TSTP Solution File: NUM636^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM636^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n016.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 11:53:28 EDT 2022

% Result   : Theorem 150.36s 150.59s
% Output   : CNFRefutation 150.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    8
% Syntax   : Number of formulae    :  133 (  30 unt;   4 typ;   0 def)
%            Number of atoms       :  862 ( 589 equ;   0 cnn)
%            Maximal formula atoms :    3 (   6 avg)
%            Number of connectives :  754 ( 169   ~; 195   |;   4   &; 380   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   45 (  45   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :  292 ( 123   ^ 169   !;   0   ?; 292   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_one,type,
    one: $i ).

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

thf(tp_sK2_X,type,
    sK2_X: ( $i > $o ) > $i ).

thf(tp_succ,type,
    succ: $i > $i ).

thf(1,axiom,
    ! [M: $i > $o] :
      ( ( ( M @ one )
        & ! [X: $i] :
            ( ( M @ X )
           => ( M @ ( succ @ X ) ) ) )
     => ! [Y: $i] : ( M @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).

thf(2,axiom,
    ! [X: $i,Y: $i] :
      ( ( ( succ @ X )
        = ( succ @ Y ) )
     => ( X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_injective) ).

thf(3,axiom,
    ! [X: $i] :
      ( ( succ @ X )
     != one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_is_first) ).

thf(4,conjecture,
    ! [X: $i] :
      ( ( succ @ X )
     != X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz2) ).

thf(5,negated_conjecture,
    ( ( ! [X: $i] :
          ( ( succ @ X )
         != X ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[4]) ).

thf(6,plain,
    ( ( ! [X: $i] :
          ( ( succ @ X )
         != X ) )
    = $false ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [M: $i > $o] :
          ( ( ( M @ one )
            & ! [X: $i] :
                ( ( M @ X )
               => ( M @ ( succ @ X ) ) ) )
         => ! [Y: $i] : ( M @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(8,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( succ @ X )
            = ( succ @ Y ) )
         => ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(9,plain,
    ( ( ! [X: $i] :
          ( ( succ @ X )
         != one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(10,plain,
    ( ( ( ( succ @ sK1_X )
       != sK1_X ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[6]) ).

