TSTP Solution File: PUZ087^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : PUZ087^1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n021.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 18:19:35 EDT 2022

% Result   : Theorem 0.46s 0.66s
% Output   : CNFRefutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :  122
% Syntax   : Number of formulae    :  622 ( 179 unt;  58 typ;  31 def)
%            Number of atoms       : 4737 (1204 equ;   0 cnn)
%            Maximal formula atoms :   12 (   8 avg)
%            Number of connectives : 6969 (1086   ~;1429   |;   8   &;4438   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  582 ( 582   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   60 (  57 usr;   4 con; 0-4 aty)
%            Number of variables   : 1835 (  83   ^1746   !;   6   ?;1835   :)

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

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

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

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

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

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_mcountersatisfiable,type,
    mcountersatisfiable: ( $i > $o ) > $o ).

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

thf(tp_meq_ind,type,
    meq_ind: mu > mu > $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_sK10_SY129,type,
    sK10_SY129: ( $i > $o ) > $i > $i ).

thf(tp_sK11_SY133,type,
    sK11_SY133: ( $i > $o ) > $i > $i ).

thf(tp_sK12_SY137,type,
    sK12_SY137: ( $i > $o ) > $i > $i ).

thf(tp_sK13_SY143,type,
    sK13_SY143: ( $i > $o ) > $i > $i ).

thf(tp_sK14_SY145,type,
    sK14_SY145: ( $i > $o ) > $i > $i ).

thf(tp_sK15_SY146,type,
    sK15_SY146: ( $i > $o ) > $i > $i ).

thf(tp_sK16_SY163,type,
    sK16_SY163: $i > $i > ( $i > $o ) > $i > $i ).

thf(tp_sK17_SY164,type,
    sK17_SY164: $i > $i > ( $i > $o ) > $i > $i ).

thf(tp_sK18_SY165,type,
    sK18_SY165: $i > $i > ( $i > $o ) > $i > $i ).

thf(tp_sK19_SY166,type,
    sK19_SY166: $i > $i > ( $i > $o ) > $i > $i ).

thf(tp_sK1_SX0,type,
    sK1_SX0: $i ).

thf(tp_sK20_SY167,type,
    sK20_SY167: $i > $i > ( $i > $o ) > $i > $i ).

thf(tp_sK21_SY168,type,
    sK21_SY168: $i > $i > ( $i > $o ) > $i > $i ).

thf(tp_sK2_SY2,type,
    sK2_SY2: $i > $i ).

thf(tp_sK3_SY52,type,
    sK3_SY52: $i > $i ).

thf(tp_sK4_SY132,type,
    sK4_SY132: $i ).

thf(tp_sK5_SY104,type,
    sK5_SY104: ( $i > $o ) > $i > $i ).

thf(tp_sK6_SY107,type,
    sK6_SY107: ( $i > $o ) > $i > $i ).

thf(tp_sK7_SY114,type,
    sK7_SY114: ( $i > $o ) > $i > $i ).

thf(tp_sK8_SY120,type,
    sK8_SY120: ( $i > $o ) > $i > $i ).

thf(tp_sK9_SY124,type,
    sK9_SY124: ( $i > $o ) > $i > $i ).

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

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(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(meq_ind,definition,
    ( meq_ind
    = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_ind) ).

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] : ( 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 @ ( mnot @ ( mbox @ b @ ( ws @ b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

thf(2,axiom,
    mvalid @ ( mnot @ ( mbox @ a @ ( ws @ a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

thf(3,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ Phi ) ) @ ( mbox @ b @ ( mnot @ ( mbox @ c @ Phi ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_c_b) ).

thf(4,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ Phi ) ) @ ( mbox @ a @ ( mnot @ ( mbox @ c @ Phi ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_c_a) ).

thf(5,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ b @ Phi ) ) @ ( mbox @ c @ ( mnot @ ( mbox @ b @ Phi ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_b_c) ).

thf(6,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ b @ Phi ) ) @ ( mbox @ a @ ( mnot @ ( mbox @ b @ Phi ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_b_a) ).

thf(7,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a @ Phi ) ) @ ( mbox @ c @ ( mnot @ ( mbox @ a @ Phi ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_a_c) ).

thf(8,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a @ Phi ) ) @ ( mbox @ b @ ( mnot @ ( mbox @ a @ Phi ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_a_b) ).

thf(9,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ c @ Phi ) @ ( mbox @ b @ ( mbox @ c @ Phi ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_c_b) ).

thf(10,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ c @ Phi ) @ ( mbox @ a @ ( mbox @ c @ Phi ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_c_a) ).

thf(11,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ b @ Phi ) @ ( mbox @ c @ ( mbox @ b @ Phi ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_b_c) ).

thf(12,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ b @ Phi ) @ ( mbox @ a @ ( mbox @ b @ Phi ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_b_a) ).

thf(13,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a @ Phi ) @ ( mbox @ c @ ( mbox @ a @ Phi ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_a_c) ).

thf(14,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a @ Phi ) @ ( mbox @ b @ ( mbox @ a @ Phi ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_a_b) ).

thf(15,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ c @ Phi ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_c) ).

thf(16,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ b @ Phi ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_b) ).

thf(17,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ a @ Phi ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_a) ).

thf(18,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ fool @ ( mbox @ fool @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_axiom_for_fool) ).

thf(19,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_axiom_for_fool) ).

thf(20,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ c ) ) @ ( mbox @ b @ ( mnot @ ( ws @ c ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_c_b) ).

thf(21,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ c ) ) @ ( mbox @ a @ ( mnot @ ( ws @ c ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_c_a) ).

thf(22,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ b ) ) @ ( mbox @ c @ ( mnot @ ( ws @ b ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_b_c) ).

thf(23,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ b ) ) @ ( mbox @ a @ ( mnot @ ( ws @ b ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_b_a) ).

thf(24,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ a ) ) @ ( mbox @ c @ ( mnot @ ( ws @ a ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_a_c) ).

thf(25,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ a ) ) @ ( mbox @ b @ ( mnot @ ( ws @ a ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_a_b) ).

thf(26,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ c ) @ ( mbox @ b @ ( ws @ c ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_c_b) ).

thf(27,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ c ) @ ( mbox @ a @ ( ws @ c ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_c_a) ).

thf(28,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ b ) @ ( mbox @ c @ ( ws @ b ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_b_c) ).

thf(29,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ b ) @ ( mbox @ a @ ( ws @ b ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_b_a) ).

thf(30,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ a ) @ ( mbox @ c @ ( ws @ a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_a_c) ).

thf(31,axiom,
    mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ a ) @ ( mbox @ b @ ( ws @ a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_a_b) ).

thf(32,axiom,
    mvalid @ ( mbox @ fool @ ( mor @ ( ws @ a ) @ ( mor @ ( ws @ b ) @ ( ws @ c ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

thf(33,conjecture,
    mvalid @ ( mbox @ c @ ( ws @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(34,negated_conjecture,
    ( ( mvalid @ ( mbox @ c @ ( ws @ c ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[33]) ).

thf(35,plain,
    ( ( ~ ( mvalid @ ( mbox @ c @ ( ws @ c ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[34]) ).

thf(36,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mor @ ( ws @ a ) @ ( mor @ ( ws @ b ) @ ( ws @ c ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(37,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ a ) @ ( mbox @ b @ ( ws @ a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(38,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ a ) @ ( mbox @ c @ ( ws @ a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(39,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ b ) @ ( mbox @ a @ ( ws @ b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(40,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ b ) @ ( mbox @ c @ ( ws @ b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(41,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ c ) @ ( mbox @ a @ ( ws @ c ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(42,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ c ) @ ( mbox @ b @ ( ws @ c ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(43,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ a ) ) @ ( mbox @ b @ ( mnot @ ( ws @ a ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(44,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ a ) ) @ ( mbox @ c @ ( mnot @ ( ws @ a ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(45,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ b ) ) @ ( mbox @ a @ ( mnot @ ( ws @ b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(46,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ b ) ) @ ( mbox @ c @ ( mnot @ ( ws @ b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(47,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ c ) ) @ ( mbox @ a @ ( mnot @ ( ws @ c ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(48,plain,
    ( ( mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ c ) ) @ ( mbox @ b @ ( mnot @ ( ws @ c ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(49,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(50,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ fool @ ( mbox @ fool @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(51,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ a @ Phi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(52,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ b @ Phi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(53,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ c @ Phi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(54,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a @ Phi ) @ ( mbox @ b @ ( mbox @ a @ Phi ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(55,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a @ Phi ) @ ( mbox @ c @ ( mbox @ a @ Phi ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(56,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ b @ Phi ) @ ( mbox @ a @ ( mbox @ b @ Phi ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(57,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ b @ Phi ) @ ( mbox @ c @ ( mbox @ b @ Phi ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(58,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ c @ Phi ) @ ( mbox @ a @ ( mbox @ c @ Phi ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(59,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ c @ Phi ) @ ( mbox @ b @ ( mbox @ c @ Phi ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(60,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a @ Phi ) ) @ ( mbox @ b @ ( mnot @ ( mbox @ a @ Phi ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(61,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a @ Phi ) ) @ ( mbox @ c @ ( mnot @ ( mbox @ a @ Phi ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(62,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ b @ Phi ) ) @ ( mbox @ a @ ( mnot @ ( mbox @ b @ Phi ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(63,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ b @ Phi ) ) @ ( mbox @ c @ ( mnot @ ( mbox @ b @ Phi ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(64,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ Phi ) ) @ ( mbox @ a @ ( mnot @ ( mbox @ c @ Phi ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[4]) ).

thf(65,plain,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ Phi ) ) @ ( mbox @ b @ ( mnot @ ( mbox @ c @ Phi ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[3]) ).

thf(66,plain,
    ( ( mvalid @ ( mnot @ ( mbox @ a @ ( ws @ a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2]) ).

thf(67,plain,
    ( ( mvalid @ ( mnot @ ( mbox @ b @ ( ws @ b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1]) ).

thf(68,plain,
    ( ( ~ ( mvalid @ ( mbox @ c @ ( ws @ c ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(69,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ~ ( ws @ a @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( b @ SX1 @ SX2 )
              | ~ ( ws @ a @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[43,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(70,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i] :
              ( ~ ( a @ SX0 @ SX1 )
              | ( ws @ a @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[66,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(71,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ( ws @ b @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( a @ SX1 @ SX2 )
              | ( ws @ b @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(72,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ~ ( ws @ b @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( c @ SX1 @ SX2 )
              | ~ ( ws @ b @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[46,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(73,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ( ws @ c @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( b @ SX1 @ SX2 )
              | ( ws @ c @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[42,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(74,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ( ws @ c @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( a @ SX1 @ SX2 )
              | ( ws @ c @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[41,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(75,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ( ~ ( c @ SX0 @ SX2 )
                  | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( a @ SX0 @ SX2 )
              | ~ ! [SX3: $i] :
                    ( ~ ( c @ SX2 @ SX3 )
                    | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[64,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(76,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ( ws @ a @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( b @ SX1 @ SX2 )
              | ( ws @ a @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(77,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ~ ( ws @ a @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( c @ SX1 @ SX2 )
              | ~ ( ws @ a @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[44,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(78,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ~ ( ws @ c @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( a @ SX1 @ SX2 )
              | ~ ( ws @ c @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[47,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(79,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ( ~ ( c @ SX0 @ SX2 )
                  | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( b @ SX0 @ SX2 )
              | ~ ! [SX3: $i] :
                    ( ~ ( c @ SX2 @ SX3 )
                    | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[65,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(80,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( fool @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( c @ SX0 @ SX2 )
              | ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[53,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(81,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ~ ( ws @ c @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( b @ SX1 @ SX2 )
              | ~ ( ws @ c @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[48,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(82,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( c @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( a @ SX0 @ SX2 )
              | ! [SX3: $i] :
                  ( ~ ( c @ SX2 @ SX3 )
                  | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[58,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(83,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ( ~ ( a @ SX0 @ SX2 )
                  | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( c @ SX0 @ SX2 )
              | ~ ! [SX3: $i] :
                    ( ~ ( a @ SX2 @ SX3 )
                    | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[61,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(84,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ( ws @ a @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( c @ SX1 @ SX2 )
              | ( ws @ a @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[38,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(85,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( c @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( b @ SX0 @ SX2 )
              | ! [SX3: $i] :
                  ( ~ ( c @ SX2 @ SX3 )
                  | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[59,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(86,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ( ~ ( a @ SX0 @ SX2 )
                  | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( b @ SX0 @ SX2 )
              | ~ ! [SX3: $i] :
                    ( ~ ( a @ SX2 @ SX3 )
                    | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[60,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(87,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( a @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( c @ SX0 @ SX2 )
              | ! [SX3: $i] :
                  ( ~ ( a @ SX2 @ SX3 )
                  | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[55,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(88,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i] :
              ( ~ ( b @ SX0 @ SX1 )
              | ( ws @ b @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[67,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(89,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ( ws @ b @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( c @ SX1 @ SX2 )
              | ( ws @ b @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[40,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(90,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( fool @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( a @ SX0 @ SX2 )
              | ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[51,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(91,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ( ~ ( b @ SX0 @ SX2 )
                  | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( c @ SX0 @ SX2 )
              | ~ ! [SX3: $i] :
                    ( ~ ( b @ SX2 @ SX3 )
                    | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[63,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(92,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( b @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( c @ SX0 @ SX2 )
              | ! [SX3: $i] :
                  ( ~ ( b @ SX2 @ SX3 )
                  | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[57,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(93,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( c @ SX0 @ SX1 )
            | ( ws @ c @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[68,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(94,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ( ws @ a @ SX1 )
          | ( ws @ b @ SX1 )
          | ( ws @ c @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(95,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( a @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( b @ SX0 @ SX2 )
              | ! [SX3: $i] :
                  ( ~ ( a @ SX2 @ SX3 )
                  | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[54,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(96,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( fool @ SX0 @ SX1 )
          | ~ ~ ( ws @ b @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( a @ SX1 @ SX2 )
              | ~ ( ws @ b @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[45,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(97,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( b @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( a @ SX0 @ SX2 )
              | ! [SX3: $i] :
                  ( ~ ( b @ SX2 @ SX3 )
                  | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[56,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(98,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ( ~ ( b @ SX0 @ SX2 )
                  | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( a @ SX0 @ SX2 )
              | ~ ! [SX3: $i] :
                    ( ~ ( b @ SX2 @ SX3 )
                    | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[62,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(99,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( fool @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( b @ SX0 @ SX2 )
              | ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[52,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(100,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( fool @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ( SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[49,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(101,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( fool @ SX0 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( fool @ SX0 @ SX2 )
              | ! [SX3: $i] :
                  ( ~ ( fool @ SX2 @ SX3 )
                  | ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[50,mand,mbox,mcountersatisfiable,mdia,meq_ind,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(102,plain,
    ! [SV1: $i] :
      ( ( ! [SY0: $i] :
            ( ~ ( fool @ SV1 @ SY0 )
            | ~ ~ ( ws @ a @ SY0 )
            | ! [SX2: $i] :
                ( ~ ( b @ SY0 @ SX2 )
                | ~ ( ws @ a @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(103,plain,
    ! [SV2: $i] :
      ( ( ~ ! [SY2: $i] :
              ( ~ ( a @ SV2 @ SY2 )
              | ( ws @ a @ SY2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(104,plain,
    ! [SV3: $i] :
      ( ( ! [SY3: $i] :
            ( ~ ( fool @ SV3 @ SY3 )
            | ~ ( ws @ b @ SY3 )
            | ! [SX2: $i] :
                ( ~ ( a @ SY3 @ SX2 )
                | ( ws @ b @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(105,plain,
    ! [SV4: $i] :
      ( ( ! [SY5: $i] :
            ( ~ ( fool @ SV4 @ SY5 )
            | ~ ~ ( ws @ b @ SY5 )
            | ! [SX2: $i] :
                ( ~ ( c @ SY5 @ SX2 )
                | ~ ( ws @ b @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(106,plain,
    ! [SV5: $i] :
      ( ( ! [SY7: $i] :
            ( ~ ( fool @ SV5 @ SY7 )
            | ~ ( ws @ c @ SY7 )
            | ! [SX2: $i] :
                ( ~ ( b @ SY7 @ SX2 )
                | ( ws @ c @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(107,plain,
    ! [SV6: $i] :
      ( ( ! [SY9: $i] :
            ( ~ ( fool @ SV6 @ SY9 )
            | ~ ( ws @ c @ SY9 )
            | ! [SX2: $i] :
                ( ~ ( a @ SY9 @ SX2 )
                | ( ws @ c @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(108,plain,
    ! [SV7: $i] :
      ( ( ! [SY11: $i > $o] :
            ( ~ ~ ! [SY12: $i] :
                    ( ~ ( c @ SV7 @ SY12 )
                    | ( SY11 @ SY12 ) )
            | ! [SY13: $i] :
                ( ~ ( a @ SV7 @ SY13 )
                | ~ ! [SX3: $i] :
                      ( ~ ( c @ SY13 @ SX3 )
                      | ( SY11 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(109,plain,
    ! [SV8: $i] :
      ( ( ! [SY15: $i] :
            ( ~ ( fool @ SV8 @ SY15 )
            | ~ ( ws @ a @ SY15 )
            | ! [SX2: $i] :
                ( ~ ( b @ SY15 @ SX2 )
                | ( ws @ a @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(110,plain,
    ! [SV9: $i] :
      ( ( ! [SY17: $i] :
            ( ~ ( fool @ SV9 @ SY17 )
            | ~ ~ ( ws @ a @ SY17 )
            | ! [SX2: $i] :
                ( ~ ( c @ SY17 @ SX2 )
                | ~ ( ws @ a @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(111,plain,
    ! [SV10: $i] :
      ( ( ! [SY19: $i] :
            ( ~ ( fool @ SV10 @ SY19 )
            | ~ ~ ( ws @ c @ SY19 )
            | ! [SX2: $i] :
                ( ~ ( a @ SY19 @ SX2 )
                | ~ ( ws @ c @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(112,plain,
    ! [SV11: $i] :
      ( ( ! [SY21: $i > $o] :
            ( ~ ~ ! [SY22: $i] :
                    ( ~ ( c @ SV11 @ SY22 )
                    | ( SY21 @ SY22 ) )
            | ! [SY23: $i] :
                ( ~ ( b @ SV11 @ SY23 )
                | ~ ! [SX3: $i] :
                      ( ~ ( c @ SY23 @ SX3 )
                      | ( SY21 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(113,plain,
    ! [SV12: $i] :
      ( ( ! [SY25: $i > $o] :
            ( ~ ! [SY26: $i] :
                  ( ~ ( fool @ SV12 @ SY26 )
                  | ( SY25 @ SY26 ) )
            | ! [SY27: $i] :
                ( ~ ( c @ SV12 @ SY27 )
                | ( SY25 @ SY27 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(114,plain,
    ! [SV13: $i] :
      ( ( ! [SY28: $i] :
            ( ~ ( fool @ SV13 @ SY28 )
            | ~ ~ ( ws @ c @ SY28 )
            | ! [SX2: $i] :
                ( ~ ( b @ SY28 @ SX2 )
                | ~ ( ws @ c @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(115,plain,
    ! [SV14: $i] :
      ( ( ! [SY30: $i > $o] :
            ( ~ ! [SY31: $i] :
                  ( ~ ( c @ SV14 @ SY31 )
                  | ( SY30 @ SY31 ) )
            | ! [SY32: $i] :
                ( ~ ( a @ SV14 @ SY32 )
                | ! [SX3: $i] :
                    ( ~ ( c @ SY32 @ SX3 )
                    | ( SY30 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(116,plain,
    ! [SV15: $i] :
      ( ( ! [SY34: $i > $o] :
            ( ~ ~ ! [SY35: $i] :
                    ( ~ ( a @ SV15 @ SY35 )
                    | ( SY34 @ SY35 ) )
            | ! [SY36: $i] :
                ( ~ ( c @ SV15 @ SY36 )
                | ~ ! [SX3: $i] :
                      ( ~ ( a @ SY36 @ SX3 )
                      | ( SY34 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(117,plain,
    ! [SV16: $i] :
      ( ( ! [SY38: $i] :
            ( ~ ( fool @ SV16 @ SY38 )
            | ~ ( ws @ a @ SY38 )
            | ! [SX2: $i] :
                ( ~ ( c @ SY38 @ SX2 )
                | ( ws @ a @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(118,plain,
    ! [SV17: $i] :
      ( ( ! [SY40: $i > $o] :
            ( ~ ! [SY41: $i] :
                  ( ~ ( c @ SV17 @ SY41 )
                  | ( SY40 @ SY41 ) )
            | ! [SY42: $i] :
                ( ~ ( b @ SV17 @ SY42 )
                | ! [SX3: $i] :
                    ( ~ ( c @ SY42 @ SX3 )
                    | ( SY40 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(119,plain,
    ! [SV18: $i] :
      ( ( ! [SY44: $i > $o] :
            ( ~ ~ ! [SY45: $i] :
                    ( ~ ( a @ SV18 @ SY45 )
                    | ( SY44 @ SY45 ) )
            | ! [SY46: $i] :
                ( ~ ( b @ SV18 @ SY46 )
                | ~ ! [SX3: $i] :
                      ( ~ ( a @ SY46 @ SX3 )
                      | ( SY44 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(120,plain,
    ! [SV19: $i] :
      ( ( ! [SY48: $i > $o] :
            ( ~ ! [SY49: $i] :
                  ( ~ ( a @ SV19 @ SY49 )
                  | ( SY48 @ SY49 ) )
            | ! [SY50: $i] :
                ( ~ ( c @ SV19 @ SY50 )
                | ! [SX3: $i] :
                    ( ~ ( a @ SY50 @ SX3 )
                    | ( SY48 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(121,plain,
    ! [SV20: $i] :
      ( ( ~ ! [SY52: $i] :
              ( ~ ( b @ SV20 @ SY52 )
              | ( ws @ b @ SY52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(122,plain,
    ! [SV21: $i] :
      ( ( ! [SY53: $i] :
            ( ~ ( fool @ SV21 @ SY53 )
            | ~ ( ws @ b @ SY53 )
            | ! [SX2: $i] :
                ( ~ ( c @ SY53 @ SX2 )
                | ( ws @ b @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(123,plain,
    ! [SV22: $i] :
      ( ( ! [SY55: $i > $o] :
            ( ~ ! [SY56: $i] :
                  ( ~ ( fool @ SV22 @ SY56 )
                  | ( SY55 @ SY56 ) )
            | ! [SY57: $i] :
                ( ~ ( a @ SV22 @ SY57 )
                | ( SY55 @ SY57 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(124,plain,
    ! [SV23: $i] :
      ( ( ! [SY58: $i > $o] :
            ( ~ ~ ! [SY59: $i] :
                    ( ~ ( b @ SV23 @ SY59 )
                    | ( SY58 @ SY59 ) )
            | ! [SY60: $i] :
                ( ~ ( c @ SV23 @ SY60 )
                | ~ ! [SX3: $i] :
                      ( ~ ( b @ SY60 @ SX3 )
                      | ( SY58 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(125,plain,
    ! [SV24: $i] :
      ( ( ! [SY62: $i > $o] :
            ( ~ ! [SY63: $i] :
                  ( ~ ( b @ SV24 @ SY63 )
                  | ( SY62 @ SY63 ) )
            | ! [SY64: $i] :
                ( ~ ( c @ SV24 @ SY64 )
                | ! [SX3: $i] :
                    ( ~ ( b @ SY64 @ SX3 )
                    | ( SY62 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(126,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( c @ SX0 @ SX1 )
          | ( ws @ c @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[93]) ).

