TSTP Solution File: NLP264^7 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NLP264^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% 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  : 600s
% DateTime : Mon Jul 18 03:05:28 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   95
% Syntax   : Number of formulae    :  201 ( 100 unt;  47 typ;  32 def)
%            Number of atoms       :  802 ( 215 equ;   0 cnn)
%            Maximal formula atoms :    7 (   5 avg)
%            Number of connectives : 1104 ( 200   ~; 163   |;   9   &; 722   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  187 ( 187   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   49 (  46 usr;   9 con; 0-3 aty)
%            Number of variables   :  276 (  49   ^ 220   !;   7   ?; 276   :)

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

thf(tp_class,type,
    class: mu > $i > $o ).

thf(tp_dest,type,
    dest: mu > $i > $o ).

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

thf(tp_first,type,
    first: mu ).

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

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

thf(tp_mbox_s4,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

thf(tp_mcountersatisfiable,type,
    mcountersatisfiable: ( $i > $o ) > $o ).

thf(tp_mdia,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_mdia_s4,type,
    mdia_s4: ( $i > $o ) > $i > $o ).

thf(tp_meq_prop,type,
    meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

thf(tp_meuclidean,type,
    meuclidean: ( $i > $i > $o ) > $o ).

thf(tp_mexists_ind,type,
    mexists_ind: ( mu > $i > $o ) > $i > $o ).

thf(tp_mexists_prop,type,
    mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(tp_mfalse,type,
    mfalse: $i > $o ).

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

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

thf(tp_mfunctional,type,
    mfunctional: ( $i > $i > $o ) > $o ).

thf(tp_mimplied,type,
    mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

thf(tp_minvalid,type,
    minvalid: ( $i > $o ) > $o ).

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

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

thf(tp_mpartially_functional,type,
    mpartially_functional: ( $i > $i > $o ) > $o ).

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

thf(tp_msatisfiable,type,
    msatisfiable: ( $i > $o ) > $o ).

thf(tp_mserial,type,
    mserial: ( $i > $i > $o ) > $o ).

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

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

thf(tp_mtrue,type,
    mtrue: $i > $o ).

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

thf(tp_mweakly_connected,type,
    mweakly_connected: ( $i > $i > $o ) > $o ).

thf(tp_mweakly_dense,type,
    mweakly_dense: ( $i > $i > $o ) > $o ).

thf(tp_mweakly_directed,type,
    mweakly_directed: ( $i > $i > $o ) > $o ).

thf(tp_mxor,type,
    mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_ninetyfive,type,
    ninetyfive: mu ).

thf(tp_paris,type,
    paris: mu ).

thf(tp_price,type,
    price: mu > $i > $o ).

thf(tp_qmltpeq,type,
    qmltpeq: mu > mu > $i > $o ).

thf(tp_rel_s4,type,
    rel_s4: $i > $i > $o ).

thf(tp_sK1_X,type,
    sK1_X: $i > mu ).

thf(tp_sK2_SX0,type,
    sK2_SX0: $i ).

thf(tp_sK3_SY11,type,
    sK3_SY11: $i ).

thf(tp_second,type,
    second: mu ).

thf(tp_seventy,type,
    seventy: mu ).

thf(mand,definition,
    ( mand
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).

thf(mbox,definition,
    ( mbox
    = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ~ ( R @ W @ V )
          | ( Phi @ V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).

thf(mbox_s4,definition,
    ( mbox_s4
    = ( ^ [Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ~ ( rel_s4 @ W @ V )
          | ( Phi @ V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4) ).

thf(mcountersatisfiable,definition,
    ( mcountersatisfiable
    = ( ^ [Phi: $i > $o] :
        ? [W: $i] :
          ~ ( Phi @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).

thf(mdia,definition,
    ( mdia
    = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).

thf(mdia_s4,definition,
    ( mdia_s4
    = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4) ).

thf(meq_prop,definition,
    ( meq_prop
    = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
          ( ( X @ W )
          = ( Y @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_prop) ).

thf(mequiv,definition,
    ( mequiv
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).

thf(meuclidean,definition,
    ( meuclidean
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ S @ U ) )
         => ( R @ T @ U ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean) ).

