thf(zip_derived_cl3_023,plain,
    ! [X0: mu,X1: $i,X2: $i] :
      ( ~ ( exists_in_world @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X2 )
      | ( exists_in_world @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[cumulative_ax]) ).

thf(zip_derived_cl39,plain,
    ! [X0: $i,X1: $i] :
      ( ( exists_in_world @ ( sk_ @ X0 ) @ X1 )
      | ~ ( rel_s4 @ X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl3]) ).

thf(zip_derived_cl16,plain,
    ! [X0: mu,X1: $i,X3: $i,X5: $i] :
      ( ~ ( exists_in_world @ X0 @ X1 )
      | ~ ( rel_s4 @ X1 @ X5 )
      | ( p @ X5 )
      | ~ ( rel_s4 @ X1 @ X3 )
      | ( rel_s4 @ X3 @ ( sk__10 @ X3 ) )
      | ~ ( rel_s4 @ sk__9 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( rel_s4 @ X1 @ X0 )
      | ~ ( rel_s4 @ sk__9 @ X0 )
      | ( rel_s4 @ X2 @ ( sk__10 @ X2 ) )
      | ~ ( rel_s4 @ X0 @ X2 )
      | ( p @ X3 )
      | ~ ( rel_s4 @ X0 @ X3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl16]) ).

thf(zip_derived_cl3408,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( rel_s4 @ X1 @ X0 )
      | ~ ( rel_s4 @ sk__9 @ X1 )
      | ( rel_s4 @ X2 @ ( sk__10 @ X2 ) )
      | ~ ( rel_s4 @ X1 @ X2 )
      | ( p @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl173]) ).

thf(zip_derived_cl3421,plain,
    ! [X0: $i] :
      ( ( p @ ( sk__10 @ sk__11 ) )
      | ~ ( rel_s4 @ sk__9 @ X0 )
      | ( rel_s4 @ X0 @ ( sk__10 @ X0 ) )
      | ~ ( rel_s4 @ sk__9 @ sk__9 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl598,zip_derived_cl3408]) ).

thf(zip_derived_cl1_024,plain,
    ! [X0: $i] : ( rel_s4 @ X0 @ X0 ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl3485,plain,
    ! [X0: $i] :
      ( ( p @ ( sk__10 @ sk__11 ) )
      | ~ ( rel_s4 @ sk__9 @ X0 )
      | ( rel_s4 @ X0 @ ( sk__10 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3421,zip_derived_cl1]) ).

thf(zip_derived_cl1_025,plain,
    ! [X0: $i] : ( rel_s4 @ X0 @ X0 ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl1288_026,plain,
    ! [X0: $i] :
      ( ~ ( rel_s4 @ sk__11 @ X0 )
      | ~ ( p @ ( sk__10 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1191,zip_derived_cl10]) ).

thf(zip_derived_cl1292,plain,
    ~ ( p @ ( sk__10 @ sk__11 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl1288]) ).

thf(zip_derived_cl4041,plain,
    ! [X0: $i] :
      ( ( rel_s4 @ X0 @ ( sk__10 @ X0 ) )
      | ~ ( rel_s4 @ sk__9 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl3485,zip_derived_cl1292]) ).

thf(zip_derived_cl4124,plain,
    ( ( p @ ( sk__10 @ sk__14 ) )
    | ~ ( rel_s4 @ sk__9 @ sk__14 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl260,zip_derived_cl4041]) ).

thf(zip_derived_cl8_027,plain,
    rel_s4 @ sk__9 @ sk__14,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4260,plain,
    p @ ( sk__10 @ sk__14 ),
    inference(demod,[status(thm)],[zip_derived_cl4124,zip_derived_cl8]) ).

thf(zip_derived_cl4436,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl1786,zip_derived_cl4260]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYN367^7 : TPTP v8.1.2. Released v5.5.0.
% 0.11/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.RsrS0wWNDg true
% 0.13/0.34  % Computer : n024.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 18:40:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox2/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
% 0.56/0.67  % Total configuration time : 828
% 0.56/0.67  % Estimated wc time : 1656
% 0.56/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.73  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.74  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.77  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.61/0.79  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.61/0.93  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 6.72/1.46  % Solved by lams/40_c.s.sh.
% 6.72/1.46  % done 940 iterations in 0.693s
% 6.72/1.46  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 6.72/1.46  % SZS output start Refutation
% See solution above
% 6.72/1.46  
% 6.72/1.46  
% 6.72/1.46  % Terminating...
% 7.41/1.58  % Runner terminated.
% 7.41/1.60  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------