TSTP Solution File: PUZ087^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : PUZ087^2 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WjnxP9eohb true

% Computer : n027.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 13:31:06 EDT 2023

% Result   : Theorem 259.66s 34.31s
% Output   : Refutation 259.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   70
% Syntax   : Number of formulae    :  126 (  41 unt;  27 typ;   0 def)
%            Number of atoms       :  352 (  19 equ;   8 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  827 ( 127   ~; 129   |;   0   &; 571   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  151 ( 151   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   30 (  27 usr;   6 con; 0-3 aty)
%            Number of variables   :  221 (  52   ^; 169   !;   0   ?; 221   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk__29_type,type,
    sk__29: $i ).

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

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

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

thf('#l_lift3543_type',type,
    '#l_lift3543': ( $i > $o ) > $i > $o ).

thf(a_type,type,
    a: $i > $i > $o ).

thf(sk__24_type,type,
    sk__24: $i > $i ).

thf(sk__21_type,type,
    sk__21: $i > ( $i > $o ) > $i ).

thf(ws_type,type,
    ws: ( $i > $i > $o ) > $i > $o ).

thf(sk__25_type,type,
    sk__25: $i > $i ).

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

thf(sk__30_type,type,
    sk__30: $i ).

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

thf(sk__7_type,type,
    sk__7: ( $i > $o ) > $i > $i ).

thf(sk__22_type,type,
    sk__22: $i > ( $i > $o ) > $i ).

thf(priorG_type,type,
    priorG: $i > $i > $o ).

thf(b_type,type,
    b: $i > $i > $o ).

thf(c_type,type,
    c: $i > $i > $o ).

thf(fool_type,type,
    fool: $i > $i > $o ).

thf(sk__23_type,type,
    sk__23: $i > ( $i > $o ) > $i ).

thf(sk__28_type,type,
    sk__28: $i ).

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

thf(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(sk__27_type,type,
    sk__27: $i ).

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

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

thf(sk__19_type,type,
    sk__19: $i > ( $i > $o ) > $i ).

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

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

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

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

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

thf('3',plain,
    ( mbox
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
        ! [X4: $i] :
          ( ( V_2 @ X4 )
          | ~ ( V_1 @ V_3 @ X4 ) ) ) ),
    define([status(thm)]) ).

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

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

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

thf(axiom_5,axiom,
    mvalid @ ( mbox @ priorG @ ( mbox @ priorG @ ( mnot @ ( mbox @ b @ ( ws @ b ) ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ! [X4: $i,X6: $i] :
      ( ! [X8: $i] :
          ( ~ ! [X10: $i] :
                ( ( ws @ b @ X10 )
                | ~ ( b @ X8 @ X10 ) )
          | ~ ( priorG @ X6 @ X8 ) )
      | ~ ( priorG @ X4 @ X6 ) ) ).

thf(zip_derived_cl52,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( priorG @ X0 @ X1 )
      | ~ ( ws @ b @ ( sk__25 @ X1 ) )
      | ~ ( priorG @ X2 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

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

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

thf('7',plain,
    ( mforall_prop
    = ( ^ [V_1: ( $i > $o ) > $i > $o,V_2: $i] :
        ! [X4: $i > $o] : ( 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('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','5']) ).

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

thf(i_axiom_for_fool_b,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ b @ Phi ) ) ) ) ).

thf(zf_stmt_1,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ~ ! [X8: $i] :
            ( ( X6 @ X8 )
            | ~ ( fool @ X4 @ X8 ) )
      | ! [X10: $i] :
          ( ( X6 @ X10 )
          | ~ ( b @ X4 @ X10 ) ) ) ).

thf(zip_derived_cl21,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ~ ( X0 @ ( sk__10 @ X0 @ X1 ) )
      | ~ ( b @ X1 @ X2 )
      | ( X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl22,plain,
    ! [X0: $i,X1: $i > $o,X2: $i] :
      ( ( fool @ X0 @ ( sk__10 @ X1 @ X0 ) )
      | ~ ( b @ X0 @ X2 )
      | ( X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(conj,conjecture,
    mvalid @ ( mbox @ priorG @ ( mbox @ priorG @ ( mbox @ priorG @ ( mbox @ c @ ( ws @ c ) ) ) ) ) ).