thf(mexists_ind,definition,
    ( mexists_ind
    = ( ^ [Phi: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind) ).

thf(mexists_prop,definition,
    ( mexists_prop
    = ( ^ [Phi: ( $i > $o ) > $i > $o] :
          ( mnot
          @ ( mforall_prop
            @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop) ).

thf(mfalse,definition,
    ( mfalse
    = ( mnot @ mtrue ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).

thf(mforall_ind,definition,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] :
          ( ( exists_in_world @ X @ W )
         => ( Phi @ X @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind) ).

thf(mforall_prop,definition,
    ( mforall_prop
    = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
        ! [P: $i > $o] : ( Phi @ P @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop) ).

thf(mfunctional,definition,
    ( mfunctional
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] :
        ? [T: $i] :
          ( ( R @ S @ T )
          & ! [U: $i] :
              ( ( R @ S @ U )
             => ( T = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfunctional) ).

thf(mimplied,definition,
    ( mimplied
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).

thf(mimplies,definition,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).

thf(minvalid,definition,
    ( minvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] :
          ~ ( Phi @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).

thf(mnot,definition,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).

thf(mor,definition,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).

thf(mpartially_functional,definition,
    ( mpartially_functional
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ S @ U ) )
         => ( T = U ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).

thf(mreflexive,definition,
    ( mreflexive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] : ( R @ S @ S ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).

thf(msatisfiable,definition,
    ( msatisfiable
    = ( ^ [Phi: $i > $o] :
        ? [W: $i] : ( Phi @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).

thf(mserial,definition,
    ( mserial
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] :
        ? [T: $i] : ( R @ S @ T ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial) ).

thf(msymmetric,definition,
    ( msymmetric
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i] :
          ( ( R @ S @ T )
         => ( R @ T @ S ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric) ).

thf(mtransitive,definition,
    ( mtransitive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ T @ U ) )
         => ( R @ S @ U ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive) ).

thf(mtrue,definition,
    ( mtrue
    = ( ^ [W: $i] : $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).

thf(mvalid,definition,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).

thf(mweakly_connected,definition,
    ( mweakly_connected
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ S @ U ) )
         => ( ( R @ T @ U )
            | ( T = U )
            | ( R @ U @ T ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_connected) ).

thf(mweakly_dense,definition,
    ( mweakly_dense
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( R @ S @ T )
         => ? [U: $i] :
              ( ( R @ S @ U )
              & ( R @ U @ T ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense) ).

thf(mweakly_directed,definition,
    ( mweakly_directed
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ S @ U ) )
         => ? [V: $i] :
              ( ( R @ T @ V )
              & ( R @ U @ V ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).

thf(mxor,definition,
    ( mxor
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).

thf(1,axiom,
    mvalid @ ( mbox_s4 @ ( class @ second ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',belief2) ).

thf(2,axiom,
    mvalid @ ( mbox_s4 @ ( dest @ paris ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',belief1) ).

thf(3,axiom,
    mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',law4) ).

thf(4,axiom,
    mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',law3) ).

thf(5,axiom,
    mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',law2) ).

thf(6,axiom,
    mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',law1) ).

thf(7,axiom,
    ! [V: $i] : ( exists_in_world @ seventy @ V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_seventy_ax) ).

thf(8,axiom,
    ! [V: $i] : ( exists_in_world @ second @ V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_second_ax) ).

thf(9,axiom,
    ! [V: $i] : ( exists_in_world @ paris @ V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_paris_ax) ).

thf(10,axiom,
    ! [V: $i] : ( exists_in_world @ ninetyfive @ V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_ninetyfive_ax) ).

thf(11,axiom,
    ! [V: $i] : ( exists_in_world @ first @ V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_first_ax) ).

thf(12,axiom,
    ! [X: mu,V: $i,W: $i] :
      ( ( ( exists_in_world @ X @ V )
        & ( rel_s4 @ V @ W ) )
     => ( exists_in_world @ X @ W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax) ).

thf(13,axiom,
    mtransitive @ rel_s4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).

thf(14,axiom,
    mreflexive @ rel_s4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).

thf(15,axiom,
    ! [V: $i] :
    ? [X: mu] : ( exists_in_world @ X @ V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax) ).