thf(11,plain,
    ( ( ~ ( ( ( succ @ sK1_X )
           != sK1_X ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ( succ @ sK1_X )
      = sK1_X )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(13,plain,
    ( ( ! [M: $i > $o] :
          ( ( ( M @ ( sK2_X @ M ) )
            & ~ ( M @ ( succ @ ( sK2_X @ M ) ) ) )
          | ~ ( M @ one )
          | ! [Y: $i] : ( M @ Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(14,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( succ @ X )
           != ( succ @ Y ) )
          | ( X = Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(15,plain,
    ( ( ! [X: $i] :
          ( ( succ @ X )
         != one ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(16,plain,
    ( ( ! [X: $i] :
          ( ( succ @ X )
         != one ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( succ @ X )
           != ( succ @ Y ) )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ! [M: $i > $o] :
          ( ( ( M @ ( sK2_X @ M ) )
            & ~ ( M @ ( succ @ ( sK2_X @ M ) ) ) )
          | ~ ( M @ one )
          | ! [Y: $i] : ( M @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(19,plain,
    ( ( ( succ @ sK1_X )
      = sK1_X )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(20,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ( ~ ( SX0 @ ( sK2_X @ SX0 ) )
              | ~ ~ ( SX0 @ ( succ @ ( sK2_X @ SX0 ) ) ) )
          | ~ ( SX0 @ one )
          | ! [SX1: $i] : ( SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(21,plain,
    ! [SV1: $i] :
      ( ( ( ( succ @ SV1 )
         != one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(22,plain,
    ! [SV2: $i] :
      ( ( ! [SY170: $i] :
            ( ( ( succ @ SV2 )
             != ( succ @ SY170 ) )
            | ( SV2 = SY170 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(23,plain,
    ! [SV3: $i > $o] :
      ( ( ~ ( ~ ( SV3 @ ( sK2_X @ SV3 ) )
            | ~ ~ ( SV3 @ ( succ @ ( sK2_X @ SV3 ) ) ) )
        | ~ ( SV3 @ one )
        | ! [SY171: $i] : ( SV3 @ SY171 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV1: $i] :
      ( ( ( succ @ SV1 )
        = one )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ( succ @ SV2 )
         != ( succ @ SV4 ) )
        | ( SV2 = SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV3: $i > $o] :
      ( ( ( ~ ( ~ ( SV3 @ ( sK2_X @ SV3 ) )
              | ~ ~ ( SV3 @ ( succ @ ( sK2_X @ SV3 ) ) ) )
          | ~ ( SV3 @ one ) )
        = $true )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(27,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ( ( succ @ SV2 )
           != ( succ @ SV4 ) ) )
        = $true )
      | ( ( SV2 = SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(28,plain,
    ! [SV3: $i > $o] :
      ( ( ( ~ ( ~ ( SV3 @ ( sK2_X @ SV3 ) )
              | ~ ~ ( SV3 @ ( succ @ ( sK2_X @ SV3 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV3 @ one ) )
        = $true )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ( succ @ SV2 )
          = ( succ @ SV4 ) )
        = $false )
      | ( ( SV2 = SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(30,plain,
    ! [SV3: $i > $o] :
      ( ( ( ~ ( SV3 @ ( sK2_X @ SV3 ) )
          | ~ ~ ( SV3 @ ( succ @ ( sK2_X @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( SV3 @ one ) )
        = $true )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(31,plain,
    ! [SV3: $i > $o] :
      ( ( ( ~ ( SV3 @ ( sK2_X @ SV3 ) ) )
        = $false )
      | ( ( ~ ( SV3 @ one ) )
        = $true )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(32,plain,
    ! [SV3: $i > $o] :
      ( ( ( ~ ~ ( SV3 @ ( succ @ ( sK2_X @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( SV3 @ one ) )
        = $true )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(33,plain,
    ! [SV3: $i > $o] :
      ( ( ( SV3 @ ( sK2_X @ SV3 ) )
        = $true )
      | ( ( ~ ( SV3 @ one ) )
        = $true )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV3: $i > $o] :
      ( ( ( ~ ( SV3 @ ( succ @ ( sK2_X @ SV3 ) ) ) )
        = $true )
      | ( ( ~ ( SV3 @ one ) )
        = $true )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[32]) ).

thf(35,plain,
    ! [SV3: $i > $o] :
      ( ( ( SV3 @ one )
        = $false )
      | ( ( SV3 @ ( sK2_X @ SV3 ) )
        = $true )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(36,plain,
    ! [SV3: $i > $o] :
      ( ( ( SV3 @ ( succ @ ( sK2_X @ SV3 ) ) )
        = $false )
      | ( ( ~ ( SV3 @ one ) )
        = $true )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV5: $i,SV3: $i > $o] :
      ( ( ( SV3 @ SV5 )
        = $true )
      | ( ( SV3 @ ( sK2_X @ SV3 ) )
        = $true )
      | ( ( SV3 @ one )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV3: $i > $o] :
      ( ( ( SV3 @ one )
        = $false )
      | ( ( SV3 @ ( succ @ ( sK2_X @ SV3 ) ) )
        = $false )
      | ( ( ! [SY171: $i] : ( SV3 @ SY171 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV6: $i,SV3: $i > $o] :
      ( ( ( SV3 @ SV6 )
        = $true )
      | ( ( SV3 @ ( succ @ ( sK2_X @ SV3 ) ) )
        = $false )
      | ( ( SV3 @ one )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(40,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( one = one )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[37:[bind(SV3,$thf( ^ [SV7: $i] : ( SV7 = one ) ))]]) ).

