TSTP Solution File: NUM817^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM817^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n006.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 11:55:45 EDT 2022

% Result   : Theorem 150.30s 150.50s
% Output   : CNFRefutation 150.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    8
% Syntax   : Number of formulae    :  117 (  23 unt;   5 typ;   2 def)
%            Number of atoms       :  751 ( 501 equ;   0 cnn)
%            Maximal formula atoms :    4 (   6 avg)
%            Number of connectives :  901 ( 173   ~; 186   |;   9   &; 518   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   49 (  49   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  265 (  94   ^ 166   !;   5   ?; 265   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c0,type,
    c0: $i ).

thf(tp_cEVEN1,type,
    cEVEN1: $i > $o ).

thf(tp_cODD1,type,
    cODD1: $i > $o ).

thf(tp_cS,type,
    cS: $i > $i ).

thf(tp_sK1_Xx,type,
    sK1_Xx: ( $i > $o ) > $i > $i ).

thf(cEVEN1,definition,
    ( cEVEN1
    = ( ^ [Xn: $i] :
        ! [Xp: $i > $o] :
          ( ( ( Xp @ c0 )
            & ! [Xx: $i] :
                ( ( Xp @ Xx )
               => ( Xp @ ( cS @ ( cS @ Xx ) ) ) ) )
         => ( Xp @ Xn ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEVEN1) ).

thf(cODD1,definition,
    ( cODD1
    = ( ^ [Xn: $i] :
          ~ ( cEVEN1 @ Xn ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cODD1) ).

thf(1,conjecture,
    ( ( ! [Xu: $i] :
          ( ( cS @ Xu )
         != c0 )
      & ! [Xv: $i,Xw: $i] :
          ( ( ( cS @ Xv )
            = ( cS @ Xw ) )
         => ( Xv = Xw ) ) )
   => ? [Xn: $i] : ( cODD1 @ Xn ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM405) ).

thf(2,negated_conjecture,
    ( ( ( ! [Xu: $i] :
            ( ( cS @ Xu )
           != c0 )
        & ! [Xv: $i,Xw: $i] :
            ( ( ( cS @ Xv )
              = ( cS @ Xw ) )
           => ( Xv = Xw ) ) )
     => ? [Xn: $i] : ( cODD1 @ Xn ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ! [Xu: $i] :
            ( ( cS @ Xu )
           != c0 )
        & ! [Xv: $i,Xw: $i] :
            ( ( ( cS @ Xv )
              = ( cS @ Xw ) )
           => ( Xv = Xw ) ) )
     => ? [SY158: $i] :
          ~ ! [SY159: $i > $o] :
              ( ( ( SY159 @ c0 )
                & ! [Xx: $i] :
                    ( ( SY159 @ Xx )
                   => ( SY159 @ ( cS @ ( cS @ Xx ) ) ) ) )
             => ( SY159 @ SY158 ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,cEVEN1,cODD1]) ).