thf(16,conjecture,
    mvalid @ ( mbox_s4 @ ( price @ seventy ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(17,negated_conjecture,
    ( ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[16]) ).

thf(18,plain,
    ( ( ~ ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[17]) ).

thf(19,plain,
    ( ( ! [X: mu,V: $i,W: $i] :
          ( ~ ( exists_in_world @ X @ V )
          | ~ ( rel_s4 @ V @ W )
          | ( exists_in_world @ X @ W ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(20,plain,
    ( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(21,plain,
    ( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(22,plain,
    ( ( mreflexive @ rel_s4 )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(23,plain,
    ( ( mtransitive @ rel_s4 )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(24,plain,
    ( ( ! [X: mu,V: $i,W: $i] :
          ( ~ ( exists_in_world @ X @ V )
          | ~ ( rel_s4 @ V @ W )
          | ( exists_in_world @ X @ W ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(25,plain,
    ( ( ! [V: $i] : ( exists_in_world @ first @ V ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(26,plain,
    ( ( ! [V: $i] : ( exists_in_world @ ninetyfive @ V ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(27,plain,
    ( ( ! [V: $i] : ( exists_in_world @ paris @ V ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(28,plain,
    ( ( ! [V: $i] : ( exists_in_world @ second @ V ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(29,plain,
    ( ( ! [V: $i] : ( exists_in_world @ seventy @ V ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(30,plain,
    ( ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(31,plain,
    ( ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(32,plain,
    ( ( mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[4]) ).

thf(33,plain,
    ( ( mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[3]) ).

thf(34,plain,
    ( ( mvalid @ ( mbox_s4 @ ( dest @ paris ) ) )
    = $true ),
    inference(copy,[status(thm)],[2]) ).

thf(35,plain,
    ( ( mvalid @ ( mbox_s4 @ ( class @ second ) ) )
    = $true ),
    inference(copy,[status(thm)],[1]) ).

thf(36,plain,
    ( ( ~ ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(37,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( rel_s4 @ SX0 @ SX1 )
          | ( class @ second @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).

thf(38,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( rel_s4 @ SX0 @ SX1 )
            | ( price @ seventy @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).

thf(39,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( rel_s4 @ SX0 @ SX1 )
          | ~ ~ ( ~ ( price @ ninetyfive @ SX1 )
                | ~ ( price @ seventy @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).

thf(40,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( ~ ( rel_s4 @ SX0 @ SX1 )
                | ~ ( rel_s4 @ SX1 @ SX2 ) )
          | ( rel_s4 @ SX0 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).

thf(41,plain,
    ( ( ! [SX0: $i] : ( rel_s4 @ SX0 @ SX0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).

thf(42,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( rel_s4 @ SX0 @ SX1 )
          | ( dest @ paris @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).

thf(43,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( rel_s4 @ SX0 @ SX1 )
          | ~ ~ ( ~ ( dest @ paris @ SX1 )
                | ~ ( class @ second @ SX1 ) )
          | ( price @ seventy @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[31,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).

thf(44,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( rel_s4 @ SX0 @ SX1 )
          | ~ ~ ( ~ ( dest @ paris @ SX1 )
                | ~ ( class @ first @ SX1 ) )
          | ( price @ ninetyfive @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).

thf(45,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( rel_s4 @ SX0 @ SX1 )
          | ~ ~ ( ~ ( class @ first @ SX1 )
                | ~ ( class @ second @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).