thf(41,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(sim,[status(thm)],[40]) ).

thf(42,plain,
    ! [SV6: $i] :
      ( ( ( SV6 = one )
        = $true )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) ) )
          = one )
        = $false )
      | ( ( one = one )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[39:[bind(SV3,$thf( ^ [SV8: $i] : ( SV8 = one ) ))]]) ).

thf(43,plain,
    ! [SV6: $i] :
      ( ( ( SV6 = one )
        = $true )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) ) )
          = one )
        = $false ) ),
    inference(sim,[status(thm)],[42]) ).

thf(46,plain,
    ! [SV5: $i,SV10: $i > $o] :
      ( ( ( ~ ( SV10 @ SV5 ) )
        = $true )
      | ( ( ~ ( SV10
              @ ( sK2_X
                @ ^ [SX0: $i] :
                    ~ ( SV10 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV10 @ one ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV9: $i] : ~ ( SV10 @ SV9 ) ))]]) ).

thf(47,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( one = one )
        = $false ) ),
    inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV13: $i] : ( SV13 = one ) ))]]) ).

thf(51,plain,
    ! [SV6: $i,SV10: $i > $o] :
      ( ( ( ~ ( SV10 @ SV6 ) )
        = $true )
      | ( ( ~ ( SV10
              @ ( succ
                @ ( sK2_X
                  @ ^ [SX0: $i] :
                      ~ ( SV10 @ SX0 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV10 @ one ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[39:[bind(SV3,$thf( ^ [SV9: $i] : ~ ( SV10 @ SV9 ) ))]]) ).

thf(54,plain,
    ! [SV5: $i] :
      ( ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( ( SV5 = one )
          = ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[41]) ).

thf(55,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( SV5 = one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one ) )
          | ~ ( ( SV5 != one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
               != one ) ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[54]) ).

thf(56,plain,
    ! [SV5: $i] :
      ( ( ( ( SV5 = one )
          = ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[54]) ).

thf(57,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( SV5 = one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one ) ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(59,plain,
    ! [SV5: $i] :
      ( ( ( ( SV5 = one )
          | ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[57]) ).

thf(61,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(65,plain,
    ( ( ( sK2_X
        @ ^ [SX0: $i] : ( SX0 = one ) )
      = one )
    = $true ),
    inference(extuni,[status(esa)],[56:[bind(SV5,$thf( sK2_X @ ^ [SX0: $i] : ( SX0 = one ) ))]]) ).

thf(67,plain,
    ! [SV5: $i,SV10: $i > $o] :
      ( ( ( SV10 @ SV5 )
        = $false )
      | ( ( ~ ( SV10
              @ ( sK2_X
                @ ^ [SX0: $i] :
                    ~ ( SV10 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV10 @ one ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(68,plain,
    ! [SV6: $i,SV10: $i > $o] :
      ( ( ( SV10 @ SV6 )
        = $false )
      | ( ( ~ ( SV10
              @ ( succ
                @ ( sK2_X
                  @ ^ [SX0: $i] :
                      ~ ( SV10 @ SX0 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV10 @ one ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(69,plain,
    ! [SV5: $i,SV10: $i > $o] :
      ( ( ( SV10
          @ ( sK2_X
            @ ^ [SX0: $i] :
                ~ ( SV10 @ SX0 ) ) )
        = $false )
      | ( ( SV10 @ SV5 )
        = $false )
      | ( ( ~ ( SV10 @ one ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(70,plain,
    ! [SV6: $i,SV10: $i > $o] :
      ( ( ( SV10
          @ ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] :
                  ~ ( SV10 @ SX0 ) ) ) )
        = $true )
      | ( ( SV10 @ SV6 )
        = $false )
      | ( ( ~ ( SV10 @ one ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[68]) ).