thf(4,plain,
    ( ( ! [Xu: $i] :
          ( ( cS @ Xu )
         != c0 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xv: $i,Xw: $i] :
          ( ( ( cS @ Xv )
            = ( cS @ Xw ) )
         => ( Xv = Xw ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ? [SY158: $i] :
          ~ ! [SY159: $i > $o] :
              ( ( ( SY159 @ c0 )
                & ! [Xx: $i] :
                    ( ( SY159 @ Xx )
                   => ( SY159 @ ( cS @ ( cS @ Xx ) ) ) ) )
             => ( SY159 @ SY158 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ~ ? [SY158: $i] :
            ~ ! [SY159: $i > $o] :
                ( ( ( SY159 @ c0 )
                  & ! [Xx: $i] :
                      ( ( SY159 @ Xx )
                     => ( SY159 @ ( cS @ ( cS @ Xx ) ) ) ) )
               => ( SY159 @ SY158 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [SY158: $i,SY159: $i > $o] :
          ( ( ( SY159 @ ( sK1_Xx @ SY159 @ SY158 ) )
            & ~ ( SY159 @ ( cS @ ( cS @ ( sK1_Xx @ SY159 @ SY158 ) ) ) ) )
          | ~ ( SY159 @ c0 )
          | ( SY159 @ SY158 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(9,plain,
    ( ( ! [Xu: $i] :
          ( ( cS @ Xu )
         != c0 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(10,plain,
    ( ( ! [Xv: $i,Xw: $i] :
          ( ( ( cS @ Xv )
           != ( cS @ Xw ) )
          | ( Xv = Xw ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(11,plain,
    ( ( ! [Xv: $i,Xw: $i] :
          ( ( ( cS @ Xv )
           != ( cS @ Xw ) )
          | ( Xv = Xw ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ! [Xu: $i] :
          ( ( cS @ Xu )
         != c0 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ! [SY158: $i,SY159: $i > $o] :
          ( ( ( SY159 @ ( sK1_Xx @ SY159 @ SY158 ) )
            & ~ ( SY159 @ ( cS @ ( cS @ ( sK1_Xx @ SY159 @ SY158 ) ) ) ) )
          | ~ ( SY159 @ c0 )
          | ( SY159 @ SY158 ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(14,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ( ~ ( SX1 @ ( sK1_Xx @ SX1 @ SX0 ) )
              | ~ ~ ( SX1 @ ( cS @ ( cS @ ( sK1_Xx @ SX1 @ SX0 ) ) ) ) )
          | ~ ( SX1 @ c0 )
          | ( SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13,cEVEN1,cODD1]) ).

thf(15,plain,
    ! [SV1: $i] :
      ( ( ! [SY167: $i] :
            ( ( ( cS @ SV1 )
             != ( cS @ SY167 ) )
            | ( SV1 = SY167 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(16,plain,
    ! [SV2: $i] :
      ( ( ( ( cS @ SV2 )
         != c0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(17,plain,
    ! [SV3: $i] :
      ( ( ! [SY168: $i > $o] :
            ( ~ ( ~ ( SY168 @ ( sK1_Xx @ SY168 @ SV3 ) )
                | ~ ~ ( SY168 @ ( cS @ ( cS @ ( sK1_Xx @ SY168 @ SV3 ) ) ) ) )
            | ~ ( SY168 @ c0 )
            | ( SY168 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ( cS @ SV1 )
         != ( cS @ SV4 ) )
        | ( SV1 = SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV2: $i] :
      ( ( ( cS @ SV2 )
        = c0 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ~ ( ~ ( SV5 @ ( sK1_Xx @ SV5 @ SV3 ) )
            | ~ ~ ( SV5 @ ( cS @ ( cS @ ( sK1_Xx @ SV5 @ SV3 ) ) ) ) )
        | ~ ( SV5 @ c0 )
        | ( SV5 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ( ( cS @ SV1 )
           != ( cS @ SV4 ) ) )
        = $true )
      | ( ( SV1 = SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( ~ ( ~ ( SV5 @ ( sK1_Xx @ SV5 @ SV3 ) )
              | ~ ~ ( SV5 @ ( cS @ ( cS @ ( sK1_Xx @ SV5 @ SV3 ) ) ) ) )
          | ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ( cS @ SV1 )
          = ( cS @ SV4 ) )
        = $false )
      | ( ( SV1 = SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(24,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( ~ ( ~ ( SV5 @ ( sK1_Xx @ SV5 @ SV3 ) )
              | ~ ~ ( SV5 @ ( cS @ ( cS @ ( sK1_Xx @ SV5 @ SV3 ) ) ) ) ) )
        = $true )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( ~ ( SV5 @ ( sK1_Xx @ SV5 @ SV3 ) )
          | ~ ~ ( SV5 @ ( cS @ ( cS @ ( sK1_Xx @ SV5 @ SV3 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(26,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( ~ ( SV5 @ ( sK1_Xx @ SV5 @ SV3 ) ) )
        = $false )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(27,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( ~ ~ ( SV5 @ ( cS @ ( cS @ ( sK1_Xx @ SV5 @ SV3 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(28,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( SV5 @ ( sK1_Xx @ SV5 @ SV3 ) )
        = $true )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( ~ ( SV5 @ ( cS @ ( cS @ ( sK1_Xx @ SV5 @ SV3 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(30,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( SV5 @ c0 )
        = $false )
      | ( ( SV5 @ ( sK1_Xx @ SV5 @ SV3 ) )
        = $true )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(31,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( SV5 @ ( cS @ ( cS @ ( sK1_Xx @ SV5 @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(32,plain,
    ! [SV3: $i,SV5: $i > $o] :
      ( ( ( SV5 @ c0 )
        = $false )
      | ( ( SV5 @ ( cS @ ( cS @ ( sK1_Xx @ SV5 @ SV3 ) ) ) )
        = $false )
      | ( ( SV5 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(33,plain,
    ! [SV3: $i] :
      ( ( ( c0 = c0 )
        = $false )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[30:[bind(SV5,$thf( ^ [SV6: $i] : ( SV6 = c0 ) ))]]) ).