thf(46,plain,
    ! [SV1: $i] :
      ( ( exists_in_world @ ( sK1_X @ SV1 ) @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(47,plain,
    ! [SV2: mu] :
      ( ( ! [SY0: $i,SY1: $i] :
            ( ~ ( exists_in_world @ SV2 @ SY0 )
            | ~ ( rel_s4 @ SY0 @ SY1 )
            | ( exists_in_world @ SV2 @ SY1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(48,plain,
    ! [SV3: $i] :
      ( ( exists_in_world @ first @ SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(49,plain,
    ! [SV4: $i] :
      ( ( exists_in_world @ ninetyfive @ SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(50,plain,
    ! [SV5: $i] :
      ( ( exists_in_world @ paris @ SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(51,plain,
    ! [SV6: $i] :
      ( ( exists_in_world @ second @ SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(52,plain,
    ! [SV7: $i] :
      ( ( exists_in_world @ seventy @ SV7 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(53,plain,
    ! [SV8: $i] :
      ( ( ! [SY2: $i] :
            ( ~ ( rel_s4 @ SV8 @ SY2 )
            | ( class @ second @ SY2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(54,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( rel_s4 @ SX0 @ SX1 )
          | ( price @ seventy @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(55,plain,
    ! [SV9: $i] :
      ( ( ! [SY3: $i] :
            ( ~ ( rel_s4 @ SV9 @ SY3 )
            | ~ ~ ( ~ ( price @ ninetyfive @ SY3 )
                  | ~ ( price @ seventy @ SY3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(56,plain,
    ! [SV10: $i] :
      ( ( ! [SY4: $i,SY5: $i] :
            ( ~ ~ ( ~ ( rel_s4 @ SV10 @ SY4 )
                  | ~ ( rel_s4 @ SY4 @ SY5 ) )
            | ( rel_s4 @ SV10 @ SY5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(57,plain,
    ! [SV11: $i] :
      ( ( rel_s4 @ SV11 @ SV11 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(58,plain,
    ! [SV12: $i] :
      ( ( ! [SY6: $i] :
            ( ~ ( rel_s4 @ SV12 @ SY6 )
            | ( dest @ paris @ SY6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(59,plain,
    ! [SV13: $i] :
      ( ( ! [SY7: $i] :
            ( ~ ( rel_s4 @ SV13 @ SY7 )
            | ~ ~ ( ~ ( dest @ paris @ SY7 )
                  | ~ ( class @ second @ SY7 ) )
            | ( price @ seventy @ SY7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(60,plain,
    ! [SV14: $i] :
      ( ( ! [SY8: $i] :
            ( ~ ( rel_s4 @ SV14 @ SY8 )
            | ~ ~ ( ~ ( dest @ paris @ SY8 )
                  | ~ ( class @ first @ SY8 ) )
            | ( price @ ninetyfive @ SY8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(61,plain,
    ! [SV15: $i] :
      ( ( ! [SY9: $i] :
            ( ~ ( rel_s4 @ SV15 @ SY9 )
            | ~ ~ ( ~ ( class @ first @ SY9 )
                  | ~ ( class @ second @ SY9 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(62,plain,
    ! [SV16: $i,SV2: mu] :
      ( ( ! [SY10: $i] :
            ( ~ ( exists_in_world @ SV2 @ SV16 )
            | ~ ( rel_s4 @ SV16 @ SY10 )
            | ( exists_in_world @ SV2 @ SY10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(63,plain,
    ! [SV17: $i,SV8: $i] :
      ( ( ~ ( rel_s4 @ SV8 @ SV17 )
        | ( class @ second @ SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(64,plain,
    ( ( ! [SY11: $i] :
          ( ~ ( rel_s4 @ sK2_SX0 @ SY11 )
          | ( price @ seventy @ SY11 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[54]) ).