thf(71,plain,
    ! [SV5: $i,SV10: $i > $o] :
      ( ( ( SV10 @ one )
        = $true )
      | ( ( SV10 @ SV5 )
        = $false )
      | ( ( SV10
          @ ( sK2_X
            @ ^ [SX0: $i] :
                ~ ( SV10 @ SX0 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(72,plain,
    ! [SV6: $i,SV10: $i > $o] :
      ( ( ( SV10 @ one )
        = $true )
      | ( ( SV10 @ SV6 )
        = $false )
      | ( ( SV10
          @ ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] :
                  ~ ( SV10 @ SX0 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(73,plain,
    ! [SV5: $i] :
      ( ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( SV5 = one )
        = $true ) ),
    inference(extuni,[status(esa)],[47]) ).

thf(74,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(sim,[status(thm)],[61]) ).

thf(75,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( one = one )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[37:[bind(SV3,$thf( ^ [SV15: $i] : ( SV15 = one ) ))]]) ).

thf(76,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(sim,[status(thm)],[75]) ).

thf(77,plain,
    ! [SV6: $i] :
      ( ( ( SV6 = one )
        = $true )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) ) )
          = one )
        = $false )
      | ( ( one = one )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[39:[bind(SV3,$thf( ^ [SV16: $i] : ( SV16 = one ) ))]]) ).

thf(78,plain,
    ! [SV6: $i] :
      ( ( ( SV6 = one )
        = $true )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) ) )
          = one )
        = $false ) ),
    inference(sim,[status(thm)],[77]) ).

thf(79,plain,
    ! [SV5: $i] :
      ( ( ( one = SV5 )
        = $true )
      | ( ( SV5 = SV5 )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 != SV5 ) )
          = SV5 )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[71:[bind(SV10,$thf( ^ [SV17: $i] : ( SV17 = SV5 ) ))]]) ).

thf(80,plain,
    ! [SV5: $i] :
      ( ( ( one = SV5 )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 != SV5 ) )
          = SV5 )
        = $false ) ),
    inference(sim,[status(thm)],[79]) ).

thf(81,plain,
    ! [SV6: $i] :
      ( ( ( one = SV6 )
        = $true )
      | ( ( SV6 = SV6 )
        = $false )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
          = SV6 )
        = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[72:[bind(SV10,$thf( ^ [SV18: $i] : ( SV18 = SV6 ) ))]]) ).

thf(82,plain,
    ! [SV6: $i] :
      ( ( ( one = SV6 )
        = $true )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
          = SV6 )
        = $true ) ),
    inference(sim,[status(thm)],[81]) ).

thf(85,plain,
    ! [SV5: $i,SV26: $i > $o] :
      ( ( ( ~ ( SV26 @ SV5 ) )
        = $true )
      | ( ( ~ ( SV26
              @ ( sK2_X
                @ ^ [SX0: $i] :
                    ~ ( SV26 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV26 @ one ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV25: $i] : ~ ( SV26 @ SV25 ) ))]]) ).

thf(86,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( one = one )
        = $false ) ),
    inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV29: $i] : ( SV29 = one ) ))]]) ).

thf(90,plain,
    ! [SV6: $i,SV26: $i > $o] :
      ( ( ( ~ ( SV26 @ SV6 ) )
        = $true )
      | ( ( ~ ( SV26
              @ ( succ
                @ ( sK2_X
                  @ ^ [SX0: $i] :
                      ~ ( SV26 @ SX0 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV26 @ one ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[39:[bind(SV3,$thf( ^ [SV25: $i] : ~ ( SV26 @ SV25 ) ))]]) ).

thf(95,plain,
    ! [SV5: $i,SV20: $i > $o] :
      ( ( ( ~ ( SV20 @ one ) )
        = $true )
      | ( ( ~ ( SV20 @ SV5 ) )
        = $false )
      | ( ( ~ ( SV20
              @ ( sK2_X
                @ ^ [SX0: $i] :
                    ~ ~ ( SV20 @ SX0 ) ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[71:[bind(SV10,$thf( ^ [SV19: $i] : ~ ( SV20 @ SV19 ) ))]]) ).