thf(34,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(sim,[status(thm)],[33]) ).

thf(35,plain,
    ! [SV3: $i] :
      ( ( ( c0 = c0 )
        = $false )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 = c0 )
                @ SV3 ) ) )
          = c0 )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[32:[bind(SV5,$thf( ^ [SV7: $i] : ( SV7 = c0 ) ))]]) ).

thf(36,plain,
    ! [SV3: $i] :
      ( ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 = c0 )
                @ SV3 ) ) )
          = c0 )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(sim,[status(thm)],[35]) ).

thf(39,plain,
    ! [SV3: $i,SV9: $i > $o] :
      ( ( ( ~ ( SV9 @ c0 ) )
        = $false )
      | ( ( ~ ( SV9
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ( SV9 @ SX0 )
                @ SV3 ) ) )
        = $true )
      | ( ( ~ ( SV9 @ SV3 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[30:[bind(SV5,$thf( ^ [SV8: $i] : ~ ( SV9 @ SV8 ) ))]]) ).

thf(40,plain,
    ! [SV3: $i] :
      ( ( ( c0 = c0 )
        = $false )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(prim_subst,[status(thm)],[30:[bind(SV5,$thf( ^ [SV12: $i] : ( SV12 = c0 ) ))]]) ).

thf(43,plain,
    ! [SV3: $i,SV9: $i > $o] :
      ( ( ( ~ ( SV9 @ c0 ) )
        = $false )
      | ( ( ~ ( SV9
              @ ( cS
                @ ( cS
                  @ ( sK1_Xx
                    @ ^ [SX0: $i] :
                        ~ ( SV9 @ SX0 )
                    @ SV3 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV9 @ SV3 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[32:[bind(SV5,$thf( ^ [SV8: $i] : ~ ( SV9 @ SV8 ) ))]]) ).

thf(45,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = c0 )
        = $true )
      | ( ( ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 )
          = ( SV3 = c0 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[34]) ).

thf(46,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 )
              | ( SV3 = c0 ) )
          | ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
               != c0 )
              | ( SV3 != c0 ) ) )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[45]) ).

thf(48,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 )
              | ( SV3 = c0 ) ) )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV3: $i] :
      ( ( ( ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 )
          | ( SV3 = c0 ) )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[50]) ).