thf(zf_stmt_2,conjecture,
    ! [X4: $i,X6: $i] :
      ( ! [X8: $i] :
          ( ! [X10: $i] :
              ( ! [X12: $i] :
                  ( ( ws @ c @ X12 )
                  | ~ ( c @ X10 @ X12 ) )
              | ~ ( priorG @ X8 @ X10 ) )
          | ~ ( priorG @ X6 @ X8 ) )
      | ~ ( priorG @ X4 @ X6 ) ) ).

thf(zf_stmt_3,negated_conjecture,
    ~ ! [X4: $i,X6: $i] :
        ( ! [X8: $i] :
            ( ! [X10: $i] :
                ( ! [X12: $i] :
                    ( ( ws @ c @ X12 )
                    | ~ ( c @ X10 @ X12 ) )
                | ~ ( priorG @ X8 @ X10 ) )
            | ~ ( priorG @ X6 @ X8 ) )
        | ~ ( priorG @ X4 @ X6 ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl56,plain,
    c @ sk__29 @ sk__30,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(a6_axiom_for_fool_c_b,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ Phi ) ) @ ( mbox @ b @ ( mnot @ ( mbox @ c @ Phi ) ) ) ) ) ) ).

thf(zf_stmt_4,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ! [X8: $i] :
          ( ( X6 @ X8 )
          | ~ ( c @ X4 @ X8 ) )
      | ! [X10: $i] :
          ( ~ ! [X12: $i] :
                ( ( X6 @ X12 )
                | ~ ( c @ X10 @ X12 ) )
          | ~ ( b @ X4 @ X10 ) ) ) ).

thf(zip_derived_cl47,plain,
    ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
      ( ~ ( c @ X0 @ X1 )
      | ( X2 @ X1 )
      | ~ ( b @ X0 @ X3 )
      | ~ ( X2 @ ( sk__23 @ X3 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl1271,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ~ ( X0 @ ( sk__23 @ X1 @ X0 ) )
      | ~ ( b @ sk__29 @ X1 )
      | ( X0 @ sk__30 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl56,zip_derived_cl47]) ).

thf(zip_derived_cl56_001,plain,
    c @ sk__29 @ sk__30,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl48,plain,
    ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
      ( ~ ( c @ X0 @ X1 )
      | ( X2 @ X1 )
      | ~ ( b @ X0 @ X3 )
      | ( c @ X3 @ ( sk__23 @ X3 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl2373,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( c @ X1 @ ( sk__23 @ X1 @ X0 ) )
      | ~ ( b @ sk__29 @ X1 )
      | ( X0 @ sk__30 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl56,zip_derived_cl48]) ).

thf(a6_axiom_for_fool_b_c,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ b @ Phi ) ) @ ( mbox @ c @ ( mnot @ ( mbox @ b @ Phi ) ) ) ) ) ) ).

thf(zf_stmt_5,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ! [X8: $i] :
          ( ( X6 @ X8 )
          | ~ ( b @ X4 @ X8 ) )
      | ! [X10: $i] :
          ( ~ ! [X12: $i] :
                ( ( X6 @ X12 )
                | ~ ( b @ X10 @ X12 ) )
          | ~ ( c @ X4 @ X10 ) ) ) ).

thf(zip_derived_cl43,plain,
    ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
      ( ~ ( b @ X0 @ X1 )
      | ( X2 @ X1 )
      | ~ ( c @ X0 @ X3 )
      | ~ ( X2 @ ( sk__21 @ X3 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_5]) ).

thf(axiom_2_b_c,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ b ) @ ( mbox @ c @ ( ws @ b ) ) ) ) ).

thf(zf_stmt_6,axiom,
    ! [X4: $i,X6: $i] :
      ( ~ ( ws @ b @ X6 )
      | ! [X8: $i] :
          ( ( ws @ b @ X8 )
          | ~ ( c @ X6 @ X8 ) )
      | ~ ( fool @ X4 @ X6 ) ) ).

thf(zip_derived_cl6,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ws @ b @ X0 )
      | ~ ( c @ X0 @ X1 )
      | ( ws @ b @ X1 )
      | ~ ( fool @ X2 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_6]) ).

thf(zip_derived_cl57,plain,
    priorG @ sk__27 @ sk__28,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl44,plain,
    ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
      ( ~ ( b @ X0 @ X1 )
      | ( X2 @ X1 )
      | ~ ( c @ X0 @ X3 )
      | ( b @ X3 @ ( sk__21 @ X3 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_5]) ).