thf(127,plain,
    ! [SV25: $i] :
      ( ( ! [SY66: $i] :
            ( ~ ( fool @ SV25 @ SY66 )
            | ( ws @ a @ SY66 )
            | ( ws @ b @ SY66 )
            | ( ws @ c @ SY66 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(128,plain,
    ! [SV26: $i] :
      ( ( ! [SY67: $i > $o] :
            ( ~ ! [SY68: $i] :
                  ( ~ ( a @ SV26 @ SY68 )
                  | ( SY67 @ SY68 ) )
            | ! [SY69: $i] :
                ( ~ ( b @ SV26 @ SY69 )
                | ! [SX3: $i] :
                    ( ~ ( a @ SY69 @ SX3 )
                    | ( SY67 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(129,plain,
    ! [SV27: $i] :
      ( ( ! [SY71: $i] :
            ( ~ ( fool @ SV27 @ SY71 )
            | ~ ~ ( ws @ b @ SY71 )
            | ! [SX2: $i] :
                ( ~ ( a @ SY71 @ SX2 )
                | ~ ( ws @ b @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(130,plain,
    ! [SV28: $i] :
      ( ( ! [SY73: $i > $o] :
            ( ~ ! [SY74: $i] :
                  ( ~ ( b @ SV28 @ SY74 )
                  | ( SY73 @ SY74 ) )
            | ! [SY75: $i] :
                ( ~ ( a @ SV28 @ SY75 )
                | ! [SX3: $i] :
                    ( ~ ( b @ SY75 @ SX3 )
                    | ( SY73 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(131,plain,
    ! [SV29: $i] :
      ( ( ! [SY77: $i > $o] :
            ( ~ ~ ! [SY78: $i] :
                    ( ~ ( b @ SV29 @ SY78 )
                    | ( SY77 @ SY78 ) )
            | ! [SY79: $i] :
                ( ~ ( a @ SV29 @ SY79 )
                | ~ ! [SX3: $i] :
                      ( ~ ( b @ SY79 @ SX3 )
                      | ( SY77 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(132,plain,
    ! [SV30: $i] :
      ( ( ! [SY81: $i > $o] :
            ( ~ ! [SY82: $i] :
                  ( ~ ( fool @ SV30 @ SY82 )
                  | ( SY81 @ SY82 ) )
            | ! [SY83: $i] :
                ( ~ ( b @ SV30 @ SY83 )
                | ( SY81 @ SY83 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[99]) ).

thf(133,plain,
    ! [SV31: $i] :
      ( ( ! [SY84: $i > $o] :
            ( ~ ! [SY85: $i] :
                  ( ~ ( fool @ SV31 @ SY85 )
                  | ( SY84 @ SY85 ) )
            | ( SY84 @ SV31 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[100]) ).

thf(134,plain,
    ! [SV32: $i] :
      ( ( ! [SY86: $i > $o] :
            ( ~ ! [SY87: $i] :
                  ( ~ ( fool @ SV32 @ SY87 )
                  | ( SY86 @ SY87 ) )
            | ! [SY88: $i] :
                ( ~ ( fool @ SV32 @ SY88 )
                | ! [SX3: $i] :
                    ( ~ ( fool @ SY88 @ SX3 )
                    | ( SY86 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(135,plain,
    ! [SV33: $i,SV1: $i] :
      ( ( ~ ( fool @ SV1 @ SV33 )
        | ~ ~ ( ws @ a @ SV33 )
        | ! [SY90: $i] :
            ( ~ ( b @ SV33 @ SY90 )
            | ~ ( ws @ a @ SY90 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[102]) ).

thf(136,plain,
    ! [SV2: $i] :
      ( ( ! [SY2: $i] :
            ( ~ ( a @ SV2 @ SY2 )
            | ( ws @ a @ SY2 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[103]) ).

thf(137,plain,
    ! [SV34: $i,SV3: $i] :
      ( ( ~ ( fool @ SV3 @ SV34 )
        | ~ ( ws @ b @ SV34 )
        | ! [SY91: $i] :
            ( ~ ( a @ SV34 @ SY91 )
            | ( ws @ b @ SY91 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[104]) ).

thf(138,plain,
    ! [SV35: $i,SV4: $i] :
      ( ( ~ ( fool @ SV4 @ SV35 )
        | ~ ~ ( ws @ b @ SV35 )
        | ! [SY92: $i] :
            ( ~ ( c @ SV35 @ SY92 )
            | ~ ( ws @ b @ SY92 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(139,plain,
    ! [SV36: $i,SV5: $i] :
      ( ( ~ ( fool @ SV5 @ SV36 )
        | ~ ( ws @ c @ SV36 )
        | ! [SY93: $i] :
            ( ~ ( b @ SV36 @ SY93 )
            | ( ws @ c @ SY93 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[106]) ).

thf(140,plain,
    ! [SV37: $i,SV6: $i] :
      ( ( ~ ( fool @ SV6 @ SV37 )
        | ~ ( ws @ c @ SV37 )
        | ! [SY94: $i] :
            ( ~ ( a @ SV37 @ SY94 )
            | ( ws @ c @ SY94 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(141,plain,
    ! [SV38: $i > $o,SV7: $i] :
      ( ( ~ ~ ! [SY95: $i] :
                ( ~ ( c @ SV7 @ SY95 )
                | ( SV38 @ SY95 ) )
        | ! [SY96: $i] :
            ( ~ ( a @ SV7 @ SY96 )
            | ~ ! [SY97: $i] :
                  ( ~ ( c @ SY96 @ SY97 )
                  | ( SV38 @ SY97 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(142,plain,
    ! [SV39: $i,SV8: $i] :
      ( ( ~ ( fool @ SV8 @ SV39 )
        | ~ ( ws @ a @ SV39 )
        | ! [SY98: $i] :
            ( ~ ( b @ SV39 @ SY98 )
            | ( ws @ a @ SY98 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(143,plain,
    ! [SV40: $i,SV9: $i] :
      ( ( ~ ( fool @ SV9 @ SV40 )
        | ~ ~ ( ws @ a @ SV40 )
        | ! [SY99: $i] :
            ( ~ ( c @ SV40 @ SY99 )
            | ~ ( ws @ a @ SY99 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(144,plain,
    ! [SV41: $i,SV10: $i] :
      ( ( ~ ( fool @ SV10 @ SV41 )
        | ~ ~ ( ws @ c @ SV41 )
        | ! [SY100: $i] :
            ( ~ ( a @ SV41 @ SY100 )
            | ~ ( ws @ c @ SY100 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[111]) ).

thf(145,plain,
    ! [SV42: $i > $o,SV11: $i] :
      ( ( ~ ~ ! [SY101: $i] :
                ( ~ ( c @ SV11 @ SY101 )
                | ( SV42 @ SY101 ) )
        | ! [SY102: $i] :
            ( ~ ( b @ SV11 @ SY102 )
            | ~ ! [SY103: $i] :
                  ( ~ ( c @ SY102 @ SY103 )
                  | ( SV42 @ SY103 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(146,plain,
    ! [SV43: $i > $o,SV12: $i] :
      ( ( ~ ! [SY104: $i] :
              ( ~ ( fool @ SV12 @ SY104 )
              | ( SV43 @ SY104 ) )
        | ! [SY105: $i] :
            ( ~ ( c @ SV12 @ SY105 )
            | ( SV43 @ SY105 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(147,plain,
    ! [SV44: $i,SV13: $i] :
      ( ( ~ ( fool @ SV13 @ SV44 )
        | ~ ~ ( ws @ c @ SV44 )
        | ! [SY106: $i] :
            ( ~ ( b @ SV44 @ SY106 )
            | ~ ( ws @ c @ SY106 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[114]) ).

thf(148,plain,
    ! [SV45: $i > $o,SV14: $i] :
      ( ( ~ ! [SY107: $i] :
              ( ~ ( c @ SV14 @ SY107 )
              | ( SV45 @ SY107 ) )
        | ! [SY108: $i] :
            ( ~ ( a @ SV14 @ SY108 )
            | ! [SY109: $i] :
                ( ~ ( c @ SY108 @ SY109 )
                | ( SV45 @ SY109 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(149,plain,
    ! [SV46: $i > $o,SV15: $i] :
      ( ( ~ ~ ! [SY110: $i] :
                ( ~ ( a @ SV15 @ SY110 )
                | ( SV46 @ SY110 ) )
        | ! [SY111: $i] :
            ( ~ ( c @ SV15 @ SY111 )
            | ~ ! [SY112: $i] :
                  ( ~ ( a @ SY111 @ SY112 )
                  | ( SV46 @ SY112 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(150,plain,
    ! [SV47: $i,SV16: $i] :
      ( ( ~ ( fool @ SV16 @ SV47 )
        | ~ ( ws @ a @ SV47 )
        | ! [SY113: $i] :
            ( ~ ( c @ SV47 @ SY113 )
            | ( ws @ a @ SY113 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[117]) ).

thf(151,plain,
    ! [SV48: $i > $o,SV17: $i] :
      ( ( ~ ! [SY114: $i] :
              ( ~ ( c @ SV17 @ SY114 )
              | ( SV48 @ SY114 ) )
        | ! [SY115: $i] :
            ( ~ ( b @ SV17 @ SY115 )
            | ! [SY116: $i] :
                ( ~ ( c @ SY115 @ SY116 )
                | ( SV48 @ SY116 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(152,plain,
    ! [SV49: $i > $o,SV18: $i] :
      ( ( ~ ~ ! [SY117: $i] :
                ( ~ ( a @ SV18 @ SY117 )
                | ( SV49 @ SY117 ) )
        | ! [SY118: $i] :
            ( ~ ( b @ SV18 @ SY118 )
            | ~ ! [SY119: $i] :
                  ( ~ ( a @ SY118 @ SY119 )
                  | ( SV49 @ SY119 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[119]) ).

thf(153,plain,
    ! [SV50: $i > $o,SV19: $i] :
      ( ( ~ ! [SY120: $i] :
              ( ~ ( a @ SV19 @ SY120 )
              | ( SV50 @ SY120 ) )
        | ! [SY121: $i] :
            ( ~ ( c @ SV19 @ SY121 )
            | ! [SY122: $i] :
                ( ~ ( a @ SY121 @ SY122 )
                | ( SV50 @ SY122 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(154,plain,
    ! [SV20: $i] :
      ( ( ! [SY52: $i] :
            ( ~ ( b @ SV20 @ SY52 )
            | ( ws @ b @ SY52 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(155,plain,
    ! [SV51: $i,SV21: $i] :
      ( ( ~ ( fool @ SV21 @ SV51 )
        | ~ ( ws @ b @ SV51 )
        | ! [SY123: $i] :
            ( ~ ( c @ SV51 @ SY123 )
            | ( ws @ b @ SY123 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(156,plain,
    ! [SV52: $i > $o,SV22: $i] :
      ( ( ~ ! [SY124: $i] :
              ( ~ ( fool @ SV22 @ SY124 )
              | ( SV52 @ SY124 ) )
        | ! [SY125: $i] :
            ( ~ ( a @ SV22 @ SY125 )
            | ( SV52 @ SY125 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(157,plain,
    ! [SV53: $i > $o,SV23: $i] :
      ( ( ~ ~ ! [SY126: $i] :
                ( ~ ( b @ SV23 @ SY126 )
                | ( SV53 @ SY126 ) )
        | ! [SY127: $i] :
            ( ~ ( c @ SV23 @ SY127 )
            | ~ ! [SY128: $i] :
                  ( ~ ( b @ SY127 @ SY128 )
                  | ( SV53 @ SY128 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(158,plain,
    ! [SV54: $i > $o,SV24: $i] :
      ( ( ~ ! [SY129: $i] :
              ( ~ ( b @ SV24 @ SY129 )
              | ( SV54 @ SY129 ) )
        | ! [SY130: $i] :
            ( ~ ( c @ SV24 @ SY130 )
            | ! [SY131: $i] :
                ( ~ ( b @ SY130 @ SY131 )
                | ( SV54 @ SY131 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[125]) ).

thf(159,plain,
    ( ( ! [SY132: $i] :
          ( ~ ( c @ sK1_SX0 @ SY132 )
          | ( ws @ c @ SY132 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[126]) ).

thf(160,plain,
    ! [SV55: $i,SV25: $i] :
      ( ( ~ ( fool @ SV25 @ SV55 )
        | ( ws @ a @ SV55 )
        | ( ws @ b @ SV55 )
        | ( ws @ c @ SV55 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[127]) ).

thf(161,plain,
    ! [SV56: $i > $o,SV26: $i] :
      ( ( ~ ! [SY133: $i] :
              ( ~ ( a @ SV26 @ SY133 )
              | ( SV56 @ SY133 ) )
        | ! [SY134: $i] :
            ( ~ ( b @ SV26 @ SY134 )
            | ! [SY135: $i] :
                ( ~ ( a @ SY134 @ SY135 )
                | ( SV56 @ SY135 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(162,plain,
    ! [SV57: $i,SV27: $i] :
      ( ( ~ ( fool @ SV27 @ SV57 )
        | ~ ~ ( ws @ b @ SV57 )
        | ! [SY136: $i] :
            ( ~ ( a @ SV57 @ SY136 )
            | ~ ( ws @ b @ SY136 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(163,plain,
    ! [SV58: $i > $o,SV28: $i] :
      ( ( ~ ! [SY137: $i] :
              ( ~ ( b @ SV28 @ SY137 )
              | ( SV58 @ SY137 ) )
        | ! [SY138: $i] :
            ( ~ ( a @ SV28 @ SY138 )
            | ! [SY139: $i] :
                ( ~ ( b @ SY138 @ SY139 )
                | ( SV58 @ SY139 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[130]) ).

thf(164,plain,
    ! [SV59: $i > $o,SV29: $i] :
      ( ( ~ ~ ! [SY140: $i] :
                ( ~ ( b @ SV29 @ SY140 )
                | ( SV59 @ SY140 ) )
        | ! [SY141: $i] :
            ( ~ ( a @ SV29 @ SY141 )
            | ~ ! [SY142: $i] :
                  ( ~ ( b @ SY141 @ SY142 )
                  | ( SV59 @ SY142 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[131]) ).

thf(165,plain,
    ! [SV60: $i > $o,SV30: $i] :
      ( ( ~ ! [SY143: $i] :
              ( ~ ( fool @ SV30 @ SY143 )
              | ( SV60 @ SY143 ) )
        | ! [SY144: $i] :
            ( ~ ( b @ SV30 @ SY144 )
            | ( SV60 @ SY144 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[132]) ).

thf(166,plain,
    ! [SV61: $i > $o,SV31: $i] :
      ( ( ~ ! [SY145: $i] :
              ( ~ ( fool @ SV31 @ SY145 )
              | ( SV61 @ SY145 ) )
        | ( SV61 @ SV31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(167,plain,
    ! [SV62: $i > $o,SV32: $i] :
      ( ( ~ ! [SY146: $i] :
              ( ~ ( fool @ SV32 @ SY146 )
              | ( SV62 @ SY146 ) )
        | ! [SY147: $i] :
            ( ~ ( fool @ SV32 @ SY147 )
            | ! [SY148: $i] :
                ( ~ ( fool @ SY147 @ SY148 )
                | ( SV62 @ SY148 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(168,plain,
    ! [SV33: $i,SV1: $i] :
      ( ( ( ~ ( fool @ SV1 @ SV33 ) )
        = $true )
      | ( ( ~ ~ ( ws @ a @ SV33 )
          | ! [SY90: $i] :
              ( ~ ( b @ SV33 @ SY90 )
              | ~ ( ws @ a @ SY90 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[135]) ).

thf(169,plain,
    ! [SV2: $i] :
      ( ( ~ ( a @ SV2 @ ( sK2_SY2 @ SV2 ) )
        | ( ws @ a @ ( sK2_SY2 @ SV2 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[136]) ).

thf(170,plain,
    ! [SV34: $i,SV3: $i] :
      ( ( ( ~ ( fool @ SV3 @ SV34 ) )
        = $true )
      | ( ( ~ ( ws @ b @ SV34 )
          | ! [SY91: $i] :
              ( ~ ( a @ SV34 @ SY91 )
              | ( ws @ b @ SY91 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[137]) ).

thf(171,plain,
    ! [SV35: $i,SV4: $i] :
      ( ( ( ~ ( fool @ SV4 @ SV35 ) )
        = $true )
      | ( ( ~ ~ ( ws @ b @ SV35 )
          | ! [SY92: $i] :
              ( ~ ( c @ SV35 @ SY92 )
              | ~ ( ws @ b @ SY92 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[138]) ).

thf(172,plain,
    ! [SV36: $i,SV5: $i] :
      ( ( ( ~ ( fool @ SV5 @ SV36 ) )
        = $true )
      | ( ( ~ ( ws @ c @ SV36 )
          | ! [SY93: $i] :
              ( ~ ( b @ SV36 @ SY93 )
              | ( ws @ c @ SY93 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[139]) ).

thf(173,plain,
    ! [SV37: $i,SV6: $i] :
      ( ( ( ~ ( fool @ SV6 @ SV37 ) )
        = $true )
      | ( ( ~ ( ws @ c @ SV37 )
          | ! [SY94: $i] :
              ( ~ ( a @ SV37 @ SY94 )
              | ( ws @ c @ SY94 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[140]) ).

thf(174,plain,
    ! [SV38: $i > $o,SV7: $i] :
      ( ( ( ~ ~ ! [SY95: $i] :
                  ( ~ ( c @ SV7 @ SY95 )
                  | ( SV38 @ SY95 ) ) )
        = $true )
      | ( ( ! [SY96: $i] :
              ( ~ ( a @ SV7 @ SY96 )
              | ~ ! [SY97: $i] :
                    ( ~ ( c @ SY96 @ SY97 )
                    | ( SV38 @ SY97 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[141]) ).

thf(175,plain,
    ! [SV39: $i,SV8: $i] :
      ( ( ( ~ ( fool @ SV8 @ SV39 ) )
        = $true )
      | ( ( ~ ( ws @ a @ SV39 )
          | ! [SY98: $i] :
              ( ~ ( b @ SV39 @ SY98 )
              | ( ws @ a @ SY98 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[142]) ).

thf(176,plain,
    ! [SV40: $i,SV9: $i] :
      ( ( ( ~ ( fool @ SV9 @ SV40 ) )
        = $true )
      | ( ( ~ ~ ( ws @ a @ SV40 )
          | ! [SY99: $i] :
              ( ~ ( c @ SV40 @ SY99 )
              | ~ ( ws @ a @ SY99 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[143]) ).

thf(177,plain,
    ! [SV41: $i,SV10: $i] :
      ( ( ( ~ ( fool @ SV10 @ SV41 ) )
        = $true )
      | ( ( ~ ~ ( ws @ c @ SV41 )
          | ! [SY100: $i] :
              ( ~ ( a @ SV41 @ SY100 )
              | ~ ( ws @ c @ SY100 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[144]) ).

thf(178,plain,
    ! [SV42: $i > $o,SV11: $i] :
      ( ( ( ~ ~ ! [SY101: $i] :
                  ( ~ ( c @ SV11 @ SY101 )
                  | ( SV42 @ SY101 ) ) )
        = $true )
      | ( ( ! [SY102: $i] :
              ( ~ ( b @ SV11 @ SY102 )
              | ~ ! [SY103: $i] :
                    ( ~ ( c @ SY102 @ SY103 )
                    | ( SV42 @ SY103 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[145]) ).

thf(179,plain,
    ! [SV43: $i > $o,SV12: $i] :
      ( ( ( ~ ! [SY104: $i] :
                ( ~ ( fool @ SV12 @ SY104 )
                | ( SV43 @ SY104 ) ) )
        = $true )
      | ( ( ! [SY105: $i] :
              ( ~ ( c @ SV12 @ SY105 )
              | ( SV43 @ SY105 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[146]) ).

thf(180,plain,
    ! [SV44: $i,SV13: $i] :
      ( ( ( ~ ( fool @ SV13 @ SV44 ) )
        = $true )
      | ( ( ~ ~ ( ws @ c @ SV44 )
          | ! [SY106: $i] :
              ( ~ ( b @ SV44 @ SY106 )
              | ~ ( ws @ c @ SY106 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[147]) ).

thf(181,plain,
    ! [SV45: $i > $o,SV14: $i] :
      ( ( ( ~ ! [SY107: $i] :
                ( ~ ( c @ SV14 @ SY107 )
                | ( SV45 @ SY107 ) ) )
        = $true )
      | ( ( ! [SY108: $i] :
              ( ~ ( a @ SV14 @ SY108 )
              | ! [SY109: $i] :
                  ( ~ ( c @ SY108 @ SY109 )
                  | ( SV45 @ SY109 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[148]) ).

thf(182,plain,
    ! [SV46: $i > $o,SV15: $i] :
      ( ( ( ~ ~ ! [SY110: $i] :
                  ( ~ ( a @ SV15 @ SY110 )
                  | ( SV46 @ SY110 ) ) )
        = $true )
      | ( ( ! [SY111: $i] :
              ( ~ ( c @ SV15 @ SY111 )
              | ~ ! [SY112: $i] :
                    ( ~ ( a @ SY111 @ SY112 )
                    | ( SV46 @ SY112 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[149]) ).