thf(57,plain,
    ! [SV3: $i,SV9: $i > $o] :
      ( ( ( SV9 @ c0 )
        = $true )
      | ( ( ~ ( SV9
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ( SV9 @ SX0 )
                @ SV3 ) ) )
        = $true )
      | ( ( ~ ( SV9 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(58,plain,
    ! [SV3: $i,SV9: $i > $o] :
      ( ( ( SV9 @ c0 )
        = $true )
      | ( ( ~ ( SV9
              @ ( cS
                @ ( cS
                  @ ( sK1_Xx
                    @ ^ [SX0: $i] :
                        ~ ( SV9 @ SX0 )
                    @ SV3 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV9 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(59,plain,
    ! [SV3: $i,SV9: $i > $o] :
      ( ( ( SV9
          @ ( sK1_Xx
            @ ^ [SX0: $i] :
                ~ ( SV9 @ SX0 )
            @ SV3 ) )
        = $false )
      | ( ( SV9 @ c0 )
        = $true )
      | ( ( ~ ( SV9 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(60,plain,
    ! [SV3: $i,SV9: $i > $o] :
      ( ( ( SV9
          @ ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ( SV9 @ SX0 )
                @ SV3 ) ) ) )
        = $true )
      | ( ( SV9 @ c0 )
        = $true )
      | ( ( ~ ( SV9 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[58]) ).

thf(61,plain,
    ! [SV3: $i,SV9: $i > $o] :
      ( ( ( SV9 @ SV3 )
        = $false )
      | ( ( SV9 @ c0 )
        = $true )
      | ( ( SV9
          @ ( sK1_Xx
            @ ^ [SX0: $i] :
                ~ ( SV9 @ SX0 )
            @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(62,plain,
    ! [SV3: $i,SV9: $i > $o] :
      ( ( ( SV9 @ SV3 )
        = $false )
      | ( ( SV9 @ c0 )
        = $true )
      | ( ( SV9
          @ ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ( SV9 @ SX0 )
                @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(63,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = c0 )
        = $true )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true ) ),
    inference(extuni,[status(esa)],[40]) ).

thf(64,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(sim,[status(thm)],[52]) ).

thf(65,plain,
    ! [SV3: $i] :
      ( ( ( c0 = c0 )
        = $false )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[30:[bind(SV5,$thf( ^ [SV13: $i] : ( SV13 = c0 ) ))]]) ).

thf(66,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(sim,[status(thm)],[65]) ).

thf(67,plain,
    ! [SV3: $i] :
      ( ( ( c0 = c0 )
        = $false )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 = c0 )
                @ SV3 ) ) )
          = c0 )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[32:[bind(SV5,$thf( ^ [SV14: $i] : ( SV14 = c0 ) ))]]) ).

thf(68,plain,
    ! [SV3: $i] :
      ( ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 = c0 )
                @ SV3 ) ) )
          = c0 )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(sim,[status(thm)],[67]) ).

thf(69,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = SV3 )
        = $false )
      | ( ( c0 = SV3 )
        = $true )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 != SV3 )
            @ SV3 )
          = SV3 )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[61:[bind(SV9,$thf( ^ [SV15: $i] : ( SV15 = SV3 ) ))]]) ).

thf(70,plain,
    ! [SV3: $i] :
      ( ( ( c0 = SV3 )
        = $true )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 != SV3 )
            @ SV3 )
          = SV3 )
        = $false ) ),
    inference(sim,[status(thm)],[69]) ).

thf(71,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = SV3 )
        = $false )
      | ( ( c0 = SV3 )
        = $true )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 != SV3 )
                @ SV3 ) ) )
          = SV3 )
        = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[62:[bind(SV9,$thf( ^ [SV16: $i] : ( SV16 = SV3 ) ))]]) ).

thf(72,plain,
    ! [SV3: $i] :
      ( ( ( c0 = SV3 )
        = $true )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 != SV3 )
                @ SV3 ) ) )
          = SV3 )
        = $true ) ),
    inference(sim,[status(thm)],[71]) ).

thf(75,plain,
    ! [SV3: $i,SV23: $i > $o] :
      ( ( ( ~ ( SV23 @ c0 ) )
        = $false )
      | ( ( ~ ( SV23
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ( SV23 @ SX0 )
                @ SV3 ) ) )
        = $true )
      | ( ( ~ ( SV23 @ SV3 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[30:[bind(SV5,$thf( ^ [SV22: $i] : ~ ( SV23 @ SV22 ) ))]]) ).