thf(65,plain,
    ! [SV18: $i,SV9: $i] :
      ( ( ~ ( rel_s4 @ SV9 @ SV18 )
        | ~ ~ ( ~ ( price @ ninetyfive @ SV18 )
              | ~ ( price @ seventy @ SV18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(66,plain,
    ! [SV19: $i,SV10: $i] :
      ( ( ! [SY12: $i] :
            ( ~ ~ ( ~ ( rel_s4 @ SV10 @ SV19 )
                  | ~ ( rel_s4 @ SV19 @ SY12 ) )
            | ( rel_s4 @ SV10 @ SY12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(67,plain,
    ! [SV20: $i,SV12: $i] :
      ( ( ~ ( rel_s4 @ SV12 @ SV20 )
        | ( dest @ paris @ SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(68,plain,
    ! [SV21: $i,SV13: $i] :
      ( ( ~ ( rel_s4 @ SV13 @ SV21 )
        | ~ ~ ( ~ ( dest @ paris @ SV21 )
              | ~ ( class @ second @ SV21 ) )
        | ( price @ seventy @ SV21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(69,plain,
    ! [SV22: $i,SV14: $i] :
      ( ( ~ ( rel_s4 @ SV14 @ SV22 )
        | ~ ~ ( ~ ( dest @ paris @ SV22 )
              | ~ ( class @ first @ SV22 ) )
        | ( price @ ninetyfive @ SV22 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(70,plain,
    ! [SV23: $i,SV15: $i] :
      ( ( ~ ( rel_s4 @ SV15 @ SV23 )
        | ~ ~ ( ~ ( class @ first @ SV23 )
              | ~ ( class @ second @ SV23 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(71,plain,
    ! [SV24: $i,SV16: $i,SV2: mu] :
      ( ( ~ ( exists_in_world @ SV2 @ SV16 )
        | ~ ( rel_s4 @ SV16 @ SV24 )
        | ( exists_in_world @ SV2 @ SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(72,plain,
    ! [SV17: $i,SV8: $i] :
      ( ( ( ~ ( rel_s4 @ SV8 @ SV17 ) )
        = $true )
      | ( ( class @ second @ SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(73,plain,
    ( ( ~ ( rel_s4 @ sK2_SX0 @ sK3_SY11 )
      | ( price @ seventy @ sK3_SY11 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[64]) ).

thf(74,plain,
    ! [SV18: $i,SV9: $i] :
      ( ( ( ~ ( rel_s4 @ SV9 @ SV18 ) )
        = $true )
      | ( ( ~ ~ ( ~ ( price @ ninetyfive @ SV18 )
                | ~ ( price @ seventy @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(75,plain,
    ! [SV25: $i,SV19: $i,SV10: $i] :
      ( ( ~ ~ ( ~ ( rel_s4 @ SV10 @ SV19 )
              | ~ ( rel_s4 @ SV19 @ SV25 ) )
        | ( rel_s4 @ SV10 @ SV25 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(76,plain,
    ! [SV20: $i,SV12: $i] :
      ( ( ( ~ ( rel_s4 @ SV12 @ SV20 ) )
        = $true )
      | ( ( dest @ paris @ SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[67]) ).

thf(77,plain,
    ! [SV21: $i,SV13: $i] :
      ( ( ( ~ ( rel_s4 @ SV13 @ SV21 ) )
        = $true )
      | ( ( ~ ~ ( ~ ( dest @ paris @ SV21 )
                | ~ ( class @ second @ SV21 ) )
          | ( price @ seventy @ SV21 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[68]) ).

thf(78,plain,
    ! [SV22: $i,SV14: $i] :
      ( ( ( ~ ( rel_s4 @ SV14 @ SV22 ) )
        = $true )
      | ( ( ~ ~ ( ~ ( dest @ paris @ SV22 )
                | ~ ( class @ first @ SV22 ) )
          | ( price @ ninetyfive @ SV22 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[69]) ).

thf(79,plain,
    ! [SV23: $i,SV15: $i] :
      ( ( ( ~ ( rel_s4 @ SV15 @ SV23 ) )
        = $true )
      | ( ( ~ ~ ( ~ ( class @ first @ SV23 )
                | ~ ( class @ second @ SV23 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[70]) ).

thf(80,plain,
    ! [SV24: $i,SV16: $i,SV2: mu] :
      ( ( ( ~ ( exists_in_world @ SV2 @ SV16 )
          | ~ ( rel_s4 @ SV16 @ SV24 ) )
        = $true )
      | ( ( exists_in_world @ SV2 @ SV24 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(81,plain,
    ! [SV17: $i,SV8: $i] :
      ( ( ( rel_s4 @ SV8 @ SV17 )
        = $false )
      | ( ( class @ second @ SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(82,plain,
    ( ( ~ ( rel_s4 @ sK2_SX0 @ sK3_SY11 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[73]) ).

thf(83,plain,
    ( ( price @ seventy @ sK3_SY11 )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[73]) ).