thf(183,plain,
    ! [SV47: $i,SV16: $i] :
      ( ( ( ~ ( fool @ SV16 @ SV47 ) )
        = $true )
      | ( ( ~ ( ws @ a @ SV47 )
          | ! [SY113: $i] :
              ( ~ ( c @ SV47 @ SY113 )
              | ( ws @ a @ SY113 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[150]) ).

thf(184,plain,
    ! [SV48: $i > $o,SV17: $i] :
      ( ( ( ~ ! [SY114: $i] :
                ( ~ ( c @ SV17 @ SY114 )
                | ( SV48 @ SY114 ) ) )
        = $true )
      | ( ( ! [SY115: $i] :
              ( ~ ( b @ SV17 @ SY115 )
              | ! [SY116: $i] :
                  ( ~ ( c @ SY115 @ SY116 )
                  | ( SV48 @ SY116 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[151]) ).

thf(185,plain,
    ! [SV49: $i > $o,SV18: $i] :
      ( ( ( ~ ~ ! [SY117: $i] :
                  ( ~ ( a @ SV18 @ SY117 )
                  | ( SV49 @ SY117 ) ) )
        = $true )
      | ( ( ! [SY118: $i] :
              ( ~ ( b @ SV18 @ SY118 )
              | ~ ! [SY119: $i] :
                    ( ~ ( a @ SY118 @ SY119 )
                    | ( SV49 @ SY119 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[152]) ).

thf(186,plain,
    ! [SV50: $i > $o,SV19: $i] :
      ( ( ( ~ ! [SY120: $i] :
                ( ~ ( a @ SV19 @ SY120 )
                | ( SV50 @ SY120 ) ) )
        = $true )
      | ( ( ! [SY121: $i] :
              ( ~ ( c @ SV19 @ SY121 )
              | ! [SY122: $i] :
                  ( ~ ( a @ SY121 @ SY122 )
                  | ( SV50 @ SY122 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[153]) ).

thf(187,plain,
    ! [SV20: $i] :
      ( ( ~ ( b @ SV20 @ ( sK3_SY52 @ SV20 ) )
        | ( ws @ b @ ( sK3_SY52 @ SV20 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[154]) ).

thf(188,plain,
    ! [SV51: $i,SV21: $i] :
      ( ( ( ~ ( fool @ SV21 @ SV51 ) )
        = $true )
      | ( ( ~ ( ws @ b @ SV51 )
          | ! [SY123: $i] :
              ( ~ ( c @ SV51 @ SY123 )
              | ( ws @ b @ SY123 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[155]) ).

thf(189,plain,
    ! [SV52: $i > $o,SV22: $i] :
      ( ( ( ~ ! [SY124: $i] :
                ( ~ ( fool @ SV22 @ SY124 )
                | ( SV52 @ SY124 ) ) )
        = $true )
      | ( ( ! [SY125: $i] :
              ( ~ ( a @ SV22 @ SY125 )
              | ( SV52 @ SY125 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[156]) ).

thf(190,plain,
    ! [SV53: $i > $o,SV23: $i] :
      ( ( ( ~ ~ ! [SY126: $i] :
                  ( ~ ( b @ SV23 @ SY126 )
                  | ( SV53 @ SY126 ) ) )
        = $true )
      | ( ( ! [SY127: $i] :
              ( ~ ( c @ SV23 @ SY127 )
              | ~ ! [SY128: $i] :
                    ( ~ ( b @ SY127 @ SY128 )
                    | ( SV53 @ SY128 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[157]) ).

thf(191,plain,
    ! [SV54: $i > $o,SV24: $i] :
      ( ( ( ~ ! [SY129: $i] :
                ( ~ ( b @ SV24 @ SY129 )
                | ( SV54 @ SY129 ) ) )
        = $true )
      | ( ( ! [SY130: $i] :
              ( ~ ( c @ SV24 @ SY130 )
              | ! [SY131: $i] :
                  ( ~ ( b @ SY130 @ SY131 )
                  | ( SV54 @ SY131 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[158]) ).

thf(192,plain,
    ( ( ~ ( c @ sK1_SX0 @ sK4_SY132 )
      | ( ws @ c @ sK4_SY132 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[159]) ).

thf(193,plain,
    ! [SV55: $i,SV25: $i] :
      ( ( ( ~ ( fool @ SV25 @ SV55 ) )
        = $true )
      | ( ( ( ws @ a @ SV55 )
          | ( ws @ b @ SV55 )
          | ( ws @ c @ SV55 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[160]) ).

thf(194,plain,
    ! [SV56: $i > $o,SV26: $i] :
      ( ( ( ~ ! [SY133: $i] :
                ( ~ ( a @ SV26 @ SY133 )
                | ( SV56 @ SY133 ) ) )
        = $true )
      | ( ( ! [SY134: $i] :
              ( ~ ( b @ SV26 @ SY134 )
              | ! [SY135: $i] :
                  ( ~ ( a @ SY134 @ SY135 )
                  | ( SV56 @ SY135 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[161]) ).

thf(195,plain,
    ! [SV57: $i,SV27: $i] :
      ( ( ( ~ ( fool @ SV27 @ SV57 ) )
        = $true )
      | ( ( ~ ~ ( ws @ b @ SV57 )
          | ! [SY136: $i] :
              ( ~ ( a @ SV57 @ SY136 )
              | ~ ( ws @ b @ SY136 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[162]) ).

thf(196,plain,
    ! [SV58: $i > $o,SV28: $i] :
      ( ( ( ~ ! [SY137: $i] :
                ( ~ ( b @ SV28 @ SY137 )
                | ( SV58 @ SY137 ) ) )
        = $true )
      | ( ( ! [SY138: $i] :
              ( ~ ( a @ SV28 @ SY138 )
              | ! [SY139: $i] :
                  ( ~ ( b @ SY138 @ SY139 )
                  | ( SV58 @ SY139 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[163]) ).

thf(197,plain,
    ! [SV59: $i > $o,SV29: $i] :
      ( ( ( ~ ~ ! [SY140: $i] :
                  ( ~ ( b @ SV29 @ SY140 )
                  | ( SV59 @ SY140 ) ) )
        = $true )
      | ( ( ! [SY141: $i] :
              ( ~ ( a @ SV29 @ SY141 )
              | ~ ! [SY142: $i] :
                    ( ~ ( b @ SY141 @ SY142 )
                    | ( SV59 @ SY142 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[164]) ).

thf(198,plain,
    ! [SV60: $i > $o,SV30: $i] :
      ( ( ( ~ ! [SY143: $i] :
                ( ~ ( fool @ SV30 @ SY143 )
                | ( SV60 @ SY143 ) ) )
        = $true )
      | ( ( ! [SY144: $i] :
              ( ~ ( b @ SV30 @ SY144 )
              | ( SV60 @ SY144 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[165]) ).

thf(199,plain,
    ! [SV61: $i > $o,SV31: $i] :
      ( ( ( ~ ! [SY145: $i] :
                ( ~ ( fool @ SV31 @ SY145 )
                | ( SV61 @ SY145 ) ) )
        = $true )
      | ( ( SV61 @ SV31 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[166]) ).

thf(200,plain,
    ! [SV62: $i > $o,SV32: $i] :
      ( ( ( ~ ! [SY146: $i] :
                ( ~ ( fool @ SV32 @ SY146 )
                | ( SV62 @ SY146 ) ) )
        = $true )
      | ( ( ! [SY147: $i] :
              ( ~ ( fool @ SV32 @ SY147 )
              | ! [SY148: $i] :
                  ( ~ ( fool @ SY147 @ SY148 )
                  | ( SV62 @ SY148 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[167]) ).

thf(201,plain,
    ! [SV33: $i,SV1: $i] :
      ( ( ( fool @ SV1 @ SV33 )
        = $false )
      | ( ( ~ ~ ( ws @ a @ SV33 )
          | ! [SY90: $i] :
              ( ~ ( b @ SV33 @ SY90 )
              | ~ ( ws @ a @ SY90 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[168]) ).

thf(202,plain,
    ! [SV2: $i] :
      ( ( ~ ( a @ SV2 @ ( sK2_SY2 @ SV2 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[169]) ).

thf(203,plain,
    ! [SV2: $i] :
      ( ( ws @ a @ ( sK2_SY2 @ SV2 ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[169]) ).

thf(204,plain,
    ! [SV34: $i,SV3: $i] :
      ( ( ( fool @ SV3 @ SV34 )
        = $false )
      | ( ( ~ ( ws @ b @ SV34 )
          | ! [SY91: $i] :
              ( ~ ( a @ SV34 @ SY91 )
              | ( ws @ b @ SY91 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[170]) ).

thf(205,plain,
    ! [SV35: $i,SV4: $i] :
      ( ( ( fool @ SV4 @ SV35 )
        = $false )
      | ( ( ~ ~ ( ws @ b @ SV35 )
          | ! [SY92: $i] :
              ( ~ ( c @ SV35 @ SY92 )
              | ~ ( ws @ b @ SY92 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[171]) ).

thf(206,plain,
    ! [SV36: $i,SV5: $i] :
      ( ( ( fool @ SV5 @ SV36 )
        = $false )
      | ( ( ~ ( ws @ c @ SV36 )
          | ! [SY93: $i] :
              ( ~ ( b @ SV36 @ SY93 )
              | ( ws @ c @ SY93 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[172]) ).

thf(207,plain,
    ! [SV37: $i,SV6: $i] :
      ( ( ( fool @ SV6 @ SV37 )
        = $false )
      | ( ( ~ ( ws @ c @ SV37 )
          | ! [SY94: $i] :
              ( ~ ( a @ SV37 @ SY94 )
              | ( ws @ c @ SY94 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[173]) ).

thf(208,plain,
    ! [SV38: $i > $o,SV7: $i] :
      ( ( ( ~ ! [SY95: $i] :
                ( ~ ( c @ SV7 @ SY95 )
                | ( SV38 @ SY95 ) ) )
        = $false )
      | ( ( ! [SY96: $i] :
              ( ~ ( a @ SV7 @ SY96 )
              | ~ ! [SY97: $i] :
                    ( ~ ( c @ SY96 @ SY97 )
                    | ( SV38 @ SY97 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[174]) ).

thf(209,plain,
    ! [SV39: $i,SV8: $i] :
      ( ( ( fool @ SV8 @ SV39 )
        = $false )
      | ( ( ~ ( ws @ a @ SV39 )
          | ! [SY98: $i] :
              ( ~ ( b @ SV39 @ SY98 )
              | ( ws @ a @ SY98 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[175]) ).

thf(210,plain,
    ! [SV40: $i,SV9: $i] :
      ( ( ( fool @ SV9 @ SV40 )
        = $false )
      | ( ( ~ ~ ( ws @ a @ SV40 )
          | ! [SY99: $i] :
              ( ~ ( c @ SV40 @ SY99 )
              | ~ ( ws @ a @ SY99 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[176]) ).

thf(211,plain,
    ! [SV41: $i,SV10: $i] :
      ( ( ( fool @ SV10 @ SV41 )
        = $false )
      | ( ( ~ ~ ( ws @ c @ SV41 )
          | ! [SY100: $i] :
              ( ~ ( a @ SV41 @ SY100 )
              | ~ ( ws @ c @ SY100 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[177]) ).

thf(212,plain,
    ! [SV42: $i > $o,SV11: $i] :
      ( ( ( ~ ! [SY101: $i] :
                ( ~ ( c @ SV11 @ SY101 )
                | ( SV42 @ SY101 ) ) )
        = $false )
      | ( ( ! [SY102: $i] :
              ( ~ ( b @ SV11 @ SY102 )
              | ~ ! [SY103: $i] :
                    ( ~ ( c @ SY102 @ SY103 )
                    | ( SV42 @ SY103 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[178]) ).

thf(213,plain,
    ! [SV43: $i > $o,SV12: $i] :
      ( ( ( ! [SY104: $i] :
              ( ~ ( fool @ SV12 @ SY104 )
              | ( SV43 @ SY104 ) ) )
        = $false )
      | ( ( ! [SY105: $i] :
              ( ~ ( c @ SV12 @ SY105 )
              | ( SV43 @ SY105 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[179]) ).

thf(214,plain,
    ! [SV44: $i,SV13: $i] :
      ( ( ( fool @ SV13 @ SV44 )
        = $false )
      | ( ( ~ ~ ( ws @ c @ SV44 )
          | ! [SY106: $i] :
              ( ~ ( b @ SV44 @ SY106 )
              | ~ ( ws @ c @ SY106 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[180]) ).

thf(215,plain,
    ! [SV45: $i > $o,SV14: $i] :
      ( ( ( ! [SY107: $i] :
              ( ~ ( c @ SV14 @ SY107 )
              | ( SV45 @ SY107 ) ) )
        = $false )
      | ( ( ! [SY108: $i] :
              ( ~ ( a @ SV14 @ SY108 )
              | ! [SY109: $i] :
                  ( ~ ( c @ SY108 @ SY109 )
                  | ( SV45 @ SY109 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[181]) ).

thf(216,plain,
    ! [SV46: $i > $o,SV15: $i] :
      ( ( ( ~ ! [SY110: $i] :
                ( ~ ( a @ SV15 @ SY110 )
                | ( SV46 @ SY110 ) ) )
        = $false )
      | ( ( ! [SY111: $i] :
              ( ~ ( c @ SV15 @ SY111 )
              | ~ ! [SY112: $i] :
                    ( ~ ( a @ SY111 @ SY112 )
                    | ( SV46 @ SY112 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[182]) ).

thf(217,plain,
    ! [SV47: $i,SV16: $i] :
      ( ( ( fool @ SV16 @ SV47 )
        = $false )
      | ( ( ~ ( ws @ a @ SV47 )
          | ! [SY113: $i] :
              ( ~ ( c @ SV47 @ SY113 )
              | ( ws @ a @ SY113 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[183]) ).

thf(218,plain,
    ! [SV48: $i > $o,SV17: $i] :
      ( ( ( ! [SY114: $i] :
              ( ~ ( c @ SV17 @ SY114 )
              | ( SV48 @ SY114 ) ) )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ~ ( b @ SV17 @ SY115 )
              | ! [SY116: $i] :
                  ( ~ ( c @ SY115 @ SY116 )
                  | ( SV48 @ SY116 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[184]) ).

thf(219,plain,
    ! [SV49: $i > $o,SV18: $i] :
      ( ( ( ~ ! [SY117: $i] :
                ( ~ ( a @ SV18 @ SY117 )
                | ( SV49 @ SY117 ) ) )
        = $false )
      | ( ( ! [SY118: $i] :
              ( ~ ( b @ SV18 @ SY118 )
              | ~ ! [SY119: $i] :
                    ( ~ ( a @ SY118 @ SY119 )
                    | ( SV49 @ SY119 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[185]) ).

thf(220,plain,
    ! [SV50: $i > $o,SV19: $i] :
      ( ( ( ! [SY120: $i] :
              ( ~ ( a @ SV19 @ SY120 )
              | ( SV50 @ SY120 ) ) )
        = $false )
      | ( ( ! [SY121: $i] :
              ( ~ ( c @ SV19 @ SY121 )
              | ! [SY122: $i] :
                  ( ~ ( a @ SY121 @ SY122 )
                  | ( SV50 @ SY122 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[186]) ).

thf(221,plain,
    ! [SV20: $i] :
      ( ( ~ ( b @ SV20 @ ( sK3_SY52 @ SV20 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(222,plain,
    ! [SV20: $i] :
      ( ( ws @ b @ ( sK3_SY52 @ SV20 ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(223,plain,
    ! [SV51: $i,SV21: $i] :
      ( ( ( fool @ SV21 @ SV51 )
        = $false )
      | ( ( ~ ( ws @ b @ SV51 )
          | ! [SY123: $i] :
              ( ~ ( c @ SV51 @ SY123 )
              | ( ws @ b @ SY123 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[188]) ).

thf(224,plain,
    ! [SV52: $i > $o,SV22: $i] :
      ( ( ( ! [SY124: $i] :
              ( ~ ( fool @ SV22 @ SY124 )
              | ( SV52 @ SY124 ) ) )
        = $false )
      | ( ( ! [SY125: $i] :
              ( ~ ( a @ SV22 @ SY125 )
              | ( SV52 @ SY125 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[189]) ).

thf(225,plain,
    ! [SV53: $i > $o,SV23: $i] :
      ( ( ( ~ ! [SY126: $i] :
                ( ~ ( b @ SV23 @ SY126 )
                | ( SV53 @ SY126 ) ) )
        = $false )
      | ( ( ! [SY127: $i] :
              ( ~ ( c @ SV23 @ SY127 )
              | ~ ! [SY128: $i] :
                    ( ~ ( b @ SY127 @ SY128 )
                    | ( SV53 @ SY128 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[190]) ).

thf(226,plain,
    ! [SV54: $i > $o,SV24: $i] :
      ( ( ( ! [SY129: $i] :
              ( ~ ( b @ SV24 @ SY129 )
              | ( SV54 @ SY129 ) ) )
        = $false )
      | ( ( ! [SY130: $i] :
              ( ~ ( c @ SV24 @ SY130 )
              | ! [SY131: $i] :
                  ( ~ ( b @ SY130 @ SY131 )
                  | ( SV54 @ SY131 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[191]) ).

thf(227,plain,
    ( ( ~ ( c @ sK1_SX0 @ sK4_SY132 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[192]) ).

thf(228,plain,
    ( ( ws @ c @ sK4_SY132 )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[192]) ).

thf(229,plain,
    ! [SV55: $i,SV25: $i] :
      ( ( ( fool @ SV25 @ SV55 )
        = $false )
      | ( ( ( ws @ a @ SV55 )
          | ( ws @ b @ SV55 )
          | ( ws @ c @ SV55 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[193]) ).

thf(230,plain,
    ! [SV56: $i > $o,SV26: $i] :
      ( ( ( ! [SY133: $i] :
              ( ~ ( a @ SV26 @ SY133 )
              | ( SV56 @ SY133 ) ) )
        = $false )
      | ( ( ! [SY134: $i] :
              ( ~ ( b @ SV26 @ SY134 )
              | ! [SY135: $i] :
                  ( ~ ( a @ SY134 @ SY135 )
                  | ( SV56 @ SY135 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[194]) ).

thf(231,plain,
    ! [SV57: $i,SV27: $i] :
      ( ( ( fool @ SV27 @ SV57 )
        = $false )
      | ( ( ~ ~ ( ws @ b @ SV57 )
          | ! [SY136: $i] :
              ( ~ ( a @ SV57 @ SY136 )
              | ~ ( ws @ b @ SY136 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[195]) ).

thf(232,plain,
    ! [SV58: $i > $o,SV28: $i] :
      ( ( ( ! [SY137: $i] :
              ( ~ ( b @ SV28 @ SY137 )
              | ( SV58 @ SY137 ) ) )
        = $false )
      | ( ( ! [SY138: $i] :
              ( ~ ( a @ SV28 @ SY138 )
              | ! [SY139: $i] :
                  ( ~ ( b @ SY138 @ SY139 )
                  | ( SV58 @ SY139 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[196]) ).

thf(233,plain,
    ! [SV59: $i > $o,SV29: $i] :
      ( ( ( ~ ! [SY140: $i] :
                ( ~ ( b @ SV29 @ SY140 )
                | ( SV59 @ SY140 ) ) )
        = $false )
      | ( ( ! [SY141: $i] :
              ( ~ ( a @ SV29 @ SY141 )
              | ~ ! [SY142: $i] :
                    ( ~ ( b @ SY141 @ SY142 )
                    | ( SV59 @ SY142 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[197]) ).

thf(234,plain,
    ! [SV60: $i > $o,SV30: $i] :
      ( ( ( ! [SY143: $i] :
              ( ~ ( fool @ SV30 @ SY143 )
              | ( SV60 @ SY143 ) ) )
        = $false )
      | ( ( ! [SY144: $i] :
              ( ~ ( b @ SV30 @ SY144 )
              | ( SV60 @ SY144 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[198]) ).

thf(235,plain,
    ! [SV61: $i > $o,SV31: $i] :
      ( ( ( ! [SY145: $i] :
              ( ~ ( fool @ SV31 @ SY145 )
              | ( SV61 @ SY145 ) ) )
        = $false )
      | ( ( SV61 @ SV31 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[199]) ).

thf(236,plain,
    ! [SV62: $i > $o,SV32: $i] :
      ( ( ( ! [SY146: $i] :
              ( ~ ( fool @ SV32 @ SY146 )
              | ( SV62 @ SY146 ) ) )
        = $false )
      | ( ( ! [SY147: $i] :
              ( ~ ( fool @ SV32 @ SY147 )
              | ! [SY148: $i] :
                  ( ~ ( fool @ SY147 @ SY148 )
                  | ( SV62 @ SY148 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[200]) ).

thf(237,plain,
    ! [SV1: $i,SV33: $i] :
      ( ( ( ~ ~ ( ws @ a @ SV33 ) )
        = $true )
      | ( ( ! [SY90: $i] :
              ( ~ ( b @ SV33 @ SY90 )
              | ~ ( ws @ a @ SY90 ) ) )
        = $true )
      | ( ( fool @ SV1 @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[201]) ).

thf(238,plain,
    ! [SV2: $i] :
      ( ( a @ SV2 @ ( sK2_SY2 @ SV2 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[202]) ).

thf(239,plain,
    ! [SV3: $i,SV34: $i] :
      ( ( ( ~ ( ws @ b @ SV34 ) )
        = $true )
      | ( ( ! [SY91: $i] :
              ( ~ ( a @ SV34 @ SY91 )
              | ( ws @ b @ SY91 ) ) )
        = $true )
      | ( ( fool @ SV3 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[204]) ).

thf(240,plain,
    ! [SV4: $i,SV35: $i] :
      ( ( ( ~ ~ ( ws @ b @ SV35 ) )
        = $true )
      | ( ( ! [SY92: $i] :
              ( ~ ( c @ SV35 @ SY92 )
              | ~ ( ws @ b @ SY92 ) ) )
        = $true )
      | ( ( fool @ SV4 @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[205]) ).

thf(241,plain,
    ! [SV5: $i,SV36: $i] :
      ( ( ( ~ ( ws @ c @ SV36 ) )
        = $true )
      | ( ( ! [SY93: $i] :
              ( ~ ( b @ SV36 @ SY93 )
              | ( ws @ c @ SY93 ) ) )
        = $true )
      | ( ( fool @ SV5 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[206]) ).