thf(76,plain,
    ! [SV3: $i] :
      ( ( ( c0 = c0 )
        = $false )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(prim_subst,[status(thm)],[30:[bind(SV5,$thf( ^ [SV26: $i] : ( SV26 = c0 ) ))]]) ).

thf(79,plain,
    ! [SV3: $i,SV23: $i > $o] :
      ( ( ( ~ ( SV23 @ c0 ) )
        = $false )
      | ( ( ~ ( SV23
              @ ( cS
                @ ( cS
                  @ ( sK1_Xx
                    @ ^ [SX0: $i] :
                        ~ ( SV23 @ SX0 )
                    @ SV3 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV23 @ SV3 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[32:[bind(SV5,$thf( ^ [SV22: $i] : ~ ( SV23 @ SV22 ) ))]]) ).

thf(83,plain,
    ! [SV3: $i,SV18: $i > $o] :
      ( ( ( ~ ( SV18 @ SV3 ) )
        = $false )
      | ( ( ~ ( SV18 @ c0 ) )
        = $true )
      | ( ( ~ ( SV18
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ~ ( SV18 @ SX0 )
                @ SV3 ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[61:[bind(SV9,$thf( ^ [SV17: $i] : ~ ( SV18 @ SV17 ) ))]]) ).

thf(87,plain,
    ! [SV3: $i,SV18: $i > $o] :
      ( ( ( ~ ( SV18 @ SV3 ) )
        = $false )
      | ( ( ~ ( SV18 @ c0 ) )
        = $true )
      | ( ( ~ ( SV18
              @ ( cS
                @ ( cS
                  @ ( sK1_Xx
                    @ ^ [SX0: $i] :
                        ~ ~ ( SV18 @ SX0 )
                    @ SV3 ) ) ) ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[62:[bind(SV9,$thf( ^ [SV17: $i] : ~ ( SV18 @ SV17 ) ))]]) ).

thf(89,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = c0 )
        = $true )
      | ( ( ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 )
          = ( SV3 = c0 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[66]) ).

thf(90,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = c0 )
        = $true )
      | ( ( ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 )
          = ( SV3 = c0 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[34]) ).

thf(91,plain,
    ! [SV3: $i] :
      ( ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 != SV3 )
                @ SV3 ) ) )
          = SV3 )
        = $true )
      | ( ( ( c0 = SV3 )
          = ( ( cS
              @ ( cS
                @ ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 != SV3 )
                  @ SV3 ) ) )
            = SV3 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[72]) ).

thf(92,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( ( SV3 = c0 )
          = ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[63]) ).

thf(93,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = c0 )
        = $true )
      | ( ( ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 )
          = ( SV3 = c0 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[64]) ).

thf(94,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 )
              | ( SV3 = c0 ) )
          | ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
               != c0 )
              | ( SV3 != c0 ) ) )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[89]) ).

thf(96,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 )
              | ( SV3 = c0 ) )
          | ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
               != c0 )
              | ( SV3 != c0 ) ) )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[90]) ).

thf(98,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( c0 = SV3 )
              | ( ( cS
                  @ ( cS
                    @ ( sK1_Xx
                      @ ^ [SX0: $i] : ( SX0 != SV3 )
                      @ SV3 ) ) )
                = SV3 ) )
          | ~ ( ( c0 != SV3 )
              | ( ( cS
                  @ ( cS
                    @ ( sK1_Xx
                      @ ^ [SX0: $i] : ( SX0 != SV3 )
                      @ SV3 ) ) )
               != SV3 ) ) )
        = $false )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 != SV3 )
                @ SV3 ) ) )
          = SV3 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[91]) ).

thf(100,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( SV3 = c0 )
              | ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 ) )
          | ~ ( ( SV3 != c0 )
              | ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
               != c0 ) ) )
        = $false )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[92]) ).

thf(102,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 )
              | ( SV3 = c0 ) )
          | ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
               != c0 )
              | ( SV3 != c0 ) ) )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[93]) ).