thf(84,plain,
    ! [SV18: $i,SV9: $i] :
      ( ( ( rel_s4 @ SV9 @ SV18 )
        = $false )
      | ( ( ~ ~ ( ~ ( price @ ninetyfive @ SV18 )
                | ~ ( price @ seventy @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(85,plain,
    ! [SV25: $i,SV19: $i,SV10: $i] :
      ( ( ( ~ ~ ( ~ ( rel_s4 @ SV10 @ SV19 )
                | ~ ( rel_s4 @ SV19 @ SV25 ) ) )
        = $true )
      | ( ( rel_s4 @ SV10 @ SV25 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[75]) ).

thf(86,plain,
    ! [SV20: $i,SV12: $i] :
      ( ( ( rel_s4 @ SV12 @ SV20 )
        = $false )
      | ( ( dest @ paris @ SV20 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(87,plain,
    ! [SV21: $i,SV13: $i] :
      ( ( ( rel_s4 @ SV13 @ SV21 )
        = $false )
      | ( ( ~ ~ ( ~ ( dest @ paris @ SV21 )
                | ~ ( class @ second @ SV21 ) )
          | ( price @ seventy @ SV21 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[77]) ).

thf(88,plain,
    ! [SV22: $i,SV14: $i] :
      ( ( ( rel_s4 @ SV14 @ SV22 )
        = $false )
      | ( ( ~ ~ ( ~ ( dest @ paris @ SV22 )
                | ~ ( class @ first @ SV22 ) )
          | ( price @ ninetyfive @ SV22 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[78]) ).

thf(89,plain,
    ! [SV23: $i,SV15: $i] :
      ( ( ( rel_s4 @ SV15 @ SV23 )
        = $false )
      | ( ( ~ ~ ( ~ ( class @ first @ SV23 )
                | ~ ( class @ second @ SV23 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(90,plain,
    ! [SV24: $i,SV16: $i,SV2: mu] :
      ( ( ( ~ ( exists_in_world @ SV2 @ SV16 ) )
        = $true )
      | ( ( ~ ( rel_s4 @ SV16 @ SV24 ) )
        = $true )
      | ( ( exists_in_world @ SV2 @ SV24 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[80]) ).

thf(91,plain,
    ( ( rel_s4 @ sK2_SX0 @ sK3_SY11 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[82]) ).

thf(92,plain,
    ! [SV9: $i,SV18: $i] :
      ( ( ( ~ ( ~ ( price @ ninetyfive @ SV18 )
              | ~ ( price @ seventy @ SV18 ) ) )
        = $false )
      | ( ( rel_s4 @ SV9 @ SV18 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(93,plain,
    ! [SV25: $i,SV19: $i,SV10: $i] :
      ( ( ( ~ ( ~ ( rel_s4 @ SV10 @ SV19 )
              | ~ ( rel_s4 @ SV19 @ SV25 ) ) )
        = $false )
      | ( ( rel_s4 @ SV10 @ SV25 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(94,plain,
    ! [SV13: $i,SV21: $i] :
      ( ( ( ~ ~ ( ~ ( dest @ paris @ SV21 )
                | ~ ( class @ second @ SV21 ) ) )
        = $true )
      | ( ( price @ seventy @ SV21 )
        = $true )
      | ( ( rel_s4 @ SV13 @ SV21 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[87]) ).

thf(95,plain,
    ! [SV14: $i,SV22: $i] :
      ( ( ( ~ ~ ( ~ ( dest @ paris @ SV22 )
                | ~ ( class @ first @ SV22 ) ) )
        = $true )
      | ( ( price @ ninetyfive @ SV22 )
        = $true )
      | ( ( rel_s4 @ SV14 @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(96,plain,
    ! [SV15: $i,SV23: $i] :
      ( ( ( ~ ( ~ ( class @ first @ SV23 )
              | ~ ( class @ second @ SV23 ) ) )
        = $false )
      | ( ( rel_s4 @ SV15 @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[89]) ).

thf(97,plain,
    ! [SV24: $i,SV16: $i,SV2: mu] :
      ( ( ( exists_in_world @ SV2 @ SV16 )
        = $false )
      | ( ( ~ ( rel_s4 @ SV16 @ SV24 ) )
        = $true )
      | ( ( exists_in_world @ SV2 @ SV24 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(98,plain,
    ! [SV9: $i,SV18: $i] :
      ( ( ( ~ ( price @ ninetyfive @ SV18 )
          | ~ ( price @ seventy @ SV18 ) )
        = $true )
      | ( ( rel_s4 @ SV9 @ SV18 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[92]) ).