thf(242,plain,
    ! [SV6: $i,SV37: $i] :
      ( ( ( ~ ( ws @ c @ SV37 ) )
        = $true )
      | ( ( ! [SY94: $i] :
              ( ~ ( a @ SV37 @ SY94 )
              | ( ws @ c @ SY94 ) ) )
        = $true )
      | ( ( fool @ SV6 @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[207]) ).

thf(243,plain,
    ! [SV38: $i > $o,SV7: $i] :
      ( ( ( ! [SY95: $i] :
              ( ~ ( c @ SV7 @ SY95 )
              | ( SV38 @ SY95 ) ) )
        = $true )
      | ( ( ! [SY96: $i] :
              ( ~ ( a @ SV7 @ SY96 )
              | ~ ! [SY97: $i] :
                    ( ~ ( c @ SY96 @ SY97 )
                    | ( SV38 @ SY97 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[208]) ).

thf(244,plain,
    ! [SV8: $i,SV39: $i] :
      ( ( ( ~ ( ws @ a @ SV39 ) )
        = $true )
      | ( ( ! [SY98: $i] :
              ( ~ ( b @ SV39 @ SY98 )
              | ( ws @ a @ SY98 ) ) )
        = $true )
      | ( ( fool @ SV8 @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[209]) ).

thf(245,plain,
    ! [SV9: $i,SV40: $i] :
      ( ( ( ~ ~ ( ws @ a @ SV40 ) )
        = $true )
      | ( ( ! [SY99: $i] :
              ( ~ ( c @ SV40 @ SY99 )
              | ~ ( ws @ a @ SY99 ) ) )
        = $true )
      | ( ( fool @ SV9 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[210]) ).

thf(246,plain,
    ! [SV10: $i,SV41: $i] :
      ( ( ( ~ ~ ( ws @ c @ SV41 ) )
        = $true )
      | ( ( ! [SY100: $i] :
              ( ~ ( a @ SV41 @ SY100 )
              | ~ ( ws @ c @ SY100 ) ) )
        = $true )
      | ( ( fool @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[211]) ).

thf(247,plain,
    ! [SV42: $i > $o,SV11: $i] :
      ( ( ( ! [SY101: $i] :
              ( ~ ( c @ SV11 @ SY101 )
              | ( SV42 @ SY101 ) ) )
        = $true )
      | ( ( ! [SY102: $i] :
              ( ~ ( b @ SV11 @ SY102 )
              | ~ ! [SY103: $i] :
                    ( ~ ( c @ SY102 @ SY103 )
                    | ( SV42 @ SY103 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[212]) ).

thf(248,plain,
    ! [SV43: $i > $o,SV12: $i] :
      ( ( ( ~ ( fool @ SV12 @ ( sK5_SY104 @ SV43 @ SV12 ) )
          | ( SV43 @ ( sK5_SY104 @ SV43 @ SV12 ) ) )
        = $false )
      | ( ( ! [SY105: $i] :
              ( ~ ( c @ SV12 @ SY105 )
              | ( SV43 @ SY105 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[213]) ).

thf(249,plain,
    ! [SV13: $i,SV44: $i] :
      ( ( ( ~ ~ ( ws @ c @ SV44 ) )
        = $true )
      | ( ( ! [SY106: $i] :
              ( ~ ( b @ SV44 @ SY106 )
              | ~ ( ws @ c @ SY106 ) ) )
        = $true )
      | ( ( fool @ SV13 @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[214]) ).

thf(250,plain,
    ! [SV45: $i > $o,SV14: $i] :
      ( ( ( ~ ( c @ SV14 @ ( sK6_SY107 @ SV45 @ SV14 ) )
          | ( SV45 @ ( sK6_SY107 @ SV45 @ SV14 ) ) )
        = $false )
      | ( ( ! [SY108: $i] :
              ( ~ ( a @ SV14 @ SY108 )
              | ! [SY109: $i] :
                  ( ~ ( c @ SY108 @ SY109 )
                  | ( SV45 @ SY109 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[215]) ).

thf(251,plain,
    ! [SV46: $i > $o,SV15: $i] :
      ( ( ( ! [SY110: $i] :
              ( ~ ( a @ SV15 @ SY110 )
              | ( SV46 @ SY110 ) ) )
        = $true )
      | ( ( ! [SY111: $i] :
              ( ~ ( c @ SV15 @ SY111 )
              | ~ ! [SY112: $i] :
                    ( ~ ( a @ SY111 @ SY112 )
                    | ( SV46 @ SY112 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[216]) ).

thf(252,plain,
    ! [SV16: $i,SV47: $i] :
      ( ( ( ~ ( ws @ a @ SV47 ) )
        = $true )
      | ( ( ! [SY113: $i] :
              ( ~ ( c @ SV47 @ SY113 )
              | ( ws @ a @ SY113 ) ) )
        = $true )
      | ( ( fool @ SV16 @ SV47 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[217]) ).

thf(253,plain,
    ! [SV48: $i > $o,SV17: $i] :
      ( ( ( ~ ( c @ SV17 @ ( sK7_SY114 @ SV48 @ SV17 ) )
          | ( SV48 @ ( sK7_SY114 @ SV48 @ SV17 ) ) )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ~ ( b @ SV17 @ SY115 )
              | ! [SY116: $i] :
                  ( ~ ( c @ SY115 @ SY116 )
                  | ( SV48 @ SY116 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[218]) ).

thf(254,plain,
    ! [SV49: $i > $o,SV18: $i] :
      ( ( ( ! [SY117: $i] :
              ( ~ ( a @ SV18 @ SY117 )
              | ( SV49 @ SY117 ) ) )
        = $true )
      | ( ( ! [SY118: $i] :
              ( ~ ( b @ SV18 @ SY118 )
              | ~ ! [SY119: $i] :
                    ( ~ ( a @ SY118 @ SY119 )
                    | ( SV49 @ SY119 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[219]) ).

thf(255,plain,
    ! [SV50: $i > $o,SV19: $i] :
      ( ( ( ~ ( a @ SV19 @ ( sK8_SY120 @ SV50 @ SV19 ) )
          | ( SV50 @ ( sK8_SY120 @ SV50 @ SV19 ) ) )
        = $false )
      | ( ( ! [SY121: $i] :
              ( ~ ( c @ SV19 @ SY121 )
              | ! [SY122: $i] :
                  ( ~ ( a @ SY121 @ SY122 )
                  | ( SV50 @ SY122 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[220]) ).

thf(256,plain,
    ! [SV20: $i] :
      ( ( b @ SV20 @ ( sK3_SY52 @ SV20 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[221]) ).

thf(257,plain,
    ! [SV21: $i,SV51: $i] :
      ( ( ( ~ ( ws @ b @ SV51 ) )
        = $true )
      | ( ( ! [SY123: $i] :
              ( ~ ( c @ SV51 @ SY123 )
              | ( ws @ b @ SY123 ) ) )
        = $true )
      | ( ( fool @ SV21 @ SV51 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[223]) ).

thf(258,plain,
    ! [SV52: $i > $o,SV22: $i] :
      ( ( ( ~ ( fool @ SV22 @ ( sK9_SY124 @ SV52 @ SV22 ) )
          | ( SV52 @ ( sK9_SY124 @ SV52 @ SV22 ) ) )
        = $false )
      | ( ( ! [SY125: $i] :
              ( ~ ( a @ SV22 @ SY125 )
              | ( SV52 @ SY125 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[224]) ).

thf(259,plain,
    ! [SV53: $i > $o,SV23: $i] :
      ( ( ( ! [SY126: $i] :
              ( ~ ( b @ SV23 @ SY126 )
              | ( SV53 @ SY126 ) ) )
        = $true )
      | ( ( ! [SY127: $i] :
              ( ~ ( c @ SV23 @ SY127 )
              | ~ ! [SY128: $i] :
                    ( ~ ( b @ SY127 @ SY128 )
                    | ( SV53 @ SY128 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[225]) ).

thf(260,plain,
    ! [SV54: $i > $o,SV24: $i] :
      ( ( ( ~ ( b @ SV24 @ ( sK10_SY129 @ SV54 @ SV24 ) )
          | ( SV54 @ ( sK10_SY129 @ SV54 @ SV24 ) ) )
        = $false )
      | ( ( ! [SY130: $i] :
              ( ~ ( c @ SV24 @ SY130 )
              | ! [SY131: $i] :
                  ( ~ ( b @ SY130 @ SY131 )
                  | ( SV54 @ SY131 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[226]) ).

thf(261,plain,
    ( ( c @ sK1_SX0 @ sK4_SY132 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[227]) ).

thf(262,plain,
    ! [SV25: $i,SV55: $i] :
      ( ( ( ws @ a @ SV55 )
        = $true )
      | ( ( ( ws @ b @ SV55 )
          | ( ws @ c @ SV55 ) )
        = $true )
      | ( ( fool @ SV25 @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[229]) ).

thf(263,plain,
    ! [SV56: $i > $o,SV26: $i] :
      ( ( ( ~ ( a @ SV26 @ ( sK11_SY133 @ SV56 @ SV26 ) )
          | ( SV56 @ ( sK11_SY133 @ SV56 @ SV26 ) ) )
        = $false )
      | ( ( ! [SY134: $i] :
              ( ~ ( b @ SV26 @ SY134 )
              | ! [SY135: $i] :
                  ( ~ ( a @ SY134 @ SY135 )
                  | ( SV56 @ SY135 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[230]) ).

thf(264,plain,
    ! [SV27: $i,SV57: $i] :
      ( ( ( ~ ~ ( ws @ b @ SV57 ) )
        = $true )
      | ( ( ! [SY136: $i] :
              ( ~ ( a @ SV57 @ SY136 )
              | ~ ( ws @ b @ SY136 ) ) )
        = $true )
      | ( ( fool @ SV27 @ SV57 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[231]) ).

thf(265,plain,
    ! [SV58: $i > $o,SV28: $i] :
      ( ( ( ~ ( b @ SV28 @ ( sK12_SY137 @ SV58 @ SV28 ) )
          | ( SV58 @ ( sK12_SY137 @ SV58 @ SV28 ) ) )
        = $false )
      | ( ( ! [SY138: $i] :
              ( ~ ( a @ SV28 @ SY138 )
              | ! [SY139: $i] :
                  ( ~ ( b @ SY138 @ SY139 )
                  | ( SV58 @ SY139 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[232]) ).

thf(266,plain,
    ! [SV59: $i > $o,SV29: $i] :
      ( ( ( ! [SY140: $i] :
              ( ~ ( b @ SV29 @ SY140 )
              | ( SV59 @ SY140 ) ) )
        = $true )
      | ( ( ! [SY141: $i] :
              ( ~ ( a @ SV29 @ SY141 )
              | ~ ! [SY142: $i] :
                    ( ~ ( b @ SY141 @ SY142 )
                    | ( SV59 @ SY142 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[233]) ).

thf(267,plain,
    ! [SV60: $i > $o,SV30: $i] :
      ( ( ( ~ ( fool @ SV30 @ ( sK13_SY143 @ SV60 @ SV30 ) )
          | ( SV60 @ ( sK13_SY143 @ SV60 @ SV30 ) ) )
        = $false )
      | ( ( ! [SY144: $i] :
              ( ~ ( b @ SV30 @ SY144 )
              | ( SV60 @ SY144 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[234]) ).

thf(268,plain,
    ! [SV61: $i > $o,SV31: $i] :
      ( ( ( ~ ( fool @ SV31 @ ( sK14_SY145 @ SV61 @ SV31 ) )
          | ( SV61 @ ( sK14_SY145 @ SV61 @ SV31 ) ) )
        = $false )
      | ( ( SV61 @ SV31 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[235]) ).

thf(269,plain,
    ! [SV62: $i > $o,SV32: $i] :
      ( ( ( ~ ( fool @ SV32 @ ( sK15_SY146 @ SV62 @ SV32 ) )
          | ( SV62 @ ( sK15_SY146 @ SV62 @ SV32 ) ) )
        = $false )
      | ( ( ! [SY147: $i] :
              ( ~ ( fool @ SV32 @ SY147 )
              | ! [SY148: $i] :
                  ( ~ ( fool @ SY147 @ SY148 )
                  | ( SV62 @ SY148 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[236]) ).

thf(270,plain,
    ! [SV1: $i,SV33: $i] :
      ( ( ( ~ ( ws @ a @ SV33 ) )
        = $false )
      | ( ( ! [SY90: $i] :
              ( ~ ( b @ SV33 @ SY90 )
              | ~ ( ws @ a @ SY90 ) ) )
        = $true )
      | ( ( fool @ SV1 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[237]) ).

thf(271,plain,
    ! [SV3: $i,SV34: $i] :
      ( ( ( ws @ b @ SV34 )
        = $false )
      | ( ( ! [SY91: $i] :
              ( ~ ( a @ SV34 @ SY91 )
              | ( ws @ b @ SY91 ) ) )
        = $true )
      | ( ( fool @ SV3 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[239]) ).

thf(272,plain,
    ! [SV4: $i,SV35: $i] :
      ( ( ( ~ ( ws @ b @ SV35 ) )
        = $false )
      | ( ( ! [SY92: $i] :
              ( ~ ( c @ SV35 @ SY92 )
              | ~ ( ws @ b @ SY92 ) ) )
        = $true )
      | ( ( fool @ SV4 @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[240]) ).

thf(273,plain,
    ! [SV5: $i,SV36: $i] :
      ( ( ( ws @ c @ SV36 )
        = $false )
      | ( ( ! [SY93: $i] :
              ( ~ ( b @ SV36 @ SY93 )
              | ( ws @ c @ SY93 ) ) )
        = $true )
      | ( ( fool @ SV5 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[241]) ).

thf(274,plain,
    ! [SV6: $i,SV37: $i] :
      ( ( ( ws @ c @ SV37 )
        = $false )
      | ( ( ! [SY94: $i] :
              ( ~ ( a @ SV37 @ SY94 )
              | ( ws @ c @ SY94 ) ) )
        = $true )
      | ( ( fool @ SV6 @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[242]) ).

thf(275,plain,
    ! [SV38: $i > $o,SV63: $i,SV7: $i] :
      ( ( ( ~ ( c @ SV7 @ SV63 )
          | ( SV38 @ SV63 ) )
        = $true )
      | ( ( ! [SY96: $i] :
              ( ~ ( a @ SV7 @ SY96 )
              | ~ ! [SY97: $i] :
                    ( ~ ( c @ SY96 @ SY97 )
                    | ( SV38 @ SY97 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[243]) ).

thf(276,plain,
    ! [SV8: $i,SV39: $i] :
      ( ( ( ws @ a @ SV39 )
        = $false )
      | ( ( ! [SY98: $i] :
              ( ~ ( b @ SV39 @ SY98 )
              | ( ws @ a @ SY98 ) ) )
        = $true )
      | ( ( fool @ SV8 @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[244]) ).

thf(277,plain,
    ! [SV9: $i,SV40: $i] :
      ( ( ( ~ ( ws @ a @ SV40 ) )
        = $false )
      | ( ( ! [SY99: $i] :
              ( ~ ( c @ SV40 @ SY99 )
              | ~ ( ws @ a @ SY99 ) ) )
        = $true )
      | ( ( fool @ SV9 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[245]) ).

thf(278,plain,
    ! [SV10: $i,SV41: $i] :
      ( ( ( ~ ( ws @ c @ SV41 ) )
        = $false )
      | ( ( ! [SY100: $i] :
              ( ~ ( a @ SV41 @ SY100 )
              | ~ ( ws @ c @ SY100 ) ) )
        = $true )
      | ( ( fool @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[246]) ).

thf(279,plain,
    ! [SV42: $i > $o,SV64: $i,SV11: $i] :
      ( ( ( ~ ( c @ SV11 @ SV64 )
          | ( SV42 @ SV64 ) )
        = $true )
      | ( ( ! [SY102: $i] :
              ( ~ ( b @ SV11 @ SY102 )
              | ~ ! [SY103: $i] :
                    ( ~ ( c @ SY102 @ SY103 )
                    | ( SV42 @ SY103 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[247]) ).

thf(280,plain,
    ! [SV43: $i > $o,SV12: $i] :
      ( ( ( ~ ( fool @ SV12 @ ( sK5_SY104 @ SV43 @ SV12 ) ) )
        = $false )
      | ( ( ! [SY105: $i] :
              ( ~ ( c @ SV12 @ SY105 )
              | ( SV43 @ SY105 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[248]) ).

thf(281,plain,
    ! [SV12: $i,SV43: $i > $o] :
      ( ( ( SV43 @ ( sK5_SY104 @ SV43 @ SV12 ) )
        = $false )
      | ( ( ! [SY105: $i] :
              ( ~ ( c @ SV12 @ SY105 )
              | ( SV43 @ SY105 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[248]) ).

thf(282,plain,
    ! [SV13: $i,SV44: $i] :
      ( ( ( ~ ( ws @ c @ SV44 ) )
        = $false )
      | ( ( ! [SY106: $i] :
              ( ~ ( b @ SV44 @ SY106 )
              | ~ ( ws @ c @ SY106 ) ) )
        = $true )
      | ( ( fool @ SV13 @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[249]) ).

thf(283,plain,
    ! [SV45: $i > $o,SV14: $i] :
      ( ( ( ~ ( c @ SV14 @ ( sK6_SY107 @ SV45 @ SV14 ) ) )
        = $false )
      | ( ( ! [SY108: $i] :
              ( ~ ( a @ SV14 @ SY108 )
              | ! [SY109: $i] :
                  ( ~ ( c @ SY108 @ SY109 )
                  | ( SV45 @ SY109 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[250]) ).

thf(284,plain,
    ! [SV14: $i,SV45: $i > $o] :
      ( ( ( SV45 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $false )
      | ( ( ! [SY108: $i] :
              ( ~ ( a @ SV14 @ SY108 )
              | ! [SY109: $i] :
                  ( ~ ( c @ SY108 @ SY109 )
                  | ( SV45 @ SY109 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[250]) ).

thf(285,plain,
    ! [SV46: $i > $o,SV65: $i,SV15: $i] :
      ( ( ( ~ ( a @ SV15 @ SV65 )
          | ( SV46 @ SV65 ) )
        = $true )
      | ( ( ! [SY111: $i] :
              ( ~ ( c @ SV15 @ SY111 )
              | ~ ! [SY112: $i] :
                    ( ~ ( a @ SY111 @ SY112 )
                    | ( SV46 @ SY112 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[251]) ).

thf(286,plain,
    ! [SV16: $i,SV47: $i] :
      ( ( ( ws @ a @ SV47 )
        = $false )
      | ( ( ! [SY113: $i] :
              ( ~ ( c @ SV47 @ SY113 )
              | ( ws @ a @ SY113 ) ) )
        = $true )
      | ( ( fool @ SV16 @ SV47 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[252]) ).

thf(287,plain,
    ! [SV48: $i > $o,SV17: $i] :
      ( ( ( ~ ( c @ SV17 @ ( sK7_SY114 @ SV48 @ SV17 ) ) )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ~ ( b @ SV17 @ SY115 )
              | ! [SY116: $i] :
                  ( ~ ( c @ SY115 @ SY116 )
                  | ( SV48 @ SY116 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[253]) ).

thf(288,plain,
    ! [SV17: $i,SV48: $i > $o] :
      ( ( ( SV48 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ~ ( b @ SV17 @ SY115 )
              | ! [SY116: $i] :
                  ( ~ ( c @ SY115 @ SY116 )
                  | ( SV48 @ SY116 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[253]) ).

thf(289,plain,
    ! [SV49: $i > $o,SV66: $i,SV18: $i] :
      ( ( ( ~ ( a @ SV18 @ SV66 )
          | ( SV49 @ SV66 ) )
        = $true )
      | ( ( ! [SY118: $i] :
              ( ~ ( b @ SV18 @ SY118 )
              | ~ ! [SY119: $i] :
                    ( ~ ( a @ SY118 @ SY119 )
                    | ( SV49 @ SY119 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[254]) ).

thf(290,plain,
    ! [SV50: $i > $o,SV19: $i] :
      ( ( ( ~ ( a @ SV19 @ ( sK8_SY120 @ SV50 @ SV19 ) ) )
        = $false )
      | ( ( ! [SY121: $i] :
              ( ~ ( c @ SV19 @ SY121 )
              | ! [SY122: $i] :
                  ( ~ ( a @ SY121 @ SY122 )
                  | ( SV50 @ SY122 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[255]) ).

thf(291,plain,
    ! [SV19: $i,SV50: $i > $o] :
      ( ( ( SV50 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $false )
      | ( ( ! [SY121: $i] :
              ( ~ ( c @ SV19 @ SY121 )
              | ! [SY122: $i] :
                  ( ~ ( a @ SY121 @ SY122 )
                  | ( SV50 @ SY122 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[255]) ).

thf(292,plain,
    ! [SV21: $i,SV51: $i] :
      ( ( ( ws @ b @ SV51 )
        = $false )
      | ( ( ! [SY123: $i] :
              ( ~ ( c @ SV51 @ SY123 )
              | ( ws @ b @ SY123 ) ) )
        = $true )
      | ( ( fool @ SV21 @ SV51 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[257]) ).

thf(293,plain,
    ! [SV52: $i > $o,SV22: $i] :
      ( ( ( ~ ( fool @ SV22 @ ( sK9_SY124 @ SV52 @ SV22 ) ) )
        = $false )
      | ( ( ! [SY125: $i] :
              ( ~ ( a @ SV22 @ SY125 )
              | ( SV52 @ SY125 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[258]) ).

thf(294,plain,
    ! [SV22: $i,SV52: $i > $o] :
      ( ( ( SV52 @ ( sK9_SY124 @ SV52 @ SV22 ) )
        = $false )
      | ( ( ! [SY125: $i] :
              ( ~ ( a @ SV22 @ SY125 )
              | ( SV52 @ SY125 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[258]) ).

thf(295,plain,
    ! [SV53: $i > $o,SV67: $i,SV23: $i] :
      ( ( ( ~ ( b @ SV23 @ SV67 )
          | ( SV53 @ SV67 ) )
        = $true )
      | ( ( ! [SY127: $i] :
              ( ~ ( c @ SV23 @ SY127 )
              | ~ ! [SY128: $i] :
                    ( ~ ( b @ SY127 @ SY128 )
                    | ( SV53 @ SY128 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[259]) ).