thf(axiom_4,axiom,
    mvalid @ ( mbox @ priorG @ ( mnot @ ( mbox @ a @ ( ws @ a ) ) ) ) ).

thf(zf_stmt_7,axiom,
    ! [X4: $i,X6: $i] :
      ( ~ ! [X8: $i] :
            ( ( ws @ a @ X8 )
            | ~ ( a @ X6 @ X8 ) )
      | ~ ( priorG @ X4 @ X6 ) ) ).

thf(zip_derived_cl49,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ws @ a @ ( sk__24 @ X0 ) )
      | ~ ( priorG @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl54,plain,
    priorG @ sk__28 @ sk__29,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(i_axiom_for_fool_a,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ a @ Phi ) ) ) ) ).

thf(zf_stmt_8,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ~ ! [X8: $i] :
            ( ( X6 @ X8 )
            | ~ ( fool @ X4 @ X8 ) )
      | ! [X10: $i] :
          ( ( X6 @ X10 )
          | ~ ( a @ X4 @ X10 ) ) ) ).

thf(zip_derived_cl19,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ~ ( X0 @ ( sk__9 @ X0 @ X1 ) )
      | ~ ( a @ X1 @ X2 )
      | ( X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_8]) ).

thf(zip_derived_cl20,plain,
    ! [X0: $i,X1: $i > $o,X2: $i] :
      ( ( fool @ X0 @ ( sk__9 @ X1 @ X0 ) )
      | ~ ( a @ X0 @ X2 )
      | ( X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_8]) ).

thf(zip_derived_cl56_002,plain,
    c @ sk__29 @ sk__30,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(a6_axiom_for_fool_c_a,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ Phi ) ) @ ( mbox @ a @ ( mnot @ ( mbox @ c @ Phi ) ) ) ) ) ) ).

thf(zf_stmt_9,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ! [X8: $i] :
          ( ( X6 @ X8 )
          | ~ ( c @ X4 @ X8 ) )
      | ! [X10: $i] :
          ( ~ ! [X12: $i] :
                ( ( X6 @ X12 )
                | ~ ( c @ X10 @ X12 ) )
          | ~ ( a @ X4 @ X10 ) ) ) ).

thf(zip_derived_cl45,plain,
    ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
      ( ~ ( c @ X0 @ X1 )
      | ( X2 @ X1 )
      | ~ ( a @ X0 @ X3 )
      | ~ ( X2 @ ( sk__22 @ X3 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl1124,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ~ ( X0 @ ( sk__22 @ X1 @ X0 ) )
      | ~ ( a @ sk__29 @ X1 )
      | ( X0 @ sk__30 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl56,zip_derived_cl45]) ).

thf(t_axiom_for_fool,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ) ).

thf(zf_stmt_10,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ~ ! [X8: $i] :
            ( ( X6 @ X8 )
            | ~ ( fool @ X4 @ X8 ) )
      | ( X6 @ X4 ) ) ).

thf(zip_derived_cl15,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ~ ( X0 @ ( sk__7 @ X0 @ X1 ) )
      | ( X0 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_10]) ).

thf(zip_derived_cl16,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( fool @ X0 @ ( sk__7 @ X1 @ X0 ) )
      | ( X1 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_10]) ).

thf(zip_derived_cl1431,plain,
    ! [X0: $i] :
      ( ( fool @ X0 @ X0 )
      | ( fool @ X0 @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl15,zip_derived_cl16]) ).

thf(zip_derived_cl1443,plain,
    ! [X0: $i] : ( fool @ X0 @ X0 ),
    inference(simplify,[status(thm)],[zip_derived_cl1431]) ).

thf(axiom_3_a_c,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ a ) ) @ ( mbox @ c @ ( mnot @ ( ws @ a ) ) ) ) ) ).

thf(zf_stmt_11,axiom,
    ! [X4: $i,X6: $i] :
      ( ( ws @ a @ X6 )
      | ! [X8: $i] :
          ( ~ ( ws @ a @ X8 )
          | ~ ( c @ X6 @ X8 ) )
      | ~ ( fool @ X4 @ X6 ) ) ).

thf(zip_derived_cl10,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ws @ a @ X0 )
      | ~ ( c @ X0 @ X1 )
      | ~ ( ws @ a @ X1 )
      | ~ ( fool @ X2 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_11]) ).