thf(104,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 )
              | ( SV3 = c0 ) ) )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[94]) ).

thf(106,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 )
              | ( SV3 = c0 ) ) )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[96]) ).

thf(108,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( c0 = SV3 )
              | ( ( cS
                  @ ( cS
                    @ ( sK1_Xx
                      @ ^ [SX0: $i] : ( SX0 != SV3 )
                      @ SV3 ) ) )
                = SV3 ) ) )
        = $false )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 != SV3 )
                @ SV3 ) ) )
          = SV3 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[98]) ).

thf(110,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( SV3 = c0 )
              | ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 ) ) )
        = $false )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[100]) ).

thf(112,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 = c0 )
                  @ SV3 )
                = c0 )
              | ( SV3 = c0 ) ) )
        = $false )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[102]) ).

thf(114,plain,
    ! [SV3: $i] :
      ( ( ( ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 )
          | ( SV3 = c0 ) )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[104]) ).

thf(116,plain,
    ! [SV3: $i] :
      ( ( ( ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 )
          | ( SV3 = c0 ) )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[106]) ).

thf(118,plain,
    ! [SV3: $i] :
      ( ( ( ( c0 = SV3 )
          | ( ( cS
              @ ( cS
                @ ( sK1_Xx
                  @ ^ [SX0: $i] : ( SX0 != SV3 )
                  @ SV3 ) ) )
            = SV3 ) )
        = $true )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 != SV3 )
                @ SV3 ) ) )
          = SV3 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[108]) ).

thf(120,plain,
    ! [SV3: $i] :
      ( ( ( ( SV3 = c0 )
          | ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 ) )
        = $true )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[110]) ).

thf(122,plain,
    ! [SV3: $i] :
      ( ( ( ( ( sK1_Xx
              @ ^ [SX0: $i] : ( SX0 = c0 )
              @ SV3 )
            = c0 )
          | ( SV3 = c0 ) )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[112]) ).

thf(124,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[114]) ).

thf(126,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[116]) ).

thf(128,plain,
    ! [SV3: $i] :
      ( ( ( c0 = SV3 )
        = $true )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 != SV3 )
                @ SV3 ) ) )
          = SV3 )
        = $true )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 != SV3 )
                @ SV3 ) ) )
          = SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[118]) ).

thf(130,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = c0 )
        = $true )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[120]) ).

thf(132,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[122]) ).

thf(145,plain,
    ! [SV3: $i,SV23: $i > $o] :
      ( ( ( SV23 @ c0 )
        = $true )
      | ( ( ~ ( SV23
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ( SV23 @ SX0 )
                @ SV3 ) ) )
        = $true )
      | ( ( ~ ( SV23 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[75]) ).

thf(146,plain,
    ! [SV3: $i,SV23: $i > $o] :
      ( ( ( SV23 @ c0 )
        = $true )
      | ( ( ~ ( SV23
              @ ( cS
                @ ( cS
                  @ ( sK1_Xx
                    @ ^ [SX0: $i] :
                        ~ ( SV23 @ SX0 )
                    @ SV3 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV23 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(147,plain,
    ! [SV3: $i,SV18: $i > $o] :
      ( ( ( SV18 @ SV3 )
        = $true )
      | ( ( ~ ( SV18 @ c0 ) )
        = $true )
      | ( ( ~ ( SV18
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ~ ( SV18 @ SX0 )
                @ SV3 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[83]) ).

thf(148,plain,
    ! [SV3: $i,SV18: $i > $o] :
      ( ( ( SV18 @ SV3 )
        = $true )
      | ( ( ~ ( SV18 @ c0 ) )
        = $true )
      | ( ( ~ ( SV18
              @ ( cS
                @ ( cS
                  @ ( sK1_Xx
                    @ ^ [SX0: $i] :
                        ~ ~ ( SV18 @ SX0 )
                    @ SV3 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[87]) ).