thf(296,plain,
    ! [SV54: $i > $o,SV24: $i] :
      ( ( ( ~ ( b @ SV24 @ ( sK10_SY129 @ SV54 @ SV24 ) ) )
        = $false )
      | ( ( ! [SY130: $i] :
              ( ~ ( c @ SV24 @ SY130 )
              | ! [SY131: $i] :
                  ( ~ ( b @ SY130 @ SY131 )
                  | ( SV54 @ SY131 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[260]) ).

thf(297,plain,
    ! [SV24: $i,SV54: $i > $o] :
      ( ( ( SV54 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $false )
      | ( ( ! [SY130: $i] :
              ( ~ ( c @ SV24 @ SY130 )
              | ! [SY131: $i] :
                  ( ~ ( b @ SY130 @ SY131 )
                  | ( SV54 @ SY131 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[260]) ).

thf(298,plain,
    ! [SV25: $i,SV55: $i] :
      ( ( ( ws @ b @ SV55 )
        = $true )
      | ( ( ws @ c @ SV55 )
        = $true )
      | ( ( ws @ a @ SV55 )
        = $true )
      | ( ( fool @ SV25 @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[262]) ).

thf(299,plain,
    ! [SV56: $i > $o,SV26: $i] :
      ( ( ( ~ ( a @ SV26 @ ( sK11_SY133 @ SV56 @ SV26 ) ) )
        = $false )
      | ( ( ! [SY134: $i] :
              ( ~ ( b @ SV26 @ SY134 )
              | ! [SY135: $i] :
                  ( ~ ( a @ SY134 @ SY135 )
                  | ( SV56 @ SY135 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[263]) ).

thf(300,plain,
    ! [SV26: $i,SV56: $i > $o] :
      ( ( ( SV56 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $false )
      | ( ( ! [SY134: $i] :
              ( ~ ( b @ SV26 @ SY134 )
              | ! [SY135: $i] :
                  ( ~ ( a @ SY134 @ SY135 )
                  | ( SV56 @ SY135 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[263]) ).

thf(301,plain,
    ! [SV27: $i,SV57: $i] :
      ( ( ( ~ ( ws @ b @ SV57 ) )
        = $false )
      | ( ( ! [SY136: $i] :
              ( ~ ( a @ SV57 @ SY136 )
              | ~ ( ws @ b @ SY136 ) ) )
        = $true )
      | ( ( fool @ SV27 @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[264]) ).

thf(302,plain,
    ! [SV58: $i > $o,SV28: $i] :
      ( ( ( ~ ( b @ SV28 @ ( sK12_SY137 @ SV58 @ SV28 ) ) )
        = $false )
      | ( ( ! [SY138: $i] :
              ( ~ ( a @ SV28 @ SY138 )
              | ! [SY139: $i] :
                  ( ~ ( b @ SY138 @ SY139 )
                  | ( SV58 @ SY139 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[265]) ).

thf(303,plain,
    ! [SV28: $i,SV58: $i > $o] :
      ( ( ( SV58 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $false )
      | ( ( ! [SY138: $i] :
              ( ~ ( a @ SV28 @ SY138 )
              | ! [SY139: $i] :
                  ( ~ ( b @ SY138 @ SY139 )
                  | ( SV58 @ SY139 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[265]) ).

thf(304,plain,
    ! [SV59: $i > $o,SV68: $i,SV29: $i] :
      ( ( ( ~ ( b @ SV29 @ SV68 )
          | ( SV59 @ SV68 ) )
        = $true )
      | ( ( ! [SY141: $i] :
              ( ~ ( a @ SV29 @ SY141 )
              | ~ ! [SY142: $i] :
                    ( ~ ( b @ SY141 @ SY142 )
                    | ( SV59 @ SY142 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[266]) ).

thf(305,plain,
    ! [SV60: $i > $o,SV30: $i] :
      ( ( ( ~ ( fool @ SV30 @ ( sK13_SY143 @ SV60 @ SV30 ) ) )
        = $false )
      | ( ( ! [SY144: $i] :
              ( ~ ( b @ SV30 @ SY144 )
              | ( SV60 @ SY144 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[267]) ).

thf(306,plain,
    ! [SV30: $i,SV60: $i > $o] :
      ( ( ( SV60 @ ( sK13_SY143 @ SV60 @ SV30 ) )
        = $false )
      | ( ( ! [SY144: $i] :
              ( ~ ( b @ SV30 @ SY144 )
              | ( SV60 @ SY144 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[267]) ).

thf(307,plain,
    ! [SV61: $i > $o,SV31: $i] :
      ( ( ( ~ ( fool @ SV31 @ ( sK14_SY145 @ SV61 @ SV31 ) ) )
        = $false )
      | ( ( SV61 @ SV31 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[268]) ).

thf(308,plain,
    ! [SV31: $i,SV61: $i > $o] :
      ( ( ( SV61 @ ( sK14_SY145 @ SV61 @ SV31 ) )
        = $false )
      | ( ( SV61 @ SV31 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[268]) ).

thf(309,plain,
    ! [SV62: $i > $o,SV32: $i] :
      ( ( ( ~ ( fool @ SV32 @ ( sK15_SY146 @ SV62 @ SV32 ) ) )
        = $false )
      | ( ( ! [SY147: $i] :
              ( ~ ( fool @ SV32 @ SY147 )
              | ! [SY148: $i] :
                  ( ~ ( fool @ SY147 @ SY148 )
                  | ( SV62 @ SY148 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[269]) ).

thf(310,plain,
    ! [SV32: $i,SV62: $i > $o] :
      ( ( ( SV62 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $false )
      | ( ( ! [SY147: $i] :
              ( ~ ( fool @ SV32 @ SY147 )
              | ! [SY148: $i] :
                  ( ~ ( fool @ SY147 @ SY148 )
                  | ( SV62 @ SY148 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[269]) ).

thf(311,plain,
    ! [SV1: $i,SV33: $i] :
      ( ( ( ws @ a @ SV33 )
        = $true )
      | ( ( ! [SY90: $i] :
              ( ~ ( b @ SV33 @ SY90 )
              | ~ ( ws @ a @ SY90 ) ) )
        = $true )
      | ( ( fool @ SV1 @ SV33 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[270]) ).

thf(312,plain,
    ! [SV3: $i,SV69: $i,SV34: $i] :
      ( ( ( ~ ( a @ SV34 @ SV69 )
          | ( ws @ b @ SV69 ) )
        = $true )
      | ( ( ws @ b @ SV34 )
        = $false )
      | ( ( fool @ SV3 @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[271]) ).

thf(313,plain,
    ! [SV4: $i,SV35: $i] :
      ( ( ( ws @ b @ SV35 )
        = $true )
      | ( ( ! [SY92: $i] :
              ( ~ ( c @ SV35 @ SY92 )
              | ~ ( ws @ b @ SY92 ) ) )
        = $true )
      | ( ( fool @ SV4 @ SV35 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[272]) ).

thf(314,plain,
    ! [SV5: $i,SV70: $i,SV36: $i] :
      ( ( ( ~ ( b @ SV36 @ SV70 )
          | ( ws @ c @ SV70 ) )
        = $true )
      | ( ( ws @ c @ SV36 )
        = $false )
      | ( ( fool @ SV5 @ SV36 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[273]) ).

thf(315,plain,
    ! [SV6: $i,SV71: $i,SV37: $i] :
      ( ( ( ~ ( a @ SV37 @ SV71 )
          | ( ws @ c @ SV71 ) )
        = $true )
      | ( ( ws @ c @ SV37 )
        = $false )
      | ( ( fool @ SV6 @ SV37 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[274]) ).

thf(316,plain,
    ! [SV38: $i > $o,SV63: $i,SV7: $i] :
      ( ( ( ~ ( c @ SV7 @ SV63 ) )
        = $true )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( ! [SY96: $i] :
              ( ~ ( a @ SV7 @ SY96 )
              | ~ ! [SY97: $i] :
                    ( ~ ( c @ SY96 @ SY97 )
                    | ( SV38 @ SY97 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[275]) ).

thf(317,plain,
    ! [SV8: $i,SV72: $i,SV39: $i] :
      ( ( ( ~ ( b @ SV39 @ SV72 )
          | ( ws @ a @ SV72 ) )
        = $true )
      | ( ( ws @ a @ SV39 )
        = $false )
      | ( ( fool @ SV8 @ SV39 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[276]) ).

thf(318,plain,
    ! [SV9: $i,SV40: $i] :
      ( ( ( ws @ a @ SV40 )
        = $true )
      | ( ( ! [SY99: $i] :
              ( ~ ( c @ SV40 @ SY99 )
              | ~ ( ws @ a @ SY99 ) ) )
        = $true )
      | ( ( fool @ SV9 @ SV40 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[277]) ).

thf(319,plain,
    ! [SV10: $i,SV41: $i] :
      ( ( ( ws @ c @ SV41 )
        = $true )
      | ( ( ! [SY100: $i] :
              ( ~ ( a @ SV41 @ SY100 )
              | ~ ( ws @ c @ SY100 ) ) )
        = $true )
      | ( ( fool @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[278]) ).

thf(320,plain,
    ! [SV42: $i > $o,SV64: $i,SV11: $i] :
      ( ( ( ~ ( c @ SV11 @ SV64 ) )
        = $true )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( ! [SY102: $i] :
              ( ~ ( b @ SV11 @ SY102 )
              | ~ ! [SY103: $i] :
                    ( ~ ( c @ SY102 @ SY103 )
                    | ( SV42 @ SY103 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[279]) ).

thf(321,plain,
    ! [SV43: $i > $o,SV12: $i] :
      ( ( ( fool @ SV12 @ ( sK5_SY104 @ SV43 @ SV12 ) )
        = $true )
      | ( ( ! [SY105: $i] :
              ( ~ ( c @ SV12 @ SY105 )
              | ( SV43 @ SY105 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[280]) ).

thf(322,plain,
    ! [SV43: $i > $o,SV73: $i,SV12: $i] :
      ( ( ( ~ ( c @ SV12 @ SV73 )
          | ( SV43 @ SV73 ) )
        = $true )
      | ( ( SV43 @ ( sK5_SY104 @ SV43 @ SV12 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[281]) ).

thf(323,plain,
    ! [SV13: $i,SV44: $i] :
      ( ( ( ws @ c @ SV44 )
        = $true )
      | ( ( ! [SY106: $i] :
              ( ~ ( b @ SV44 @ SY106 )
              | ~ ( ws @ c @ SY106 ) ) )
        = $true )
      | ( ( fool @ SV13 @ SV44 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[282]) ).

thf(324,plain,
    ! [SV45: $i > $o,SV14: $i] :
      ( ( ( c @ SV14 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $true )
      | ( ( ! [SY108: $i] :
              ( ~ ( a @ SV14 @ SY108 )
              | ! [SY109: $i] :
                  ( ~ ( c @ SY108 @ SY109 )
                  | ( SV45 @ SY109 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[283]) ).

thf(325,plain,
    ! [SV45: $i > $o,SV74: $i,SV14: $i] :
      ( ( ( ~ ( a @ SV14 @ SV74 )
          | ! [SY149: $i] :
              ( ~ ( c @ SV74 @ SY149 )
              | ( SV45 @ SY149 ) ) )
        = $true )
      | ( ( SV45 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[284]) ).

thf(326,plain,
    ! [SV46: $i > $o,SV65: $i,SV15: $i] :
      ( ( ( ~ ( a @ SV15 @ SV65 ) )
        = $true )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( ! [SY111: $i] :
              ( ~ ( c @ SV15 @ SY111 )
              | ~ ! [SY112: $i] :
                    ( ~ ( a @ SY111 @ SY112 )
                    | ( SV46 @ SY112 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[285]) ).

thf(327,plain,
    ! [SV16: $i,SV75: $i,SV47: $i] :
      ( ( ( ~ ( c @ SV47 @ SV75 )
          | ( ws @ a @ SV75 ) )
        = $true )
      | ( ( ws @ a @ SV47 )
        = $false )
      | ( ( fool @ SV16 @ SV47 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[286]) ).

thf(328,plain,
    ! [SV48: $i > $o,SV17: $i] :
      ( ( ( c @ SV17 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $true )
      | ( ( ! [SY115: $i] :
              ( ~ ( b @ SV17 @ SY115 )
              | ! [SY116: $i] :
                  ( ~ ( c @ SY115 @ SY116 )
                  | ( SV48 @ SY116 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[287]) ).

thf(329,plain,
    ! [SV48: $i > $o,SV76: $i,SV17: $i] :
      ( ( ( ~ ( b @ SV17 @ SV76 )
          | ! [SY150: $i] :
              ( ~ ( c @ SV76 @ SY150 )
              | ( SV48 @ SY150 ) ) )
        = $true )
      | ( ( SV48 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[288]) ).

thf(330,plain,
    ! [SV49: $i > $o,SV66: $i,SV18: $i] :
      ( ( ( ~ ( a @ SV18 @ SV66 ) )
        = $true )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( ! [SY118: $i] :
              ( ~ ( b @ SV18 @ SY118 )
              | ~ ! [SY119: $i] :
                    ( ~ ( a @ SY118 @ SY119 )
                    | ( SV49 @ SY119 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[289]) ).

thf(331,plain,
    ! [SV50: $i > $o,SV19: $i] :
      ( ( ( a @ SV19 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $true )
      | ( ( ! [SY121: $i] :
              ( ~ ( c @ SV19 @ SY121 )
              | ! [SY122: $i] :
                  ( ~ ( a @ SY121 @ SY122 )
                  | ( SV50 @ SY122 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[290]) ).

thf(332,plain,
    ! [SV50: $i > $o,SV77: $i,SV19: $i] :
      ( ( ( ~ ( c @ SV19 @ SV77 )
          | ! [SY151: $i] :
              ( ~ ( a @ SV77 @ SY151 )
              | ( SV50 @ SY151 ) ) )
        = $true )
      | ( ( SV50 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[291]) ).

thf(333,plain,
    ! [SV21: $i,SV78: $i,SV51: $i] :
      ( ( ( ~ ( c @ SV51 @ SV78 )
          | ( ws @ b @ SV78 ) )
        = $true )
      | ( ( ws @ b @ SV51 )
        = $false )
      | ( ( fool @ SV21 @ SV51 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[292]) ).

thf(334,plain,
    ! [SV52: $i > $o,SV22: $i] :
      ( ( ( fool @ SV22 @ ( sK9_SY124 @ SV52 @ SV22 ) )
        = $true )
      | ( ( ! [SY125: $i] :
              ( ~ ( a @ SV22 @ SY125 )
              | ( SV52 @ SY125 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[293]) ).

thf(335,plain,
    ! [SV52: $i > $o,SV79: $i,SV22: $i] :
      ( ( ( ~ ( a @ SV22 @ SV79 )
          | ( SV52 @ SV79 ) )
        = $true )
      | ( ( SV52 @ ( sK9_SY124 @ SV52 @ SV22 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[294]) ).

thf(336,plain,
    ! [SV53: $i > $o,SV67: $i,SV23: $i] :
      ( ( ( ~ ( b @ SV23 @ SV67 ) )
        = $true )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( ! [SY127: $i] :
              ( ~ ( c @ SV23 @ SY127 )
              | ~ ! [SY128: $i] :
                    ( ~ ( b @ SY127 @ SY128 )
                    | ( SV53 @ SY128 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[295]) ).

thf(337,plain,
    ! [SV54: $i > $o,SV24: $i] :
      ( ( ( b @ SV24 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $true )
      | ( ( ! [SY130: $i] :
              ( ~ ( c @ SV24 @ SY130 )
              | ! [SY131: $i] :
                  ( ~ ( b @ SY130 @ SY131 )
                  | ( SV54 @ SY131 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[296]) ).

thf(338,plain,
    ! [SV54: $i > $o,SV80: $i,SV24: $i] :
      ( ( ( ~ ( c @ SV24 @ SV80 )
          | ! [SY152: $i] :
              ( ~ ( b @ SV80 @ SY152 )
              | ( SV54 @ SY152 ) ) )
        = $true )
      | ( ( SV54 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[297]) ).

thf(339,plain,
    ! [SV56: $i > $o,SV26: $i] :
      ( ( ( a @ SV26 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $true )
      | ( ( ! [SY134: $i] :
              ( ~ ( b @ SV26 @ SY134 )
              | ! [SY135: $i] :
                  ( ~ ( a @ SY134 @ SY135 )
                  | ( SV56 @ SY135 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[299]) ).

thf(340,plain,
    ! [SV56: $i > $o,SV81: $i,SV26: $i] :
      ( ( ( ~ ( b @ SV26 @ SV81 )
          | ! [SY153: $i] :
              ( ~ ( a @ SV81 @ SY153 )
              | ( SV56 @ SY153 ) ) )
        = $true )
      | ( ( SV56 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[300]) ).

thf(341,plain,
    ! [SV27: $i,SV57: $i] :
      ( ( ( ws @ b @ SV57 )
        = $true )
      | ( ( ! [SY136: $i] :
              ( ~ ( a @ SV57 @ SY136 )
              | ~ ( ws @ b @ SY136 ) ) )
        = $true )
      | ( ( fool @ SV27 @ SV57 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[301]) ).

thf(342,plain,
    ! [SV58: $i > $o,SV28: $i] :
      ( ( ( b @ SV28 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $true )
      | ( ( ! [SY138: $i] :
              ( ~ ( a @ SV28 @ SY138 )
              | ! [SY139: $i] :
                  ( ~ ( b @ SY138 @ SY139 )
                  | ( SV58 @ SY139 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[302]) ).

thf(343,plain,
    ! [SV58: $i > $o,SV82: $i,SV28: $i] :
      ( ( ( ~ ( a @ SV28 @ SV82 )
          | ! [SY154: $i] :
              ( ~ ( b @ SV82 @ SY154 )
              | ( SV58 @ SY154 ) ) )
        = $true )
      | ( ( SV58 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[303]) ).

thf(344,plain,
    ! [SV59: $i > $o,SV68: $i,SV29: $i] :
      ( ( ( ~ ( b @ SV29 @ SV68 ) )
        = $true )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( ! [SY141: $i] :
              ( ~ ( a @ SV29 @ SY141 )
              | ~ ! [SY142: $i] :
                    ( ~ ( b @ SY141 @ SY142 )
                    | ( SV59 @ SY142 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[304]) ).

thf(345,plain,
    ! [SV60: $i > $o,SV30: $i] :
      ( ( ( fool @ SV30 @ ( sK13_SY143 @ SV60 @ SV30 ) )
        = $true )
      | ( ( ! [SY144: $i] :
              ( ~ ( b @ SV30 @ SY144 )
              | ( SV60 @ SY144 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[305]) ).

thf(346,plain,
    ! [SV60: $i > $o,SV83: $i,SV30: $i] :
      ( ( ( ~ ( b @ SV30 @ SV83 )
          | ( SV60 @ SV83 ) )
        = $true )
      | ( ( SV60 @ ( sK13_SY143 @ SV60 @ SV30 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[306]) ).

thf(347,plain,
    ! [SV61: $i > $o,SV31: $i] :
      ( ( ( fool @ SV31 @ ( sK14_SY145 @ SV61 @ SV31 ) )
        = $true )
      | ( ( SV61 @ SV31 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[307]) ).

thf(348,plain,
    ! [SV62: $i > $o,SV32: $i] :
      ( ( ( fool @ SV32 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $true )
      | ( ( ! [SY147: $i] :
              ( ~ ( fool @ SV32 @ SY147 )
              | ! [SY148: $i] :
                  ( ~ ( fool @ SY147 @ SY148 )
                  | ( SV62 @ SY148 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[309]) ).

thf(349,plain,
    ! [SV62: $i > $o,SV84: $i,SV32: $i] :
      ( ( ( ~ ( fool @ SV32 @ SV84 )
          | ! [SY155: $i] :
              ( ~ ( fool @ SV84 @ SY155 )
              | ( SV62 @ SY155 ) ) )
        = $true )
      | ( ( SV62 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[310]) ).

thf(350,plain,
    ! [SV1: $i,SV85: $i,SV33: $i] :
      ( ( ( ~ ( b @ SV33 @ SV85 )
          | ~ ( ws @ a @ SV85 ) )
        = $true )
      | ( ( ws @ a @ SV33 )
        = $true )
      | ( ( fool @ SV1 @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[311]) ).

thf(351,plain,
    ! [SV3: $i,SV69: $i,SV34: $i] :
      ( ( ( ~ ( a @ SV34 @ SV69 ) )
        = $true )
      | ( ( ws @ b @ SV69 )
        = $true )
      | ( ( ws @ b @ SV34 )
        = $false )
      | ( ( fool @ SV3 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[312]) ).

thf(352,plain,
    ! [SV4: $i,SV86: $i,SV35: $i] :
      ( ( ( ~ ( c @ SV35 @ SV86 )
          | ~ ( ws @ b @ SV86 ) )
        = $true )
      | ( ( ws @ b @ SV35 )
        = $true )
      | ( ( fool @ SV4 @ SV35 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[313]) ).

thf(353,plain,
    ! [SV5: $i,SV70: $i,SV36: $i] :
      ( ( ( ~ ( b @ SV36 @ SV70 ) )
        = $true )
      | ( ( ws @ c @ SV70 )
        = $true )
      | ( ( ws @ c @ SV36 )
        = $false )
      | ( ( fool @ SV5 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[314]) ).

thf(354,plain,
    ! [SV6: $i,SV71: $i,SV37: $i] :
      ( ( ( ~ ( a @ SV37 @ SV71 ) )
        = $true )
      | ( ( ws @ c @ SV71 )
        = $true )
      | ( ( ws @ c @ SV37 )
        = $false )
      | ( ( fool @ SV6 @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[315]) ).

thf(355,plain,
    ! [SV38: $i > $o,SV63: $i,SV7: $i] :
      ( ( ( c @ SV7 @ SV63 )
        = $false )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( ! [SY96: $i] :
              ( ~ ( a @ SV7 @ SY96 )
              | ~ ! [SY97: $i] :
                    ( ~ ( c @ SY96 @ SY97 )
                    | ( SV38 @ SY97 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[316]) ).

thf(356,plain,
    ! [SV8: $i,SV72: $i,SV39: $i] :
      ( ( ( ~ ( b @ SV39 @ SV72 ) )
        = $true )
      | ( ( ws @ a @ SV72 )
        = $true )
      | ( ( ws @ a @ SV39 )
        = $false )
      | ( ( fool @ SV8 @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[317]) ).