thf(99,plain,
    ! [SV25: $i,SV19: $i,SV10: $i] :
      ( ( ( ~ ( rel_s4 @ SV10 @ SV19 )
          | ~ ( rel_s4 @ SV19 @ SV25 ) )
        = $true )
      | ( ( rel_s4 @ SV10 @ SV25 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[93]) ).

thf(100,plain,
    ! [SV13: $i,SV21: $i] :
      ( ( ( ~ ( ~ ( dest @ paris @ SV21 )
              | ~ ( class @ second @ SV21 ) ) )
        = $false )
      | ( ( price @ seventy @ SV21 )
        = $true )
      | ( ( rel_s4 @ SV13 @ SV21 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(101,plain,
    ! [SV14: $i,SV22: $i] :
      ( ( ( ~ ( ~ ( dest @ paris @ SV22 )
              | ~ ( class @ first @ SV22 ) ) )
        = $false )
      | ( ( price @ ninetyfive @ SV22 )
        = $true )
      | ( ( rel_s4 @ SV14 @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(102,plain,
    ! [SV15: $i,SV23: $i] :
      ( ( ( ~ ( class @ first @ SV23 )
          | ~ ( class @ second @ SV23 ) )
        = $true )
      | ( ( rel_s4 @ SV15 @ SV23 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[96]) ).

thf(103,plain,
    ! [SV2: mu,SV24: $i,SV16: $i] :
      ( ( ( rel_s4 @ SV16 @ SV24 )
        = $false )
      | ( ( exists_in_world @ SV2 @ SV16 )
        = $false )
      | ( ( exists_in_world @ SV2 @ SV24 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(104,plain,
    ! [SV9: $i,SV18: $i] :
      ( ( ( ~ ( price @ ninetyfive @ SV18 ) )
        = $true )
      | ( ( ~ ( price @ seventy @ SV18 ) )
        = $true )
      | ( ( rel_s4 @ SV9 @ SV18 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[98]) ).

thf(105,plain,
    ! [SV25: $i,SV19: $i,SV10: $i] :
      ( ( ( ~ ( rel_s4 @ SV10 @ SV19 ) )
        = $true )
      | ( ( ~ ( rel_s4 @ SV19 @ SV25 ) )
        = $true )
      | ( ( rel_s4 @ SV10 @ SV25 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(106,plain,
    ! [SV13: $i,SV21: $i] :
      ( ( ( ~ ( dest @ paris @ SV21 )
          | ~ ( class @ second @ SV21 ) )
        = $true )
      | ( ( price @ seventy @ SV21 )
        = $true )
      | ( ( rel_s4 @ SV13 @ SV21 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[100]) ).

thf(107,plain,
    ! [SV14: $i,SV22: $i] :
      ( ( ( ~ ( dest @ paris @ SV22 )
          | ~ ( class @ first @ SV22 ) )
        = $true )
      | ( ( price @ ninetyfive @ SV22 )
        = $true )
      | ( ( rel_s4 @ SV14 @ SV22 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[101]) ).

thf(108,plain,
    ! [SV15: $i,SV23: $i] :
      ( ( ( ~ ( class @ first @ SV23 ) )
        = $true )
      | ( ( ~ ( class @ second @ SV23 ) )
        = $true )
      | ( ( rel_s4 @ SV15 @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[102]) ).

thf(109,plain,
    ! [SV9: $i,SV18: $i] :
      ( ( ( price @ ninetyfive @ SV18 )
        = $false )
      | ( ( ~ ( price @ seventy @ SV18 ) )
        = $true )
      | ( ( rel_s4 @ SV9 @ SV18 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[104]) ).

thf(110,plain,
    ! [SV25: $i,SV19: $i,SV10: $i] :
      ( ( ( rel_s4 @ SV10 @ SV19 )
        = $false )
      | ( ( ~ ( rel_s4 @ SV19 @ SV25 ) )
        = $true )
      | ( ( rel_s4 @ SV10 @ SV25 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[105]) ).