thf(zip_derived_cl15_003,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ~ ( X0 @ ( sk__7 @ X0 @ X1 ) )
      | ( X0 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_10]) ).

thf(zip_derived_cl241,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ~ ( ^ [Y0: $i] : ( (~) @ ( X0 @ Y0 ) )
          @ ( sk__7
            @ ^ [Y0: $i] : ( (~) @ ( X0 @ Y0 ) )
            @ X1 ) )
      | ( ^ [Y0: $i] : ( (~) @ ( X0 @ Y0 ) )
        @ X1 ) ),
    inference('ho.refine',[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl257,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ~ ( (~)
          @ ( X0
            @ ( sk__7
              @ ^ [Y0: $i] : ( (~) @ ( X0 @ Y0 ) )
              @ X1 ) ) )
      | ( (~) @ ( X0 @ X1 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl241]) ).

thf(zip_derived_cl258,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( X0
        @ ( sk__7
          @ ^ [Y0: $i] : ( (~) @ ( X0 @ Y0 ) )
          @ X1 ) )
      | ~ ( X0 @ X1 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl257]) ).

thf(zip_derived_cl12188,plain,
    ! [X0: $i > $o,X2: $i] :
      ( ( '#l_lift3543' @ X0 @ X2 )
      = ( (~) @ ( X0 @ X2 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl51,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( priorG @ X0 @ X1 )
      | ( b @ X1 @ ( sk__25 @ X1 ) )
      | ~ ( priorG @ X2 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl56_004,plain,
    c @ sk__29 @ sk__30,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl46,plain,
    ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
      ( ~ ( c @ X0 @ X1 )
      | ( X2 @ X1 )
      | ~ ( a @ X0 @ X3 )
      | ( c @ X3 @ ( sk__22 @ X3 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl2330,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( c @ X1 @ ( sk__22 @ X1 @ X0 ) )
      | ~ ( a @ sk__29 @ X1 )
      | ( X0 @ sk__30 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl56,zip_derived_cl46]) ).

thf(zip_derived_cl56_005,plain,
    c @ sk__29 @ sk__30,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl54_006,plain,
    priorG @ sk__28 @ sk__29,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl50,plain,
    ! [X0: $i,X1: $i] :
      ( ( a @ X0 @ ( sk__24 @ X0 ) )
      | ~ ( priorG @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl172,plain,
    a @ sk__29 @ ( sk__24 @ sk__29 ),
    inference('sup-',[status(thm)],[zip_derived_cl54,zip_derived_cl50]) ).

thf(a6_axiom_for_fool_a_c,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a @ Phi ) ) @ ( mbox @ c @ ( mnot @ ( mbox @ a @ Phi ) ) ) ) ) ) ).

thf(zf_stmt_12,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ! [X8: $i] :
          ( ( X6 @ X8 )
          | ~ ( a @ X4 @ X8 ) )
      | ! [X10: $i] :
          ( ~ ! [X12: $i] :
                ( ( X6 @ X12 )
                | ~ ( a @ X10 @ X12 ) )
          | ~ ( c @ X4 @ X10 ) ) ) ).

thf(zip_derived_cl39,plain,
    ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
      ( ~ ( a @ X0 @ X1 )
      | ( X2 @ X1 )
      | ~ ( c @ X0 @ X3 )
      | ~ ( X2 @ ( sk__19 @ X3 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_12]) ).

thf(zip_derived_cl55,plain,
    ~ ( ws @ c @ sk__30 ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(axiom_3_b_c,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ b ) ) @ ( mbox @ c @ ( mnot @ ( ws @ b ) ) ) ) ) ).

thf(zf_stmt_13,axiom,
    ! [X4: $i,X6: $i] :
      ( ( ws @ b @ X6 )
      | ! [X8: $i] :
          ( ~ ( ws @ b @ X8 )
          | ~ ( c @ X6 @ X8 ) )
      | ~ ( fool @ X4 @ X6 ) ) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ws @ b @ X0 )
      | ~ ( c @ X0 @ X1 )
      | ~ ( ws @ b @ X1 )
      | ~ ( fool @ X2 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_13]) ).

thf(zip_derived_cl56_007,plain,
    c @ sk__29 @ sk__30,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(i_axiom_for_fool_c,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ c @ Phi ) ) ) ) ).