thf(149,plain,
    ! [SV3: $i,SV23: $i > $o] :
      ( ( ( SV23
          @ ( sK1_Xx
            @ ^ [SX0: $i] :
                ~ ( SV23 @ SX0 )
            @ SV3 ) )
        = $false )
      | ( ( SV23 @ c0 )
        = $true )
      | ( ( ~ ( SV23 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[145]) ).

thf(150,plain,
    ! [SV3: $i,SV23: $i > $o] :
      ( ( ( SV23
          @ ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ( SV23 @ SX0 )
                @ SV3 ) ) ) )
        = $true )
      | ( ( SV23 @ c0 )
        = $true )
      | ( ( ~ ( SV23 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[146]) ).

thf(151,plain,
    ! [SV3: $i,SV18: $i > $o] :
      ( ( ( SV18 @ c0 )
        = $false )
      | ( ( SV18 @ SV3 )
        = $true )
      | ( ( ~ ( SV18
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ~ ( SV18 @ SX0 )
                @ SV3 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(152,plain,
    ! [SV3: $i,SV18: $i > $o] :
      ( ( ( SV18 @ c0 )
        = $false )
      | ( ( SV18 @ SV3 )
        = $true )
      | ( ( ~ ( SV18
              @ ( cS
                @ ( cS
                  @ ( sK1_Xx
                    @ ^ [SX0: $i] :
                        ~ ~ ( SV18 @ SX0 )
                    @ SV3 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[148]) ).

thf(153,plain,
    ! [SV3: $i,SV23: $i > $o] :
      ( ( ( SV23 @ SV3 )
        = $false )
      | ( ( SV23 @ c0 )
        = $true )
      | ( ( SV23
          @ ( sK1_Xx
            @ ^ [SX0: $i] :
                ~ ( SV23 @ SX0 )
            @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(154,plain,
    ! [SV3: $i,SV23: $i > $o] :
      ( ( ( SV23 @ SV3 )
        = $false )
      | ( ( SV23 @ c0 )
        = $true )
      | ( ( SV23
          @ ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ( SV23 @ SX0 )
                @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[150]) ).

thf(155,plain,
    ! [SV3: $i,SV18: $i > $o] :
      ( ( ( SV18
          @ ( sK1_Xx
            @ ^ [SX0: $i] :
                ~ ~ ( SV18 @ SX0 )
            @ SV3 ) )
        = $true )
      | ( ( SV18 @ SV3 )
        = $true )
      | ( ( SV18 @ c0 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[151]) ).

thf(156,plain,
    ! [SV3: $i,SV18: $i > $o] :
      ( ( ( SV18
          @ ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] :
                    ~ ~ ( SV18 @ SX0 )
                @ SV3 ) ) ) )
        = $false )
      | ( ( SV18 @ SV3 )
        = $true )
      | ( ( SV18 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(157,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = c0 )
        = $true )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true ) ),
    inference(extuni,[status(esa)],[76]) ).

thf(159,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(sim,[status(thm)],[124]) ).

thf(160,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(sim,[status(thm)],[126]) ).

thf(161,plain,
    ! [SV3: $i] :
      ( ( ( c0 = SV3 )
        = $true )
      | ( ( ( cS
            @ ( cS
              @ ( sK1_Xx
                @ ^ [SX0: $i] : ( SX0 != SV3 )
                @ SV3 ) ) )
          = SV3 )
        = $true ) ),
    inference(sim,[status(thm)],[128]) ).

thf(162,plain,
    ! [SV3: $i] :
      ( ( ( SV3 = c0 )
        = $true )
      | ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true ) ),
    inference(sim,[status(thm)],[130]) ).

thf(163,plain,
    ! [SV3: $i] :
      ( ( ( ( sK1_Xx
            @ ^ [SX0: $i] : ( SX0 = c0 )
            @ SV3 )
          = c0 )
        = $true )
      | ( ( SV3 = c0 )
        = $true ) ),
    inference(sim,[status(thm)],[132]) ).