thf(100,plain,
    ! [SV6: $i,SV20: $i > $o] :
      ( ( ( ~ ( SV20 @ one ) )
        = $true )
      | ( ( ~ ( SV20 @ SV6 ) )
        = $false )
      | ( ( ~ ( SV20
              @ ( succ
                @ ( sK2_X
                  @ ^ [SX0: $i] :
                      ~ ~ ( SV20 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[72:[bind(SV10,$thf( ^ [SV19: $i] : ~ ( SV20 @ SV19 ) ))]]) ).

thf(102,plain,
    ! [SV6: $i] :
      ( ( ( one = sK1_X )
        = $true )
      | ( ( SV6 = sK1_X )
        = $false )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != sK1_X ) ) )
          = sK1_X )
        = $true ) ),
    inference(prim_subst,[status(thm)],[72:[bind(SV10,$thf( ^ [SV24: $i] : ( SV24 = sK1_X ) ))]]) ).

thf(103,plain,
    ! [SV5: $i] :
      ( ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( ( SV5 = one )
          = ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[76]) ).

thf(104,plain,
    ! [SV5: $i] :
      ( ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( ( SV5 = one )
          = ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[41]) ).

thf(105,plain,
    ! [SV6: $i] :
      ( ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
          = SV6 )
        = $true )
      | ( ( ( one = SV6 )
          = ( ( succ
              @ ( sK2_X
                @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
            = SV6 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[82]) ).

thf(106,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one )
          = ( SV5 = one ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[73]) ).

thf(107,plain,
    ! [SV5: $i] :
      ( ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( ( SV5 = one )
          = ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[74]) ).

thf(108,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( SV5 = one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one ) )
          | ~ ( ( SV5 != one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
               != one ) ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[103]) ).

thf(109,plain,
    ! [SV5: $i] :
      ( ( ( ( SV5 = one )
          = ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[103]) ).

thf(110,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( SV5 = one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one ) )
          | ~ ( ( SV5 != one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
               != one ) ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[104]) ).

thf(111,plain,
    ! [SV5: $i] :
      ( ( ( ( SV5 = one )
          = ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[104]) ).

thf(112,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( ( one = SV6 )
              | ( ( succ
                  @ ( sK2_X
                    @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
                = SV6 ) )
          | ~ ( ( one != SV6 )
              | ( ( succ
                  @ ( sK2_X
                    @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
               != SV6 ) ) )
        = $false )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
          = SV6 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[105]) ).

thf(114,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one )
              | ( SV5 = one ) )
          | ~ ( ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
               != one )
              | ( SV5 != one ) ) )
        = $false )
      | ( ( SV5 = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[106]) ).

thf(115,plain,
    ! [SV5: $i] :
      ( ( ( ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one )
          = ( SV5 = one ) )
        = $false )
      | ( ( SV5 = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[106]) ).

thf(116,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( SV5 = one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one ) )
          | ~ ( ( SV5 != one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
               != one ) ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[107]) ).

thf(117,plain,
    ! [SV5: $i] :
      ( ( ( ( SV5 = one )
          = ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[107]) ).

thf(118,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( SV5 = one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one ) ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[108]) ).

thf(120,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( SV5 = one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one ) ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[110]) ).

thf(122,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( ( one = SV6 )
              | ( ( succ
                  @ ( sK2_X
                    @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
                = SV6 ) ) )
        = $false )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
          = SV6 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[112]) ).

thf(124,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one )
              | ( SV5 = one ) ) )
        = $false )
      | ( ( SV5 = one )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[114]) ).

thf(126,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ( SV5 = one )
              | ( ( sK2_X
                  @ ^ [SX0: $i] : ( SX0 = one ) )
                = one ) ) )
        = $false )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[116]) ).