thf(357,plain,
    ! [SV9: $i,SV87: $i,SV40: $i] :
      ( ( ( ~ ( c @ SV40 @ SV87 )
          | ~ ( ws @ a @ SV87 ) )
        = $true )
      | ( ( ws @ a @ SV40 )
        = $true )
      | ( ( fool @ SV9 @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[318]) ).

thf(358,plain,
    ! [SV10: $i,SV88: $i,SV41: $i] :
      ( ( ( ~ ( a @ SV41 @ SV88 )
          | ~ ( ws @ c @ SV88 ) )
        = $true )
      | ( ( ws @ c @ SV41 )
        = $true )
      | ( ( fool @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[319]) ).

thf(359,plain,
    ! [SV42: $i > $o,SV64: $i,SV11: $i] :
      ( ( ( c @ SV11 @ SV64 )
        = $false )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( ! [SY102: $i] :
              ( ~ ( b @ SV11 @ SY102 )
              | ~ ! [SY103: $i] :
                    ( ~ ( c @ SY102 @ SY103 )
                    | ( SV42 @ SY103 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[320]) ).

thf(360,plain,
    ! [SV43: $i > $o,SV89: $i,SV12: $i] :
      ( ( ( ~ ( c @ SV12 @ SV89 )
          | ( SV43 @ SV89 ) )
        = $true )
      | ( ( fool @ SV12 @ ( sK5_SY104 @ SV43 @ SV12 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[321]) ).

thf(361,plain,
    ! [SV43: $i > $o,SV73: $i,SV12: $i] :
      ( ( ( ~ ( c @ SV12 @ SV73 ) )
        = $true )
      | ( ( SV43 @ SV73 )
        = $true )
      | ( ( SV43 @ ( sK5_SY104 @ SV43 @ SV12 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[322]) ).

thf(362,plain,
    ! [SV13: $i,SV90: $i,SV44: $i] :
      ( ( ( ~ ( b @ SV44 @ SV90 )
          | ~ ( ws @ c @ SV90 ) )
        = $true )
      | ( ( ws @ c @ SV44 )
        = $true )
      | ( ( fool @ SV13 @ SV44 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[323]) ).

thf(363,plain,
    ! [SV45: $i > $o,SV91: $i,SV14: $i] :
      ( ( ( ~ ( a @ SV14 @ SV91 )
          | ! [SY156: $i] :
              ( ~ ( c @ SV91 @ SY156 )
              | ( SV45 @ SY156 ) ) )
        = $true )
      | ( ( c @ SV14 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[324]) ).

thf(364,plain,
    ! [SV45: $i > $o,SV74: $i,SV14: $i] :
      ( ( ( ~ ( a @ SV14 @ SV74 ) )
        = $true )
      | ( ( ! [SY149: $i] :
              ( ~ ( c @ SV74 @ SY149 )
              | ( SV45 @ SY149 ) ) )
        = $true )
      | ( ( SV45 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[325]) ).

thf(365,plain,
    ! [SV46: $i > $o,SV65: $i,SV15: $i] :
      ( ( ( a @ SV15 @ SV65 )
        = $false )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( ! [SY111: $i] :
              ( ~ ( c @ SV15 @ SY111 )
              | ~ ! [SY112: $i] :
                    ( ~ ( a @ SY111 @ SY112 )
                    | ( SV46 @ SY112 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[326]) ).

thf(366,plain,
    ! [SV16: $i,SV75: $i,SV47: $i] :
      ( ( ( ~ ( c @ SV47 @ SV75 ) )
        = $true )
      | ( ( ws @ a @ SV75 )
        = $true )
      | ( ( ws @ a @ SV47 )
        = $false )
      | ( ( fool @ SV16 @ SV47 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[327]) ).

thf(367,plain,
    ! [SV48: $i > $o,SV92: $i,SV17: $i] :
      ( ( ( ~ ( b @ SV17 @ SV92 )
          | ! [SY157: $i] :
              ( ~ ( c @ SV92 @ SY157 )
              | ( SV48 @ SY157 ) ) )
        = $true )
      | ( ( c @ SV17 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[328]) ).

thf(368,plain,
    ! [SV48: $i > $o,SV76: $i,SV17: $i] :
      ( ( ( ~ ( b @ SV17 @ SV76 ) )
        = $true )
      | ( ( ! [SY150: $i] :
              ( ~ ( c @ SV76 @ SY150 )
              | ( SV48 @ SY150 ) ) )
        = $true )
      | ( ( SV48 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[329]) ).

thf(369,plain,
    ! [SV49: $i > $o,SV66: $i,SV18: $i] :
      ( ( ( a @ SV18 @ SV66 )
        = $false )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( ! [SY118: $i] :
              ( ~ ( b @ SV18 @ SY118 )
              | ~ ! [SY119: $i] :
                    ( ~ ( a @ SY118 @ SY119 )
                    | ( SV49 @ SY119 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[330]) ).

thf(370,plain,
    ! [SV50: $i > $o,SV93: $i,SV19: $i] :
      ( ( ( ~ ( c @ SV19 @ SV93 )
          | ! [SY158: $i] :
              ( ~ ( a @ SV93 @ SY158 )
              | ( SV50 @ SY158 ) ) )
        = $true )
      | ( ( a @ SV19 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[331]) ).

thf(371,plain,
    ! [SV50: $i > $o,SV77: $i,SV19: $i] :
      ( ( ( ~ ( c @ SV19 @ SV77 ) )
        = $true )
      | ( ( ! [SY151: $i] :
              ( ~ ( a @ SV77 @ SY151 )
              | ( SV50 @ SY151 ) ) )
        = $true )
      | ( ( SV50 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[332]) ).

thf(372,plain,
    ! [SV21: $i,SV78: $i,SV51: $i] :
      ( ( ( ~ ( c @ SV51 @ SV78 ) )
        = $true )
      | ( ( ws @ b @ SV78 )
        = $true )
      | ( ( ws @ b @ SV51 )
        = $false )
      | ( ( fool @ SV21 @ SV51 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[333]) ).

thf(373,plain,
    ! [SV52: $i > $o,SV94: $i,SV22: $i] :
      ( ( ( ~ ( a @ SV22 @ SV94 )
          | ( SV52 @ SV94 ) )
        = $true )
      | ( ( fool @ SV22 @ ( sK9_SY124 @ SV52 @ SV22 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[334]) ).

thf(374,plain,
    ! [SV52: $i > $o,SV79: $i,SV22: $i] :
      ( ( ( ~ ( a @ SV22 @ SV79 ) )
        = $true )
      | ( ( SV52 @ SV79 )
        = $true )
      | ( ( SV52 @ ( sK9_SY124 @ SV52 @ SV22 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[335]) ).

thf(375,plain,
    ! [SV53: $i > $o,SV67: $i,SV23: $i] :
      ( ( ( b @ SV23 @ SV67 )
        = $false )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( ! [SY127: $i] :
              ( ~ ( c @ SV23 @ SY127 )
              | ~ ! [SY128: $i] :
                    ( ~ ( b @ SY127 @ SY128 )
                    | ( SV53 @ SY128 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[336]) ).

thf(376,plain,
    ! [SV54: $i > $o,SV95: $i,SV24: $i] :
      ( ( ( ~ ( c @ SV24 @ SV95 )
          | ! [SY159: $i] :
              ( ~ ( b @ SV95 @ SY159 )
              | ( SV54 @ SY159 ) ) )
        = $true )
      | ( ( b @ SV24 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[337]) ).

thf(377,plain,
    ! [SV54: $i > $o,SV80: $i,SV24: $i] :
      ( ( ( ~ ( c @ SV24 @ SV80 ) )
        = $true )
      | ( ( ! [SY152: $i] :
              ( ~ ( b @ SV80 @ SY152 )
              | ( SV54 @ SY152 ) ) )
        = $true )
      | ( ( SV54 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[338]) ).

thf(378,plain,
    ! [SV56: $i > $o,SV96: $i,SV26: $i] :
      ( ( ( ~ ( b @ SV26 @ SV96 )
          | ! [SY160: $i] :
              ( ~ ( a @ SV96 @ SY160 )
              | ( SV56 @ SY160 ) ) )
        = $true )
      | ( ( a @ SV26 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[339]) ).

thf(379,plain,
    ! [SV56: $i > $o,SV81: $i,SV26: $i] :
      ( ( ( ~ ( b @ SV26 @ SV81 ) )
        = $true )
      | ( ( ! [SY153: $i] :
              ( ~ ( a @ SV81 @ SY153 )
              | ( SV56 @ SY153 ) ) )
        = $true )
      | ( ( SV56 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[340]) ).

thf(380,plain,
    ! [SV27: $i,SV97: $i,SV57: $i] :
      ( ( ( ~ ( a @ SV57 @ SV97 )
          | ~ ( ws @ b @ SV97 ) )
        = $true )
      | ( ( ws @ b @ SV57 )
        = $true )
      | ( ( fool @ SV27 @ SV57 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[341]) ).

thf(381,plain,
    ! [SV58: $i > $o,SV98: $i,SV28: $i] :
      ( ( ( ~ ( a @ SV28 @ SV98 )
          | ! [SY161: $i] :
              ( ~ ( b @ SV98 @ SY161 )
              | ( SV58 @ SY161 ) ) )
        = $true )
      | ( ( b @ SV28 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[342]) ).

thf(382,plain,
    ! [SV58: $i > $o,SV82: $i,SV28: $i] :
      ( ( ( ~ ( a @ SV28 @ SV82 ) )
        = $true )
      | ( ( ! [SY154: $i] :
              ( ~ ( b @ SV82 @ SY154 )
              | ( SV58 @ SY154 ) ) )
        = $true )
      | ( ( SV58 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[343]) ).

thf(383,plain,
    ! [SV59: $i > $o,SV68: $i,SV29: $i] :
      ( ( ( b @ SV29 @ SV68 )
        = $false )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( ! [SY141: $i] :
              ( ~ ( a @ SV29 @ SY141 )
              | ~ ! [SY142: $i] :
                    ( ~ ( b @ SY141 @ SY142 )
                    | ( SV59 @ SY142 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[344]) ).

thf(384,plain,
    ! [SV60: $i > $o,SV99: $i,SV30: $i] :
      ( ( ( ~ ( b @ SV30 @ SV99 )
          | ( SV60 @ SV99 ) )
        = $true )
      | ( ( fool @ SV30 @ ( sK13_SY143 @ SV60 @ SV30 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[345]) ).

thf(385,plain,
    ! [SV60: $i > $o,SV83: $i,SV30: $i] :
      ( ( ( ~ ( b @ SV30 @ SV83 ) )
        = $true )
      | ( ( SV60 @ SV83 )
        = $true )
      | ( ( SV60 @ ( sK13_SY143 @ SV60 @ SV30 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[346]) ).

thf(386,plain,
    ! [SV62: $i > $o,SV100: $i,SV32: $i] :
      ( ( ( ~ ( fool @ SV32 @ SV100 )
          | ! [SY162: $i] :
              ( ~ ( fool @ SV100 @ SY162 )
              | ( SV62 @ SY162 ) ) )
        = $true )
      | ( ( fool @ SV32 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[348]) ).

thf(387,plain,
    ! [SV62: $i > $o,SV84: $i,SV32: $i] :
      ( ( ( ~ ( fool @ SV32 @ SV84 ) )
        = $true )
      | ( ( ! [SY155: $i] :
              ( ~ ( fool @ SV84 @ SY155 )
              | ( SV62 @ SY155 ) ) )
        = $true )
      | ( ( SV62 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[349]) ).

thf(388,plain,
    ! [SV1: $i,SV85: $i,SV33: $i] :
      ( ( ( ~ ( b @ SV33 @ SV85 ) )
        = $true )
      | ( ( ~ ( ws @ a @ SV85 ) )
        = $true )
      | ( ( ws @ a @ SV33 )
        = $true )
      | ( ( fool @ SV1 @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[350]) ).

thf(389,plain,
    ! [SV3: $i,SV69: $i,SV34: $i] :
      ( ( ( a @ SV34 @ SV69 )
        = $false )
      | ( ( ws @ b @ SV69 )
        = $true )
      | ( ( ws @ b @ SV34 )
        = $false )
      | ( ( fool @ SV3 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[351]) ).

thf(390,plain,
    ! [SV4: $i,SV86: $i,SV35: $i] :
      ( ( ( ~ ( c @ SV35 @ SV86 ) )
        = $true )
      | ( ( ~ ( ws @ b @ SV86 ) )
        = $true )
      | ( ( ws @ b @ SV35 )
        = $true )
      | ( ( fool @ SV4 @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[352]) ).

thf(391,plain,
    ! [SV5: $i,SV70: $i,SV36: $i] :
      ( ( ( b @ SV36 @ SV70 )
        = $false )
      | ( ( ws @ c @ SV70 )
        = $true )
      | ( ( ws @ c @ SV36 )
        = $false )
      | ( ( fool @ SV5 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[353]) ).

thf(392,plain,
    ! [SV6: $i,SV71: $i,SV37: $i] :
      ( ( ( a @ SV37 @ SV71 )
        = $false )
      | ( ( ws @ c @ SV71 )
        = $true )
      | ( ( ws @ c @ SV37 )
        = $false )
      | ( ( fool @ SV6 @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[354]) ).

thf(393,plain,
    ! [SV63: $i,SV38: $i > $o,SV101: $i,SV7: $i] :
      ( ( ( ~ ( a @ SV7 @ SV101 )
          | ~ ! [SY163: $i] :
                ( ~ ( c @ SV101 @ SY163 )
                | ( SV38 @ SY163 ) ) )
        = $true )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( c @ SV7 @ SV63 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[355]) ).

thf(394,plain,
    ! [SV8: $i,SV72: $i,SV39: $i] :
      ( ( ( b @ SV39 @ SV72 )
        = $false )
      | ( ( ws @ a @ SV72 )
        = $true )
      | ( ( ws @ a @ SV39 )
        = $false )
      | ( ( fool @ SV8 @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[356]) ).

thf(395,plain,
    ! [SV9: $i,SV87: $i,SV40: $i] :
      ( ( ( ~ ( c @ SV40 @ SV87 ) )
        = $true )
      | ( ( ~ ( ws @ a @ SV87 ) )
        = $true )
      | ( ( ws @ a @ SV40 )
        = $true )
      | ( ( fool @ SV9 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[357]) ).

thf(396,plain,
    ! [SV10: $i,SV88: $i,SV41: $i] :
      ( ( ( ~ ( a @ SV41 @ SV88 ) )
        = $true )
      | ( ( ~ ( ws @ c @ SV88 ) )
        = $true )
      | ( ( ws @ c @ SV41 )
        = $true )
      | ( ( fool @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[358]) ).

thf(397,plain,
    ! [SV64: $i,SV42: $i > $o,SV102: $i,SV11: $i] :
      ( ( ( ~ ( b @ SV11 @ SV102 )
          | ~ ! [SY164: $i] :
                ( ~ ( c @ SV102 @ SY164 )
                | ( SV42 @ SY164 ) ) )
        = $true )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( c @ SV11 @ SV64 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[359]) ).

thf(398,plain,
    ! [SV43: $i > $o,SV89: $i,SV12: $i] :
      ( ( ( ~ ( c @ SV12 @ SV89 ) )
        = $true )
      | ( ( SV43 @ SV89 )
        = $true )
      | ( ( fool @ SV12 @ ( sK5_SY104 @ SV43 @ SV12 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[360]) ).

thf(399,plain,
    ! [SV43: $i > $o,SV73: $i,SV12: $i] :
      ( ( ( c @ SV12 @ SV73 )
        = $false )
      | ( ( SV43 @ SV73 )
        = $true )
      | ( ( SV43 @ ( sK5_SY104 @ SV43 @ SV12 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[361]) ).

thf(400,plain,
    ! [SV13: $i,SV90: $i,SV44: $i] :
      ( ( ( ~ ( b @ SV44 @ SV90 ) )
        = $true )
      | ( ( ~ ( ws @ c @ SV90 ) )
        = $true )
      | ( ( ws @ c @ SV44 )
        = $true )
      | ( ( fool @ SV13 @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[362]) ).

thf(401,plain,
    ! [SV45: $i > $o,SV91: $i,SV14: $i] :
      ( ( ( ~ ( a @ SV14 @ SV91 ) )
        = $true )
      | ( ( ! [SY156: $i] :
              ( ~ ( c @ SV91 @ SY156 )
              | ( SV45 @ SY156 ) ) )
        = $true )
      | ( ( c @ SV14 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[363]) ).

thf(402,plain,
    ! [SV45: $i > $o,SV74: $i,SV14: $i] :
      ( ( ( a @ SV14 @ SV74 )
        = $false )
      | ( ( ! [SY149: $i] :
              ( ~ ( c @ SV74 @ SY149 )
              | ( SV45 @ SY149 ) ) )
        = $true )
      | ( ( SV45 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[364]) ).

thf(403,plain,
    ! [SV65: $i,SV46: $i > $o,SV103: $i,SV15: $i] :
      ( ( ( ~ ( c @ SV15 @ SV103 )
          | ~ ! [SY165: $i] :
                ( ~ ( a @ SV103 @ SY165 )
                | ( SV46 @ SY165 ) ) )
        = $true )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( a @ SV15 @ SV65 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[365]) ).

thf(404,plain,
    ! [SV16: $i,SV75: $i,SV47: $i] :
      ( ( ( c @ SV47 @ SV75 )
        = $false )
      | ( ( ws @ a @ SV75 )
        = $true )
      | ( ( ws @ a @ SV47 )
        = $false )
      | ( ( fool @ SV16 @ SV47 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[366]) ).

thf(405,plain,
    ! [SV48: $i > $o,SV92: $i,SV17: $i] :
      ( ( ( ~ ( b @ SV17 @ SV92 ) )
        = $true )
      | ( ( ! [SY157: $i] :
              ( ~ ( c @ SV92 @ SY157 )
              | ( SV48 @ SY157 ) ) )
        = $true )
      | ( ( c @ SV17 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[367]) ).

thf(406,plain,
    ! [SV48: $i > $o,SV76: $i,SV17: $i] :
      ( ( ( b @ SV17 @ SV76 )
        = $false )
      | ( ( ! [SY150: $i] :
              ( ~ ( c @ SV76 @ SY150 )
              | ( SV48 @ SY150 ) ) )
        = $true )
      | ( ( SV48 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[368]) ).

thf(407,plain,
    ! [SV66: $i,SV49: $i > $o,SV104: $i,SV18: $i] :
      ( ( ( ~ ( b @ SV18 @ SV104 )
          | ~ ! [SY166: $i] :
                ( ~ ( a @ SV104 @ SY166 )
                | ( SV49 @ SY166 ) ) )
        = $true )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( a @ SV18 @ SV66 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[369]) ).

thf(408,plain,
    ! [SV50: $i > $o,SV93: $i,SV19: $i] :
      ( ( ( ~ ( c @ SV19 @ SV93 ) )
        = $true )
      | ( ( ! [SY158: $i] :
              ( ~ ( a @ SV93 @ SY158 )
              | ( SV50 @ SY158 ) ) )
        = $true )
      | ( ( a @ SV19 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[370]) ).

thf(409,plain,
    ! [SV50: $i > $o,SV77: $i,SV19: $i] :
      ( ( ( c @ SV19 @ SV77 )
        = $false )
      | ( ( ! [SY151: $i] :
              ( ~ ( a @ SV77 @ SY151 )
              | ( SV50 @ SY151 ) ) )
        = $true )
      | ( ( SV50 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[371]) ).

thf(410,plain,
    ! [SV21: $i,SV78: $i,SV51: $i] :
      ( ( ( c @ SV51 @ SV78 )
        = $false )
      | ( ( ws @ b @ SV78 )
        = $true )
      | ( ( ws @ b @ SV51 )
        = $false )
      | ( ( fool @ SV21 @ SV51 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[372]) ).

thf(411,plain,
    ! [SV52: $i > $o,SV94: $i,SV22: $i] :
      ( ( ( ~ ( a @ SV22 @ SV94 ) )
        = $true )
      | ( ( SV52 @ SV94 )
        = $true )
      | ( ( fool @ SV22 @ ( sK9_SY124 @ SV52 @ SV22 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[373]) ).

thf(412,plain,
    ! [SV52: $i > $o,SV79: $i,SV22: $i] :
      ( ( ( a @ SV22 @ SV79 )
        = $false )
      | ( ( SV52 @ SV79 )
        = $true )
      | ( ( SV52 @ ( sK9_SY124 @ SV52 @ SV22 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[374]) ).

thf(413,plain,
    ! [SV67: $i,SV53: $i > $o,SV105: $i,SV23: $i] :
      ( ( ( ~ ( c @ SV23 @ SV105 )
          | ~ ! [SY167: $i] :
                ( ~ ( b @ SV105 @ SY167 )
                | ( SV53 @ SY167 ) ) )
        = $true )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( b @ SV23 @ SV67 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[375]) ).

thf(414,plain,
    ! [SV54: $i > $o,SV95: $i,SV24: $i] :
      ( ( ( ~ ( c @ SV24 @ SV95 ) )
        = $true )
      | ( ( ! [SY159: $i] :
              ( ~ ( b @ SV95 @ SY159 )
              | ( SV54 @ SY159 ) ) )
        = $true )
      | ( ( b @ SV24 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[376]) ).

thf(415,plain,
    ! [SV54: $i > $o,SV80: $i,SV24: $i] :
      ( ( ( c @ SV24 @ SV80 )
        = $false )
      | ( ( ! [SY152: $i] :
              ( ~ ( b @ SV80 @ SY152 )
              | ( SV54 @ SY152 ) ) )
        = $true )
      | ( ( SV54 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[377]) ).

thf(416,plain,
    ! [SV56: $i > $o,SV96: $i,SV26: $i] :
      ( ( ( ~ ( b @ SV26 @ SV96 ) )
        = $true )
      | ( ( ! [SY160: $i] :
              ( ~ ( a @ SV96 @ SY160 )
              | ( SV56 @ SY160 ) ) )
        = $true )
      | ( ( a @ SV26 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[378]) ).

thf(417,plain,
    ! [SV56: $i > $o,SV81: $i,SV26: $i] :
      ( ( ( b @ SV26 @ SV81 )
        = $false )
      | ( ( ! [SY153: $i] :
              ( ~ ( a @ SV81 @ SY153 )
              | ( SV56 @ SY153 ) ) )
        = $true )
      | ( ( SV56 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[379]) ).