thf(zf_stmt_14,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ~ ! [X8: $i] :
            ( ( X6 @ X8 )
            | ~ ( fool @ X4 @ X8 ) )
      | ! [X10: $i] :
          ( ( X6 @ X10 )
          | ~ ( c @ X4 @ X10 ) ) ) ).

thf(zip_derived_cl24,plain,
    ! [X0: $i,X1: $i > $o,X2: $i] :
      ( ( fool @ X0 @ ( sk__11 @ X1 @ X0 ) )
      | ~ ( c @ X0 @ X2 )
      | ( X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_14]) ).

thf(zip_derived_cl1662,plain,
    ! [X0: $i > $o] :
      ( ( X0 @ sk__30 )
      | ( fool @ sk__29 @ ( sk__11 @ X0 @ sk__29 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl56,zip_derived_cl24]) ).

thf(axiom_1,axiom,
    mvalid @ ( mbox @ fool @ ( mor @ ( ws @ a ) @ ( mor @ ( ws @ b ) @ ( ws @ c ) ) ) ) ).

thf(zf_stmt_15,axiom,
    ! [X4: $i,X6: $i] :
      ( ( ws @ a @ X6 )
      | ( ws @ b @ X6 )
      | ( ws @ c @ X6 )
      | ~ ( fool @ X4 @ X6 ) ) ).

thf(zip_derived_cl2,plain,
    ! [X0: $i,X1: $i] :
      ( ( ws @ a @ X0 )
      | ( ws @ b @ X0 )
      | ( ws @ c @ X0 )
      | ~ ( fool @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_15]) ).

thf(zip_derived_cl40,plain,
    ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
      ( ~ ( a @ X0 @ X1 )
      | ( X2 @ X1 )
      | ~ ( c @ X0 @ X3 )
      | ( a @ X3 @ ( sk__19 @ X3 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_12]) ).

thf(zip_derived_cl56_008,plain,
    c @ sk__29 @ sk__30,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl23,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ~ ( X0 @ ( sk__11 @ X0 @ X1 ) )
      | ~ ( c @ X1 @ X2 )
      | ( X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_14]) ).

thf(zip_derived_cl90,plain,
    ! [X0: $i > $o] :
      ( ( X0 @ sk__30 )
      | ~ ( X0 @ ( sk__11 @ X0 @ sk__29 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl56,zip_derived_cl23]) ).

thf(zip_derived_cl12215,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl52,zip_derived_cl21,zip_derived_cl22,zip_derived_cl1271,zip_derived_cl2373,zip_derived_cl43,zip_derived_cl6,zip_derived_cl57,zip_derived_cl44,zip_derived_cl49,zip_derived_cl54,zip_derived_cl19,zip_derived_cl20,zip_derived_cl1124,zip_derived_cl1443,zip_derived_cl10,zip_derived_cl12188,zip_derived_cl51,zip_derived_cl2330,zip_derived_cl56,zip_derived_cl172,zip_derived_cl39,zip_derived_cl55,zip_derived_cl12,zip_derived_cl1662,zip_derived_cl2,zip_derived_cl40,zip_derived_cl90]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : PUZ087^2 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WjnxP9eohb true
% 0.18/0.36  % Computer : n027.cluster.edu
% 0.18/0.36  % Model    : x86_64 x86_64
% 0.18/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36  % Memory   : 8042.1875MB
% 0.18/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36  % CPULimit : 300
% 0.18/0.36  % WCLimit  : 300
% 0.18/0.36  % DateTime : Sat Aug 26 22:21:20 EDT 2023
% 0.18/0.36  % CPUTime  : 
% 0.18/0.36  % Running portfolio for 300 s
% 0.18/0.36  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.36  % Number of cores: 8
% 0.18/0.36  % Python version: Python 3.6.8
% 0.18/0.36  % Running in HO mode
% 0.22/0.62  % Total configuration time : 828
% 0.22/0.62  % Estimated wc time : 1656
% 0.22/0.62  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.69  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.70  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.70  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.84  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 31.88/4.71  % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 231.13/30.70  % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s
% 259.66/34.31  % Solved by lams/40_noforms.sh.
% 259.66/34.31  % done 993 iterations in 33.391s
% 259.66/34.31  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 259.66/34.31  % SZS output start Refutation
% See solution above
% 259.66/34.31  
% 259.66/34.31  
% 259.66/34.31  % Terminating...
% 260.71/34.66  % Runner terminated.
% 260.71/34.66  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------