thf(128,plain,
    ! [SV5: $i] :
      ( ( ( ( SV5 = one )
          | ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[118]) ).

thf(130,plain,
    ! [SV5: $i] :
      ( ( ( ( SV5 = one )
          | ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[120]) ).

thf(132,plain,
    ! [SV6: $i] :
      ( ( ( ( one = SV6 )
          | ( ( succ
              @ ( sK2_X
                @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
            = SV6 ) )
        = $true )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
          = SV6 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[122]) ).

thf(134,plain,
    ! [SV5: $i] :
      ( ( ( ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one )
          | ( SV5 = one ) )
        = $true )
      | ( ( SV5 = one )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[124]) ).

thf(136,plain,
    ! [SV5: $i] :
      ( ( ( ( SV5 = one )
          | ( ( sK2_X
              @ ^ [SX0: $i] : ( SX0 = one ) )
            = one ) )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[126]) ).

thf(138,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[128]) ).

thf(140,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[130]) ).

thf(142,plain,
    ! [SV6: $i] :
      ( ( ( one = SV6 )
        = $true )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
          = SV6 )
        = $true )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
          = SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[132]) ).

thf(144,plain,
    ! [SV5: $i] :
      ( ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( SV5 = one )
        = $true )
      | ( ( SV5 = one )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[134]) ).

thf(146,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[136]) ).

thf(158,plain,
    ( ( ( sK2_X
        @ ^ [SX0: $i] : ( SX0 = one ) )
      = one )
    = $true ),
    inference(extuni,[status(esa)],[109:[bind(SV5,$thf( sK2_X @ ^ [SX0: $i] : ( SX0 = one ) ))]]) ).

thf(159,plain,
    ( ( ( sK2_X
        @ ^ [SX0: $i] : ( SX0 = one ) )
      = one )
    = $true ),
    inference(extuni,[status(esa)],[111:[bind(SV5,$thf( sK2_X @ ^ [SX0: $i] : ( SX0 = one ) ))]]) ).

thf(160,plain,
    ( ( ( sK2_X
        @ ^ [SX0: $i] : ( SX0 = one ) )
      = one )
    = $true ),
    inference(extuni,[status(esa)],[115:[bind(SV5,$thf( sK2_X @ ^ [SX0: $i] : ( SX0 = one ) ))]]) ).

thf(161,plain,
    ( ( ( sK2_X
        @ ^ [SX0: $i] : ( SX0 = one ) )
      = one )
    = $true ),
    inference(extuni,[status(esa)],[117:[bind(SV5,$thf( sK2_X @ ^ [SX0: $i] : ( SX0 = one ) ))]]) ).

thf(163,plain,
    ! [SV5: $i,SV26: $i > $o] :
      ( ( ( SV26 @ SV5 )
        = $false )
      | ( ( ~ ( SV26
              @ ( sK2_X
                @ ^ [SX0: $i] :
                    ~ ( SV26 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV26 @ one ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(164,plain,
    ! [SV6: $i,SV26: $i > $o] :
      ( ( ( SV26 @ SV6 )
        = $false )
      | ( ( ~ ( SV26
              @ ( succ
                @ ( sK2_X
                  @ ^ [SX0: $i] :
                      ~ ( SV26 @ SX0 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV26 @ one ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(165,plain,
    ! [SV5: $i,SV20: $i > $o] :
      ( ( ( SV20 @ one )
        = $false )
      | ( ( ~ ( SV20 @ SV5 ) )
        = $false )
      | ( ( ~ ( SV20
              @ ( sK2_X
                @ ^ [SX0: $i] :
                    ~ ~ ( SV20 @ SX0 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(166,plain,
    ! [SV6: $i,SV20: $i > $o] :
      ( ( ( SV20 @ one )
        = $false )
      | ( ( ~ ( SV20 @ SV6 ) )
        = $false )
      | ( ( ~ ( SV20
              @ ( succ
                @ ( sK2_X
                  @ ^ [SX0: $i] :
                      ~ ~ ( SV20 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(167,plain,
    ! [SV5: $i,SV26: $i > $o] :
      ( ( ( SV26
          @ ( sK2_X
            @ ^ [SX0: $i] :
                ~ ( SV26 @ SX0 ) ) )
        = $false )
      | ( ( SV26 @ SV5 )
        = $false )
      | ( ( ~ ( SV26 @ one ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[163]) ).