thf(418,plain,
    ! [SV27: $i,SV97: $i,SV57: $i] :
      ( ( ( ~ ( a @ SV57 @ SV97 ) )
        = $true )
      | ( ( ~ ( ws @ b @ SV97 ) )
        = $true )
      | ( ( ws @ b @ SV57 )
        = $true )
      | ( ( fool @ SV27 @ SV57 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[380]) ).

thf(419,plain,
    ! [SV58: $i > $o,SV98: $i,SV28: $i] :
      ( ( ( ~ ( a @ SV28 @ SV98 ) )
        = $true )
      | ( ( ! [SY161: $i] :
              ( ~ ( b @ SV98 @ SY161 )
              | ( SV58 @ SY161 ) ) )
        = $true )
      | ( ( b @ SV28 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[381]) ).

thf(420,plain,
    ! [SV58: $i > $o,SV82: $i,SV28: $i] :
      ( ( ( a @ SV28 @ SV82 )
        = $false )
      | ( ( ! [SY154: $i] :
              ( ~ ( b @ SV82 @ SY154 )
              | ( SV58 @ SY154 ) ) )
        = $true )
      | ( ( SV58 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[382]) ).

thf(421,plain,
    ! [SV68: $i,SV59: $i > $o,SV106: $i,SV29: $i] :
      ( ( ( ~ ( a @ SV29 @ SV106 )
          | ~ ! [SY168: $i] :
                ( ~ ( b @ SV106 @ SY168 )
                | ( SV59 @ SY168 ) ) )
        = $true )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( b @ SV29 @ SV68 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[383]) ).

thf(422,plain,
    ! [SV60: $i > $o,SV99: $i,SV30: $i] :
      ( ( ( ~ ( b @ SV30 @ SV99 ) )
        = $true )
      | ( ( SV60 @ SV99 )
        = $true )
      | ( ( fool @ SV30 @ ( sK13_SY143 @ SV60 @ SV30 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[384]) ).

thf(423,plain,
    ! [SV60: $i > $o,SV83: $i,SV30: $i] :
      ( ( ( b @ SV30 @ SV83 )
        = $false )
      | ( ( SV60 @ SV83 )
        = $true )
      | ( ( SV60 @ ( sK13_SY143 @ SV60 @ SV30 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[385]) ).

thf(424,plain,
    ! [SV62: $i > $o,SV100: $i,SV32: $i] :
      ( ( ( ~ ( fool @ SV32 @ SV100 ) )
        = $true )
      | ( ( ! [SY162: $i] :
              ( ~ ( fool @ SV100 @ SY162 )
              | ( SV62 @ SY162 ) ) )
        = $true )
      | ( ( fool @ SV32 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[386]) ).

thf(425,plain,
    ! [SV62: $i > $o,SV84: $i,SV32: $i] :
      ( ( ( fool @ SV32 @ SV84 )
        = $false )
      | ( ( ! [SY155: $i] :
              ( ~ ( fool @ SV84 @ SY155 )
              | ( SV62 @ SY155 ) ) )
        = $true )
      | ( ( SV62 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[387]) ).

thf(426,plain,
    ! [SV1: $i,SV85: $i,SV33: $i] :
      ( ( ( b @ SV33 @ SV85 )
        = $false )
      | ( ( ~ ( ws @ a @ SV85 ) )
        = $true )
      | ( ( ws @ a @ SV33 )
        = $true )
      | ( ( fool @ SV1 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[388]) ).

thf(427,plain,
    ! [SV4: $i,SV86: $i,SV35: $i] :
      ( ( ( c @ SV35 @ SV86 )
        = $false )
      | ( ( ~ ( ws @ b @ SV86 ) )
        = $true )
      | ( ( ws @ b @ SV35 )
        = $true )
      | ( ( fool @ SV4 @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[390]) ).

thf(428,plain,
    ! [SV63: $i,SV38: $i > $o,SV101: $i,SV7: $i] :
      ( ( ( ~ ( a @ SV7 @ SV101 ) )
        = $true )
      | ( ( ~ ! [SY163: $i] :
                ( ~ ( c @ SV101 @ SY163 )
                | ( SV38 @ SY163 ) ) )
        = $true )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( c @ SV7 @ SV63 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[393]) ).

thf(429,plain,
    ! [SV9: $i,SV87: $i,SV40: $i] :
      ( ( ( c @ SV40 @ SV87 )
        = $false )
      | ( ( ~ ( ws @ a @ SV87 ) )
        = $true )
      | ( ( ws @ a @ SV40 )
        = $true )
      | ( ( fool @ SV9 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[395]) ).

thf(430,plain,
    ! [SV10: $i,SV88: $i,SV41: $i] :
      ( ( ( a @ SV41 @ SV88 )
        = $false )
      | ( ( ~ ( ws @ c @ SV88 ) )
        = $true )
      | ( ( ws @ c @ SV41 )
        = $true )
      | ( ( fool @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[396]) ).

thf(431,plain,
    ! [SV64: $i,SV42: $i > $o,SV102: $i,SV11: $i] :
      ( ( ( ~ ( b @ SV11 @ SV102 ) )
        = $true )
      | ( ( ~ ! [SY164: $i] :
                ( ~ ( c @ SV102 @ SY164 )
                | ( SV42 @ SY164 ) ) )
        = $true )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( c @ SV11 @ SV64 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[397]) ).

thf(432,plain,
    ! [SV43: $i > $o,SV89: $i,SV12: $i] :
      ( ( ( c @ SV12 @ SV89 )
        = $false )
      | ( ( SV43 @ SV89 )
        = $true )
      | ( ( fool @ SV12 @ ( sK5_SY104 @ SV43 @ SV12 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[398]) ).

thf(433,plain,
    ! [SV13: $i,SV90: $i,SV44: $i] :
      ( ( ( b @ SV44 @ SV90 )
        = $false )
      | ( ( ~ ( ws @ c @ SV90 ) )
        = $true )
      | ( ( ws @ c @ SV44 )
        = $true )
      | ( ( fool @ SV13 @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[400]) ).

thf(434,plain,
    ! [SV45: $i > $o,SV91: $i,SV14: $i] :
      ( ( ( a @ SV14 @ SV91 )
        = $false )
      | ( ( ! [SY156: $i] :
              ( ~ ( c @ SV91 @ SY156 )
              | ( SV45 @ SY156 ) ) )
        = $true )
      | ( ( c @ SV14 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[401]) ).

thf(435,plain,
    ! [SV14: $i,SV45: $i > $o,SV107: $i,SV74: $i] :
      ( ( ( ~ ( c @ SV74 @ SV107 )
          | ( SV45 @ SV107 ) )
        = $true )
      | ( ( a @ SV14 @ SV74 )
        = $false )
      | ( ( SV45 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[402]) ).

thf(436,plain,
    ! [SV65: $i,SV46: $i > $o,SV103: $i,SV15: $i] :
      ( ( ( ~ ( c @ SV15 @ SV103 ) )
        = $true )
      | ( ( ~ ! [SY165: $i] :
                ( ~ ( a @ SV103 @ SY165 )
                | ( SV46 @ SY165 ) ) )
        = $true )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( a @ SV15 @ SV65 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[403]) ).

thf(437,plain,
    ! [SV48: $i > $o,SV92: $i,SV17: $i] :
      ( ( ( b @ SV17 @ SV92 )
        = $false )
      | ( ( ! [SY157: $i] :
              ( ~ ( c @ SV92 @ SY157 )
              | ( SV48 @ SY157 ) ) )
        = $true )
      | ( ( c @ SV17 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[405]) ).

thf(438,plain,
    ! [SV17: $i,SV48: $i > $o,SV108: $i,SV76: $i] :
      ( ( ( ~ ( c @ SV76 @ SV108 )
          | ( SV48 @ SV108 ) )
        = $true )
      | ( ( b @ SV17 @ SV76 )
        = $false )
      | ( ( SV48 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[406]) ).

thf(439,plain,
    ! [SV66: $i,SV49: $i > $o,SV104: $i,SV18: $i] :
      ( ( ( ~ ( b @ SV18 @ SV104 ) )
        = $true )
      | ( ( ~ ! [SY166: $i] :
                ( ~ ( a @ SV104 @ SY166 )
                | ( SV49 @ SY166 ) ) )
        = $true )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( a @ SV18 @ SV66 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[407]) ).

thf(440,plain,
    ! [SV50: $i > $o,SV93: $i,SV19: $i] :
      ( ( ( c @ SV19 @ SV93 )
        = $false )
      | ( ( ! [SY158: $i] :
              ( ~ ( a @ SV93 @ SY158 )
              | ( SV50 @ SY158 ) ) )
        = $true )
      | ( ( a @ SV19 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[408]) ).

thf(441,plain,
    ! [SV19: $i,SV50: $i > $o,SV109: $i,SV77: $i] :
      ( ( ( ~ ( a @ SV77 @ SV109 )
          | ( SV50 @ SV109 ) )
        = $true )
      | ( ( c @ SV19 @ SV77 )
        = $false )
      | ( ( SV50 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[409]) ).

thf(442,plain,
    ! [SV52: $i > $o,SV94: $i,SV22: $i] :
      ( ( ( a @ SV22 @ SV94 )
        = $false )
      | ( ( SV52 @ SV94 )
        = $true )
      | ( ( fool @ SV22 @ ( sK9_SY124 @ SV52 @ SV22 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[411]) ).

thf(443,plain,
    ! [SV67: $i,SV53: $i > $o,SV105: $i,SV23: $i] :
      ( ( ( ~ ( c @ SV23 @ SV105 ) )
        = $true )
      | ( ( ~ ! [SY167: $i] :
                ( ~ ( b @ SV105 @ SY167 )
                | ( SV53 @ SY167 ) ) )
        = $true )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( b @ SV23 @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[413]) ).

thf(444,plain,
    ! [SV54: $i > $o,SV95: $i,SV24: $i] :
      ( ( ( c @ SV24 @ SV95 )
        = $false )
      | ( ( ! [SY159: $i] :
              ( ~ ( b @ SV95 @ SY159 )
              | ( SV54 @ SY159 ) ) )
        = $true )
      | ( ( b @ SV24 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[414]) ).

thf(445,plain,
    ! [SV24: $i,SV54: $i > $o,SV110: $i,SV80: $i] :
      ( ( ( ~ ( b @ SV80 @ SV110 )
          | ( SV54 @ SV110 ) )
        = $true )
      | ( ( c @ SV24 @ SV80 )
        = $false )
      | ( ( SV54 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[415]) ).

thf(446,plain,
    ! [SV56: $i > $o,SV96: $i,SV26: $i] :
      ( ( ( b @ SV26 @ SV96 )
        = $false )
      | ( ( ! [SY160: $i] :
              ( ~ ( a @ SV96 @ SY160 )
              | ( SV56 @ SY160 ) ) )
        = $true )
      | ( ( a @ SV26 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[416]) ).

thf(447,plain,
    ! [SV26: $i,SV56: $i > $o,SV111: $i,SV81: $i] :
      ( ( ( ~ ( a @ SV81 @ SV111 )
          | ( SV56 @ SV111 ) )
        = $true )
      | ( ( b @ SV26 @ SV81 )
        = $false )
      | ( ( SV56 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[417]) ).

thf(448,plain,
    ! [SV27: $i,SV97: $i,SV57: $i] :
      ( ( ( a @ SV57 @ SV97 )
        = $false )
      | ( ( ~ ( ws @ b @ SV97 ) )
        = $true )
      | ( ( ws @ b @ SV57 )
        = $true )
      | ( ( fool @ SV27 @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[418]) ).

thf(449,plain,
    ! [SV58: $i > $o,SV98: $i,SV28: $i] :
      ( ( ( a @ SV28 @ SV98 )
        = $false )
      | ( ( ! [SY161: $i] :
              ( ~ ( b @ SV98 @ SY161 )
              | ( SV58 @ SY161 ) ) )
        = $true )
      | ( ( b @ SV28 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[419]) ).

thf(450,plain,
    ! [SV28: $i,SV58: $i > $o,SV112: $i,SV82: $i] :
      ( ( ( ~ ( b @ SV82 @ SV112 )
          | ( SV58 @ SV112 ) )
        = $true )
      | ( ( a @ SV28 @ SV82 )
        = $false )
      | ( ( SV58 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[420]) ).

thf(451,plain,
    ! [SV68: $i,SV59: $i > $o,SV106: $i,SV29: $i] :
      ( ( ( ~ ( a @ SV29 @ SV106 ) )
        = $true )
      | ( ( ~ ! [SY168: $i] :
                ( ~ ( b @ SV106 @ SY168 )
                | ( SV59 @ SY168 ) ) )
        = $true )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( b @ SV29 @ SV68 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[421]) ).

thf(452,plain,
    ! [SV60: $i > $o,SV99: $i,SV30: $i] :
      ( ( ( b @ SV30 @ SV99 )
        = $false )
      | ( ( SV60 @ SV99 )
        = $true )
      | ( ( fool @ SV30 @ ( sK13_SY143 @ SV60 @ SV30 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[422]) ).

thf(453,plain,
    ! [SV62: $i > $o,SV100: $i,SV32: $i] :
      ( ( ( fool @ SV32 @ SV100 )
        = $false )
      | ( ( ! [SY162: $i] :
              ( ~ ( fool @ SV100 @ SY162 )
              | ( SV62 @ SY162 ) ) )
        = $true )
      | ( ( fool @ SV32 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[424]) ).

thf(454,plain,
    ! [SV32: $i,SV62: $i > $o,SV113: $i,SV84: $i] :
      ( ( ( ~ ( fool @ SV84 @ SV113 )
          | ( SV62 @ SV113 ) )
        = $true )
      | ( ( fool @ SV32 @ SV84 )
        = $false )
      | ( ( SV62 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[425]) ).

thf(455,plain,
    ! [SV1: $i,SV33: $i,SV85: $i] :
      ( ( ( ws @ a @ SV85 )
        = $false )
      | ( ( b @ SV33 @ SV85 )
        = $false )
      | ( ( ws @ a @ SV33 )
        = $true )
      | ( ( fool @ SV1 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[426]) ).

thf(456,plain,
    ! [SV4: $i,SV35: $i,SV86: $i] :
      ( ( ( ws @ b @ SV86 )
        = $false )
      | ( ( c @ SV35 @ SV86 )
        = $false )
      | ( ( ws @ b @ SV35 )
        = $true )
      | ( ( fool @ SV4 @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[427]) ).

thf(457,plain,
    ! [SV63: $i,SV38: $i > $o,SV101: $i,SV7: $i] :
      ( ( ( a @ SV7 @ SV101 )
        = $false )
      | ( ( ~ ! [SY163: $i] :
                ( ~ ( c @ SV101 @ SY163 )
                | ( SV38 @ SY163 ) ) )
        = $true )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( c @ SV7 @ SV63 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[428]) ).

thf(458,plain,
    ! [SV9: $i,SV40: $i,SV87: $i] :
      ( ( ( ws @ a @ SV87 )
        = $false )
      | ( ( c @ SV40 @ SV87 )
        = $false )
      | ( ( ws @ a @ SV40 )
        = $true )
      | ( ( fool @ SV9 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[429]) ).

thf(459,plain,
    ! [SV10: $i,SV41: $i,SV88: $i] :
      ( ( ( ws @ c @ SV88 )
        = $false )
      | ( ( a @ SV41 @ SV88 )
        = $false )
      | ( ( ws @ c @ SV41 )
        = $true )
      | ( ( fool @ SV10 @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[430]) ).

thf(460,plain,
    ! [SV64: $i,SV42: $i > $o,SV102: $i,SV11: $i] :
      ( ( ( b @ SV11 @ SV102 )
        = $false )
      | ( ( ~ ! [SY164: $i] :
                ( ~ ( c @ SV102 @ SY164 )
                | ( SV42 @ SY164 ) ) )
        = $true )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( c @ SV11 @ SV64 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[431]) ).

thf(461,plain,
    ! [SV13: $i,SV44: $i,SV90: $i] :
      ( ( ( ws @ c @ SV90 )
        = $false )
      | ( ( b @ SV44 @ SV90 )
        = $false )
      | ( ( ws @ c @ SV44 )
        = $true )
      | ( ( fool @ SV13 @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[433]) ).

thf(462,plain,
    ! [SV14: $i,SV45: $i > $o,SV114: $i,SV91: $i] :
      ( ( ( ~ ( c @ SV91 @ SV114 )
          | ( SV45 @ SV114 ) )
        = $true )
      | ( ( a @ SV14 @ SV91 )
        = $false )
      | ( ( c @ SV14 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[434]) ).

thf(463,plain,
    ! [SV14: $i,SV45: $i > $o,SV107: $i,SV74: $i] :
      ( ( ( ~ ( c @ SV74 @ SV107 ) )
        = $true )
      | ( ( SV45 @ SV107 )
        = $true )
      | ( ( a @ SV14 @ SV74 )
        = $false )
      | ( ( SV45 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[435]) ).

thf(464,plain,
    ! [SV65: $i,SV46: $i > $o,SV103: $i,SV15: $i] :
      ( ( ( c @ SV15 @ SV103 )
        = $false )
      | ( ( ~ ! [SY165: $i] :
                ( ~ ( a @ SV103 @ SY165 )
                | ( SV46 @ SY165 ) ) )
        = $true )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( a @ SV15 @ SV65 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[436]) ).

thf(465,plain,
    ! [SV17: $i,SV48: $i > $o,SV115: $i,SV92: $i] :
      ( ( ( ~ ( c @ SV92 @ SV115 )
          | ( SV48 @ SV115 ) )
        = $true )
      | ( ( b @ SV17 @ SV92 )
        = $false )
      | ( ( c @ SV17 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[437]) ).

thf(466,plain,
    ! [SV17: $i,SV48: $i > $o,SV108: $i,SV76: $i] :
      ( ( ( ~ ( c @ SV76 @ SV108 ) )
        = $true )
      | ( ( SV48 @ SV108 )
        = $true )
      | ( ( b @ SV17 @ SV76 )
        = $false )
      | ( ( SV48 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[438]) ).

thf(467,plain,
    ! [SV66: $i,SV49: $i > $o,SV104: $i,SV18: $i] :
      ( ( ( b @ SV18 @ SV104 )
        = $false )
      | ( ( ~ ! [SY166: $i] :
                ( ~ ( a @ SV104 @ SY166 )
                | ( SV49 @ SY166 ) ) )
        = $true )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( a @ SV18 @ SV66 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[439]) ).

thf(468,plain,
    ! [SV19: $i,SV50: $i > $o,SV116: $i,SV93: $i] :
      ( ( ( ~ ( a @ SV93 @ SV116 )
          | ( SV50 @ SV116 ) )
        = $true )
      | ( ( c @ SV19 @ SV93 )
        = $false )
      | ( ( a @ SV19 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[440]) ).

thf(469,plain,
    ! [SV19: $i,SV50: $i > $o,SV109: $i,SV77: $i] :
      ( ( ( ~ ( a @ SV77 @ SV109 ) )
        = $true )
      | ( ( SV50 @ SV109 )
        = $true )
      | ( ( c @ SV19 @ SV77 )
        = $false )
      | ( ( SV50 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[441]) ).

thf(470,plain,
    ! [SV67: $i,SV53: $i > $o,SV105: $i,SV23: $i] :
      ( ( ( c @ SV23 @ SV105 )
        = $false )
      | ( ( ~ ! [SY167: $i] :
                ( ~ ( b @ SV105 @ SY167 )
                | ( SV53 @ SY167 ) ) )
        = $true )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( b @ SV23 @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[443]) ).

thf(471,plain,
    ! [SV24: $i,SV54: $i > $o,SV117: $i,SV95: $i] :
      ( ( ( ~ ( b @ SV95 @ SV117 )
          | ( SV54 @ SV117 ) )
        = $true )
      | ( ( c @ SV24 @ SV95 )
        = $false )
      | ( ( b @ SV24 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[444]) ).

thf(472,plain,
    ! [SV24: $i,SV54: $i > $o,SV110: $i,SV80: $i] :
      ( ( ( ~ ( b @ SV80 @ SV110 ) )
        = $true )
      | ( ( SV54 @ SV110 )
        = $true )
      | ( ( c @ SV24 @ SV80 )
        = $false )
      | ( ( SV54 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[445]) ).

thf(473,plain,
    ! [SV26: $i,SV56: $i > $o,SV118: $i,SV96: $i] :
      ( ( ( ~ ( a @ SV96 @ SV118 )
          | ( SV56 @ SV118 ) )
        = $true )
      | ( ( b @ SV26 @ SV96 )
        = $false )
      | ( ( a @ SV26 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[446]) ).

thf(474,plain,
    ! [SV26: $i,SV56: $i > $o,SV111: $i,SV81: $i] :
      ( ( ( ~ ( a @ SV81 @ SV111 ) )
        = $true )
      | ( ( SV56 @ SV111 )
        = $true )
      | ( ( b @ SV26 @ SV81 )
        = $false )
      | ( ( SV56 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[447]) ).

thf(475,plain,
    ! [SV27: $i,SV57: $i,SV97: $i] :
      ( ( ( ws @ b @ SV97 )
        = $false )
      | ( ( a @ SV57 @ SV97 )
        = $false )
      | ( ( ws @ b @ SV57 )
        = $true )
      | ( ( fool @ SV27 @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[448]) ).

thf(476,plain,
    ! [SV28: $i,SV58: $i > $o,SV119: $i,SV98: $i] :
      ( ( ( ~ ( b @ SV98 @ SV119 )
          | ( SV58 @ SV119 ) )
        = $true )
      | ( ( a @ SV28 @ SV98 )
        = $false )
      | ( ( b @ SV28 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[449]) ).

thf(477,plain,
    ! [SV28: $i,SV58: $i > $o,SV112: $i,SV82: $i] :
      ( ( ( ~ ( b @ SV82 @ SV112 ) )
        = $true )
      | ( ( SV58 @ SV112 )
        = $true )
      | ( ( a @ SV28 @ SV82 )
        = $false )
      | ( ( SV58 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[450]) ).

thf(478,plain,
    ! [SV68: $i,SV59: $i > $o,SV106: $i,SV29: $i] :
      ( ( ( a @ SV29 @ SV106 )
        = $false )
      | ( ( ~ ! [SY168: $i] :
                ( ~ ( b @ SV106 @ SY168 )
                | ( SV59 @ SY168 ) ) )
        = $true )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( b @ SV29 @ SV68 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[451]) ).