thf(164,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,163,162,161,160,159,157,156,155,154,153,72,70,68,66,64,63,62,61,36,34,32,30,23]) ).

thf(165,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[164]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM817^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.04/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Wed Jul  6 00:14:51 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 324
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:0,ps:3,u:6,ude:true,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:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.37/0.55  
% 0.37/0.55   Prim_subst applied to clause 
% 0.37/0.55   
% 0.37/0.55  77:[ 0:<SV17@c0 = $false>-w(1)-i() 1:<SV17@((sK1_Xx@SV17)@SV16) = $true>-w(1)-i() 2:<SV17@SV16 = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 30)-o(CONJECTURE)-fv([ SV16 SV17 ])
% 0.39/0.58  
% 0.39/0.58   Prim_subst applied to clause 
% 0.39/0.58   
% 0.39/0.58  77:[ 0:<SV17@c0 = $false>-w(1)-i() 1:<SV17@((sK1_Xx@SV17)@SV16) = $true>-w(1)-i() 2:<SV17@SV16 = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 30)-o(CONJECTURE)-fv([ SV16 SV17 ])
% 0.39/0.61  .
% 0.39/0.61  
% 0.39/0.61   Prim_subst applied to clause 
% 0.39/0.61   
% 0.39/0.61  77:[ 0:<SV17@c0 = $false>-w(1)-i() 1:<SV17@((sK1_Xx@SV17)@SV16) = $true>-w(1)-i() 2:<SV17@SV16 = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 30)-o(CONJECTURE)-fv([ SV16 SV17 ])
% 1.06/1.27  ..............
% 75.14/75.31  (rf:0,axioms:0,ps:2,u:1,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:2,loop_count:0,foatp_calls:0,translation:fof_full)...
% 75.18/75.42  
% 75.18/75.42   Prim_subst applied to clause 
% 75.18/75.42   
% 75.18/75.42  75:[ 0:<SV17@(cS@(cS@((sK1_SY102@SV16)@SV17))) = $false>-w(1)-i() 1:<SV17@c0 = $false>-w(1)-i() 2:<SV17@SV16 = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 32)-o(CONJECTURE)-fv([ SV16 SV17 ])
% 75.18/75.43  
% 75.18/75.43   Prim_subst applied to clause 
% 75.18/75.43   
% 75.18/75.43  75:[ 0:<SV17@(cS@(cS@((sK1_SY102@SV16)@SV17))) = $false>-w(1)-i() 1:<SV17@c0 = $false>-w(1)-i() 2:<SV17@SV16 = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 32)-o(CONJECTURE)-fv([ SV16 SV17 ])
% 75.27/75.44  
% 75.27/75.44   Prim_subst applied to clause 
% 75.27/75.44   
% 75.27/75.44  75:[ 0:<SV17@(cS@(cS@((sK1_SY102@SV16)@SV17))) = $false>-w(1)-i() 1:<SV17@c0 = $false>-w(1)-i() 2:<SV17@SV16 = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 32)-o(CONJECTURE)-fv([ SV16 SV17 ])
% 75.57/75.78  ............................................
% 150.11/150.27  (rf:0,axioms:0,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:2,loop_count:0,foatp_calls:0,translation:fof_full)...
% 150.30/150.50  
% 150.30/150.50  ********************************
% 150.30/150.50  *   All subproblems solved!    *
% 150.30/150.50  ********************************
% 150.30/150.50  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:164,loop_count:0,foatp_calls:3,translation:fof_full)
% 150.30/150.50  
% 150.30/150.50  %**** Beginning of derivation protocol ****
% 150.30/150.50  % SZS output start CNFRefutation
% See solution above
% 150.30/150.50  
% 150.30/150.50  %**** End of derivation protocol ****
% 150.30/150.50  %**** no. of clauses in derivation: 110 ****
% 150.30/150.50  %**** clause counter: 164 ****
% 150.30/150.50  
% 150.30/150.50  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:164,loop_count:0,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------