thf(111,plain,
    ! [SV13: $i,SV21: $i] :
      ( ( ( ~ ( dest @ paris @ SV21 ) )
        = $true )
      | ( ( ~ ( class @ second @ SV21 ) )
        = $true )
      | ( ( price @ seventy @ SV21 )
        = $true )
      | ( ( rel_s4 @ SV13 @ SV21 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[106]) ).

thf(112,plain,
    ! [SV14: $i,SV22: $i] :
      ( ( ( ~ ( dest @ paris @ SV22 ) )
        = $true )
      | ( ( ~ ( class @ first @ SV22 ) )
        = $true )
      | ( ( price @ ninetyfive @ SV22 )
        = $true )
      | ( ( rel_s4 @ SV14 @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[107]) ).

thf(113,plain,
    ! [SV15: $i,SV23: $i] :
      ( ( ( class @ first @ SV23 )
        = $false )
      | ( ( ~ ( class @ second @ SV23 ) )
        = $true )
      | ( ( rel_s4 @ SV15 @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[108]) ).

thf(114,plain,
    ! [SV9: $i,SV18: $i] :
      ( ( ( price @ seventy @ SV18 )
        = $false )
      | ( ( price @ ninetyfive @ SV18 )
        = $false )
      | ( ( rel_s4 @ SV9 @ SV18 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[109]) ).

thf(115,plain,
    ! [SV10: $i,SV25: $i,SV19: $i] :
      ( ( ( rel_s4 @ SV19 @ SV25 )
        = $false )
      | ( ( rel_s4 @ SV10 @ SV19 )
        = $false )
      | ( ( rel_s4 @ SV10 @ SV25 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[110]) ).

thf(116,plain,
    ! [SV13: $i,SV21: $i] :
      ( ( ( dest @ paris @ SV21 )
        = $false )
      | ( ( ~ ( class @ second @ SV21 ) )
        = $true )
      | ( ( price @ seventy @ SV21 )
        = $true )
      | ( ( rel_s4 @ SV13 @ SV21 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(117,plain,
    ! [SV14: $i,SV22: $i] :
      ( ( ( dest @ paris @ SV22 )
        = $false )
      | ( ( ~ ( class @ first @ SV22 ) )
        = $true )
      | ( ( price @ ninetyfive @ SV22 )
        = $true )
      | ( ( rel_s4 @ SV14 @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[112]) ).

thf(118,plain,
    ! [SV15: $i,SV23: $i] :
      ( ( ( class @ second @ SV23 )
        = $false )
      | ( ( class @ first @ SV23 )
        = $false )
      | ( ( rel_s4 @ SV15 @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[113]) ).

thf(119,plain,
    ! [SV13: $i,SV21: $i] :
      ( ( ( class @ second @ SV21 )
        = $false )
      | ( ( dest @ paris @ SV21 )
        = $false )
      | ( ( price @ seventy @ SV21 )
        = $true )
      | ( ( rel_s4 @ SV13 @ SV21 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[116]) ).

thf(120,plain,
    ! [SV14: $i,SV22: $i] :
      ( ( ( class @ first @ SV22 )
        = $false )
      | ( ( dest @ paris @ SV22 )
        = $false )
      | ( ( price @ ninetyfive @ SV22 )
        = $true )
      | ( ( rel_s4 @ SV14 @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[117]) ).

thf(121,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[46,120,119,118,115,114,103,91,86,83,81,57,52,51,50,49,48]) ).

thf(122,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[121]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NLP264^7 : TPTP v8.1.0. Released v5.5.0.
% 0.06/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun 30 19:25:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 15
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 5508
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.36  (rf:0,axioms:15,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:17,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.19/0.45  
% 0.19/0.45  ********************************
% 0.19/0.45  *   All subproblems solved!    *
% 0.19/0.45  ********************************
% 0.19/0.45  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.45  
% 0.19/0.45  %**** Beginning of derivation protocol ****
% 0.19/0.45  % SZS output start CNFRefutation
% See solution above
% 0.19/0.45  
% 0.19/0.45  %**** End of derivation protocol ****
% 0.19/0.45  %**** no. of clauses in derivation: 122 ****
% 0.19/0.45  %**** clause counter: 121 ****
% 0.19/0.45  
% 0.19/0.45  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------