thf(479,plain,
    ! [SV32: $i,SV62: $i > $o,SV120: $i,SV100: $i] :
      ( ( ( ~ ( fool @ SV100 @ SV120 )
          | ( SV62 @ SV120 ) )
        = $true )
      | ( ( fool @ SV32 @ SV100 )
        = $false )
      | ( ( fool @ SV32 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[453]) ).

thf(480,plain,
    ! [SV32: $i,SV62: $i > $o,SV113: $i,SV84: $i] :
      ( ( ( ~ ( fool @ SV84 @ SV113 ) )
        = $true )
      | ( ( SV62 @ SV113 )
        = $true )
      | ( ( fool @ SV32 @ SV84 )
        = $false )
      | ( ( SV62 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[454]) ).

thf(481,plain,
    ! [SV63: $i,SV7: $i,SV38: $i > $o,SV101: $i] :
      ( ( ( ! [SY163: $i] :
              ( ~ ( c @ SV101 @ SY163 )
              | ( SV38 @ SY163 ) ) )
        = $false )
      | ( ( a @ SV7 @ SV101 )
        = $false )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( c @ SV7 @ SV63 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[457]) ).

thf(482,plain,
    ! [SV64: $i,SV11: $i,SV42: $i > $o,SV102: $i] :
      ( ( ( ! [SY164: $i] :
              ( ~ ( c @ SV102 @ SY164 )
              | ( SV42 @ SY164 ) ) )
        = $false )
      | ( ( b @ SV11 @ SV102 )
        = $false )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( c @ SV11 @ SV64 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[460]) ).

thf(483,plain,
    ! [SV14: $i,SV45: $i > $o,SV114: $i,SV91: $i] :
      ( ( ( ~ ( c @ SV91 @ SV114 ) )
        = $true )
      | ( ( SV45 @ SV114 )
        = $true )
      | ( ( a @ SV14 @ SV91 )
        = $false )
      | ( ( c @ SV14 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[462]) ).

thf(484,plain,
    ! [SV14: $i,SV45: $i > $o,SV107: $i,SV74: $i] :
      ( ( ( c @ SV74 @ SV107 )
        = $false )
      | ( ( SV45 @ SV107 )
        = $true )
      | ( ( a @ SV14 @ SV74 )
        = $false )
      | ( ( SV45 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[463]) ).

thf(485,plain,
    ! [SV65: $i,SV15: $i,SV46: $i > $o,SV103: $i] :
      ( ( ( ! [SY165: $i] :
              ( ~ ( a @ SV103 @ SY165 )
              | ( SV46 @ SY165 ) ) )
        = $false )
      | ( ( c @ SV15 @ SV103 )
        = $false )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( a @ SV15 @ SV65 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[464]) ).

thf(486,plain,
    ! [SV17: $i,SV48: $i > $o,SV115: $i,SV92: $i] :
      ( ( ( ~ ( c @ SV92 @ SV115 ) )
        = $true )
      | ( ( SV48 @ SV115 )
        = $true )
      | ( ( b @ SV17 @ SV92 )
        = $false )
      | ( ( c @ SV17 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[465]) ).

thf(487,plain,
    ! [SV17: $i,SV48: $i > $o,SV108: $i,SV76: $i] :
      ( ( ( c @ SV76 @ SV108 )
        = $false )
      | ( ( SV48 @ SV108 )
        = $true )
      | ( ( b @ SV17 @ SV76 )
        = $false )
      | ( ( SV48 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[466]) ).

thf(488,plain,
    ! [SV66: $i,SV18: $i,SV49: $i > $o,SV104: $i] :
      ( ( ( ! [SY166: $i] :
              ( ~ ( a @ SV104 @ SY166 )
              | ( SV49 @ SY166 ) ) )
        = $false )
      | ( ( b @ SV18 @ SV104 )
        = $false )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( a @ SV18 @ SV66 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[467]) ).

thf(489,plain,
    ! [SV19: $i,SV50: $i > $o,SV116: $i,SV93: $i] :
      ( ( ( ~ ( a @ SV93 @ SV116 ) )
        = $true )
      | ( ( SV50 @ SV116 )
        = $true )
      | ( ( c @ SV19 @ SV93 )
        = $false )
      | ( ( a @ SV19 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[468]) ).

thf(490,plain,
    ! [SV19: $i,SV50: $i > $o,SV109: $i,SV77: $i] :
      ( ( ( a @ SV77 @ SV109 )
        = $false )
      | ( ( SV50 @ SV109 )
        = $true )
      | ( ( c @ SV19 @ SV77 )
        = $false )
      | ( ( SV50 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[469]) ).

thf(491,plain,
    ! [SV67: $i,SV23: $i,SV53: $i > $o,SV105: $i] :
      ( ( ( ! [SY167: $i] :
              ( ~ ( b @ SV105 @ SY167 )
              | ( SV53 @ SY167 ) ) )
        = $false )
      | ( ( c @ SV23 @ SV105 )
        = $false )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( b @ SV23 @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[470]) ).

thf(492,plain,
    ! [SV24: $i,SV54: $i > $o,SV117: $i,SV95: $i] :
      ( ( ( ~ ( b @ SV95 @ SV117 ) )
        = $true )
      | ( ( SV54 @ SV117 )
        = $true )
      | ( ( c @ SV24 @ SV95 )
        = $false )
      | ( ( b @ SV24 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[471]) ).

thf(493,plain,
    ! [SV24: $i,SV54: $i > $o,SV110: $i,SV80: $i] :
      ( ( ( b @ SV80 @ SV110 )
        = $false )
      | ( ( SV54 @ SV110 )
        = $true )
      | ( ( c @ SV24 @ SV80 )
        = $false )
      | ( ( SV54 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[472]) ).

thf(494,plain,
    ! [SV26: $i,SV56: $i > $o,SV118: $i,SV96: $i] :
      ( ( ( ~ ( a @ SV96 @ SV118 ) )
        = $true )
      | ( ( SV56 @ SV118 )
        = $true )
      | ( ( b @ SV26 @ SV96 )
        = $false )
      | ( ( a @ SV26 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[473]) ).

thf(495,plain,
    ! [SV26: $i,SV56: $i > $o,SV111: $i,SV81: $i] :
      ( ( ( a @ SV81 @ SV111 )
        = $false )
      | ( ( SV56 @ SV111 )
        = $true )
      | ( ( b @ SV26 @ SV81 )
        = $false )
      | ( ( SV56 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[474]) ).

thf(496,plain,
    ! [SV28: $i,SV58: $i > $o,SV119: $i,SV98: $i] :
      ( ( ( ~ ( b @ SV98 @ SV119 ) )
        = $true )
      | ( ( SV58 @ SV119 )
        = $true )
      | ( ( a @ SV28 @ SV98 )
        = $false )
      | ( ( b @ SV28 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[476]) ).

thf(497,plain,
    ! [SV28: $i,SV58: $i > $o,SV112: $i,SV82: $i] :
      ( ( ( b @ SV82 @ SV112 )
        = $false )
      | ( ( SV58 @ SV112 )
        = $true )
      | ( ( a @ SV28 @ SV82 )
        = $false )
      | ( ( SV58 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[477]) ).

thf(498,plain,
    ! [SV68: $i,SV29: $i,SV59: $i > $o,SV106: $i] :
      ( ( ( ! [SY168: $i] :
              ( ~ ( b @ SV106 @ SY168 )
              | ( SV59 @ SY168 ) ) )
        = $false )
      | ( ( a @ SV29 @ SV106 )
        = $false )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( b @ SV29 @ SV68 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[478]) ).

thf(499,plain,
    ! [SV32: $i,SV62: $i > $o,SV120: $i,SV100: $i] :
      ( ( ( ~ ( fool @ SV100 @ SV120 ) )
        = $true )
      | ( ( SV62 @ SV120 )
        = $true )
      | ( ( fool @ SV32 @ SV100 )
        = $false )
      | ( ( fool @ SV32 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[479]) ).

thf(500,plain,
    ! [SV32: $i,SV62: $i > $o,SV113: $i,SV84: $i] :
      ( ( ( fool @ SV84 @ SV113 )
        = $false )
      | ( ( SV62 @ SV113 )
        = $true )
      | ( ( fool @ SV32 @ SV84 )
        = $false )
      | ( ( SV62 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[480]) ).

thf(501,plain,
    ! [SV38: $i > $o,SV7: $i,SV63: $i,SV101: $i] :
      ( ( ( ~ ( c @ SV101 @ ( sK16_SY163 @ SV63 @ SV7 @ SV38 @ SV101 ) )
          | ( SV38 @ ( sK16_SY163 @ SV63 @ SV7 @ SV38 @ SV101 ) ) )
        = $false )
      | ( ( a @ SV7 @ SV101 )
        = $false )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( c @ SV7 @ SV63 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[481]) ).

thf(502,plain,
    ! [SV42: $i > $o,SV11: $i,SV64: $i,SV102: $i] :
      ( ( ( ~ ( c @ SV102 @ ( sK17_SY164 @ SV64 @ SV11 @ SV42 @ SV102 ) )
          | ( SV42 @ ( sK17_SY164 @ SV64 @ SV11 @ SV42 @ SV102 ) ) )
        = $false )
      | ( ( b @ SV11 @ SV102 )
        = $false )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( c @ SV11 @ SV64 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[482]) ).

thf(503,plain,
    ! [SV14: $i,SV45: $i > $o,SV114: $i,SV91: $i] :
      ( ( ( c @ SV91 @ SV114 )
        = $false )
      | ( ( SV45 @ SV114 )
        = $true )
      | ( ( a @ SV14 @ SV91 )
        = $false )
      | ( ( c @ SV14 @ ( sK6_SY107 @ SV45 @ SV14 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[483]) ).

thf(504,plain,
    ! [SV46: $i > $o,SV15: $i,SV65: $i,SV103: $i] :
      ( ( ( ~ ( a @ SV103 @ ( sK18_SY165 @ SV65 @ SV15 @ SV46 @ SV103 ) )
          | ( SV46 @ ( sK18_SY165 @ SV65 @ SV15 @ SV46 @ SV103 ) ) )
        = $false )
      | ( ( c @ SV15 @ SV103 )
        = $false )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( a @ SV15 @ SV65 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[485]) ).

thf(505,plain,
    ! [SV17: $i,SV48: $i > $o,SV115: $i,SV92: $i] :
      ( ( ( c @ SV92 @ SV115 )
        = $false )
      | ( ( SV48 @ SV115 )
        = $true )
      | ( ( b @ SV17 @ SV92 )
        = $false )
      | ( ( c @ SV17 @ ( sK7_SY114 @ SV48 @ SV17 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[486]) ).

thf(506,plain,
    ! [SV49: $i > $o,SV18: $i,SV66: $i,SV104: $i] :
      ( ( ( ~ ( a @ SV104 @ ( sK19_SY166 @ SV66 @ SV18 @ SV49 @ SV104 ) )
          | ( SV49 @ ( sK19_SY166 @ SV66 @ SV18 @ SV49 @ SV104 ) ) )
        = $false )
      | ( ( b @ SV18 @ SV104 )
        = $false )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( a @ SV18 @ SV66 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[488]) ).

thf(507,plain,
    ! [SV19: $i,SV50: $i > $o,SV116: $i,SV93: $i] :
      ( ( ( a @ SV93 @ SV116 )
        = $false )
      | ( ( SV50 @ SV116 )
        = $true )
      | ( ( c @ SV19 @ SV93 )
        = $false )
      | ( ( a @ SV19 @ ( sK8_SY120 @ SV50 @ SV19 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[489]) ).

thf(508,plain,
    ! [SV53: $i > $o,SV23: $i,SV67: $i,SV105: $i] :
      ( ( ( ~ ( b @ SV105 @ ( sK20_SY167 @ SV67 @ SV23 @ SV53 @ SV105 ) )
          | ( SV53 @ ( sK20_SY167 @ SV67 @ SV23 @ SV53 @ SV105 ) ) )
        = $false )
      | ( ( c @ SV23 @ SV105 )
        = $false )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( b @ SV23 @ SV67 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[491]) ).

thf(509,plain,
    ! [SV24: $i,SV54: $i > $o,SV117: $i,SV95: $i] :
      ( ( ( b @ SV95 @ SV117 )
        = $false )
      | ( ( SV54 @ SV117 )
        = $true )
      | ( ( c @ SV24 @ SV95 )
        = $false )
      | ( ( b @ SV24 @ ( sK10_SY129 @ SV54 @ SV24 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[492]) ).

thf(510,plain,
    ! [SV26: $i,SV56: $i > $o,SV118: $i,SV96: $i] :
      ( ( ( a @ SV96 @ SV118 )
        = $false )
      | ( ( SV56 @ SV118 )
        = $true )
      | ( ( b @ SV26 @ SV96 )
        = $false )
      | ( ( a @ SV26 @ ( sK11_SY133 @ SV56 @ SV26 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[494]) ).

thf(511,plain,
    ! [SV28: $i,SV58: $i > $o,SV119: $i,SV98: $i] :
      ( ( ( b @ SV98 @ SV119 )
        = $false )
      | ( ( SV58 @ SV119 )
        = $true )
      | ( ( a @ SV28 @ SV98 )
        = $false )
      | ( ( b @ SV28 @ ( sK12_SY137 @ SV58 @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[496]) ).

thf(512,plain,
    ! [SV59: $i > $o,SV29: $i,SV68: $i,SV106: $i] :
      ( ( ( ~ ( b @ SV106 @ ( sK21_SY168 @ SV68 @ SV29 @ SV59 @ SV106 ) )
          | ( SV59 @ ( sK21_SY168 @ SV68 @ SV29 @ SV59 @ SV106 ) ) )
        = $false )
      | ( ( a @ SV29 @ SV106 )
        = $false )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( b @ SV29 @ SV68 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[498]) ).

thf(513,plain,
    ! [SV32: $i,SV62: $i > $o,SV120: $i,SV100: $i] :
      ( ( ( fool @ SV100 @ SV120 )
        = $false )
      | ( ( SV62 @ SV120 )
        = $true )
      | ( ( fool @ SV32 @ SV100 )
        = $false )
      | ( ( fool @ SV32 @ ( sK15_SY146 @ SV62 @ SV32 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[499]) ).

thf(514,plain,
    ! [SV38: $i > $o,SV7: $i,SV63: $i,SV101: $i] :
      ( ( ( ~ ( c @ SV101 @ ( sK16_SY163 @ SV63 @ SV7 @ SV38 @ SV101 ) ) )
        = $false )
      | ( ( a @ SV7 @ SV101 )
        = $false )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( c @ SV7 @ SV63 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[501]) ).

thf(515,plain,
    ! [SV101: $i,SV7: $i,SV63: $i,SV38: $i > $o] :
      ( ( ( SV38 @ ( sK16_SY163 @ SV63 @ SV7 @ SV38 @ SV101 ) )
        = $false )
      | ( ( a @ SV7 @ SV101 )
        = $false )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( c @ SV7 @ SV63 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[501]) ).

thf(516,plain,
    ! [SV42: $i > $o,SV11: $i,SV64: $i,SV102: $i] :
      ( ( ( ~ ( c @ SV102 @ ( sK17_SY164 @ SV64 @ SV11 @ SV42 @ SV102 ) ) )
        = $false )
      | ( ( b @ SV11 @ SV102 )
        = $false )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( c @ SV11 @ SV64 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[502]) ).

thf(517,plain,
    ! [SV102: $i,SV11: $i,SV64: $i,SV42: $i > $o] :
      ( ( ( SV42 @ ( sK17_SY164 @ SV64 @ SV11 @ SV42 @ SV102 ) )
        = $false )
      | ( ( b @ SV11 @ SV102 )
        = $false )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( c @ SV11 @ SV64 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[502]) ).

thf(518,plain,
    ! [SV46: $i > $o,SV15: $i,SV65: $i,SV103: $i] :
      ( ( ( ~ ( a @ SV103 @ ( sK18_SY165 @ SV65 @ SV15 @ SV46 @ SV103 ) ) )
        = $false )
      | ( ( c @ SV15 @ SV103 )
        = $false )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( a @ SV15 @ SV65 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[504]) ).

thf(519,plain,
    ! [SV103: $i,SV15: $i,SV65: $i,SV46: $i > $o] :
      ( ( ( SV46 @ ( sK18_SY165 @ SV65 @ SV15 @ SV46 @ SV103 ) )
        = $false )
      | ( ( c @ SV15 @ SV103 )
        = $false )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( a @ SV15 @ SV65 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[504]) ).

thf(520,plain,
    ! [SV49: $i > $o,SV18: $i,SV66: $i,SV104: $i] :
      ( ( ( ~ ( a @ SV104 @ ( sK19_SY166 @ SV66 @ SV18 @ SV49 @ SV104 ) ) )
        = $false )
      | ( ( b @ SV18 @ SV104 )
        = $false )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( a @ SV18 @ SV66 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[506]) ).

thf(521,plain,
    ! [SV104: $i,SV18: $i,SV66: $i,SV49: $i > $o] :
      ( ( ( SV49 @ ( sK19_SY166 @ SV66 @ SV18 @ SV49 @ SV104 ) )
        = $false )
      | ( ( b @ SV18 @ SV104 )
        = $false )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( a @ SV18 @ SV66 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[506]) ).

thf(522,plain,
    ! [SV53: $i > $o,SV23: $i,SV67: $i,SV105: $i] :
      ( ( ( ~ ( b @ SV105 @ ( sK20_SY167 @ SV67 @ SV23 @ SV53 @ SV105 ) ) )
        = $false )
      | ( ( c @ SV23 @ SV105 )
        = $false )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( b @ SV23 @ SV67 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[508]) ).

thf(523,plain,
    ! [SV105: $i,SV23: $i,SV67: $i,SV53: $i > $o] :
      ( ( ( SV53 @ ( sK20_SY167 @ SV67 @ SV23 @ SV53 @ SV105 ) )
        = $false )
      | ( ( c @ SV23 @ SV105 )
        = $false )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( b @ SV23 @ SV67 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[508]) ).

thf(524,plain,
    ! [SV59: $i > $o,SV29: $i,SV68: $i,SV106: $i] :
      ( ( ( ~ ( b @ SV106 @ ( sK21_SY168 @ SV68 @ SV29 @ SV59 @ SV106 ) ) )
        = $false )
      | ( ( a @ SV29 @ SV106 )
        = $false )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( b @ SV29 @ SV68 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[512]) ).

thf(525,plain,
    ! [SV106: $i,SV29: $i,SV68: $i,SV59: $i > $o] :
      ( ( ( SV59 @ ( sK21_SY168 @ SV68 @ SV29 @ SV59 @ SV106 ) )
        = $false )
      | ( ( a @ SV29 @ SV106 )
        = $false )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( b @ SV29 @ SV68 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[512]) ).

thf(526,plain,
    ! [SV38: $i > $o,SV7: $i,SV63: $i,SV101: $i] :
      ( ( ( c @ SV101 @ ( sK16_SY163 @ SV63 @ SV7 @ SV38 @ SV101 ) )
        = $true )
      | ( ( a @ SV7 @ SV101 )
        = $false )
      | ( ( SV38 @ SV63 )
        = $true )
      | ( ( c @ SV7 @ SV63 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[514]) ).

thf(527,plain,
    ! [SV42: $i > $o,SV11: $i,SV64: $i,SV102: $i] :
      ( ( ( c @ SV102 @ ( sK17_SY164 @ SV64 @ SV11 @ SV42 @ SV102 ) )
        = $true )
      | ( ( b @ SV11 @ SV102 )
        = $false )
      | ( ( SV42 @ SV64 )
        = $true )
      | ( ( c @ SV11 @ SV64 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[516]) ).

thf(528,plain,
    ! [SV46: $i > $o,SV15: $i,SV65: $i,SV103: $i] :
      ( ( ( a @ SV103 @ ( sK18_SY165 @ SV65 @ SV15 @ SV46 @ SV103 ) )
        = $true )
      | ( ( c @ SV15 @ SV103 )
        = $false )
      | ( ( SV46 @ SV65 )
        = $true )
      | ( ( a @ SV15 @ SV65 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[518]) ).

thf(529,plain,
    ! [SV49: $i > $o,SV18: $i,SV66: $i,SV104: $i] :
      ( ( ( a @ SV104 @ ( sK19_SY166 @ SV66 @ SV18 @ SV49 @ SV104 ) )
        = $true )
      | ( ( b @ SV18 @ SV104 )
        = $false )
      | ( ( SV49 @ SV66 )
        = $true )
      | ( ( a @ SV18 @ SV66 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[520]) ).

thf(530,plain,
    ! [SV53: $i > $o,SV23: $i,SV67: $i,SV105: $i] :
      ( ( ( b @ SV105 @ ( sK20_SY167 @ SV67 @ SV23 @ SV53 @ SV105 ) )
        = $true )
      | ( ( c @ SV23 @ SV105 )
        = $false )
      | ( ( SV53 @ SV67 )
        = $true )
      | ( ( b @ SV23 @ SV67 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[522]) ).

thf(531,plain,
    ! [SV59: $i > $o,SV29: $i,SV68: $i,SV106: $i] :
      ( ( ( b @ SV106 @ ( sK21_SY168 @ SV68 @ SV29 @ SV59 @ SV106 ) )
        = $true )
      | ( ( a @ SV29 @ SV106 )
        = $false )
      | ( ( SV59 @ SV68 )
        = $true )
      | ( ( b @ SV29 @ SV68 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[524]) ).

thf(532,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[203,531,530,529,528,527,526,525,523,521,519,517,515,513,511,510,509,507,505,503,500,497,495,493,490,487,484,475,461,459,458,456,455,452,442,432,423,412,410,404,399,394,392,391,389,347,308,298,261,256,238,228,222]) ).

thf(533,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[532]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : PUZ087^1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat May 28 20:26:12 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 32
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 5293
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.37  (rf:0,axioms:32,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:34,loop_count:0,foatp_calls:0,translation:fof_full)..............................
% 0.46/0.66  
% 0.46/0.66  ********************************
% 0.46/0.66  *   All subproblems solved!    *
% 0.46/0.66  ********************************
% 0.46/0.66  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,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:532,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.55/0.77  
% 0.55/0.77  %**** Beginning of derivation protocol ****
% 0.55/0.77  % SZS output start CNFRefutation
% See solution above
% 0.55/0.77  
% 0.55/0.77  %**** End of derivation protocol ****
% 0.55/0.77  %**** no. of clauses in derivation: 533 ****
% 0.55/0.77  %**** clause counter: 532 ****
% 0.55/0.77  
% 0.55/0.77  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,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:532,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------