thf(168,plain,
    ! [SV6: $i,SV26: $i > $o] :
      ( ( ( SV26
          @ ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] :
                  ~ ( SV26 @ SX0 ) ) ) )
        = $true )
      | ( ( SV26 @ SV6 )
        = $false )
      | ( ( ~ ( SV26 @ one ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[164]) ).

thf(169,plain,
    ! [SV5: $i,SV20: $i > $o] :
      ( ( ( SV20 @ SV5 )
        = $true )
      | ( ( SV20 @ one )
        = $false )
      | ( ( ~ ( SV20
              @ ( sK2_X
                @ ^ [SX0: $i] :
                    ~ ~ ( SV20 @ SX0 ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[165]) ).

thf(170,plain,
    ! [SV6: $i,SV20: $i > $o] :
      ( ( ( SV20 @ SV6 )
        = $true )
      | ( ( SV20 @ one )
        = $false )
      | ( ( ~ ( SV20
              @ ( succ
                @ ( sK2_X
                  @ ^ [SX0: $i] :
                      ~ ~ ( SV20 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[166]) ).

thf(171,plain,
    ! [SV5: $i,SV26: $i > $o] :
      ( ( ( SV26 @ one )
        = $true )
      | ( ( SV26 @ SV5 )
        = $false )
      | ( ( SV26
          @ ( sK2_X
            @ ^ [SX0: $i] :
                ~ ( SV26 @ SX0 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[167]) ).

thf(172,plain,
    ! [SV6: $i,SV26: $i > $o] :
      ( ( ( SV26 @ one )
        = $true )
      | ( ( SV26 @ SV6 )
        = $false )
      | ( ( SV26
          @ ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] :
                  ~ ( SV26 @ SX0 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[168]) ).

thf(173,plain,
    ! [SV5: $i,SV20: $i > $o] :
      ( ( ( SV20
          @ ( sK2_X
            @ ^ [SX0: $i] :
                ~ ~ ( SV20 @ SX0 ) ) )
        = $true )
      | ( ( SV20 @ one )
        = $false )
      | ( ( SV20 @ SV5 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[169]) ).

thf(174,plain,
    ! [SV6: $i,SV20: $i > $o] :
      ( ( ( SV20
          @ ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] :
                  ~ ~ ( SV20 @ SX0 ) ) ) )
        = $false )
      | ( ( SV20 @ one )
        = $false )
      | ( ( SV20 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[170]) ).

thf(175,plain,
    ! [SV5: $i] :
      ( ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( SV5 = one )
        = $true ) ),
    inference(extuni,[status(esa)],[86]) ).

thf(177,plain,
    ( ( ( ( succ
          @ ( sK2_X
            @ ^ [SX0: $i] : ( SX0 != sK1_X ) ) )
        = sK1_X )
      = $true )
    | ( ( one = sK1_X )
      = $true ) ),
    inference(extuni,[status(esa)],[102:[bind(SV6,$thf( sK1_X ))]]) ).

thf(178,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(sim,[status(thm)],[138]) ).

thf(179,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(sim,[status(thm)],[140]) ).

thf(180,plain,
    ! [SV6: $i] :
      ( ( ( one = SV6 )
        = $true )
      | ( ( ( succ
            @ ( sK2_X
              @ ^ [SX0: $i] : ( SX0 != SV6 ) ) )
          = SV6 )
        = $true ) ),
    inference(sim,[status(thm)],[142]) ).

thf(181,plain,
    ! [SV5: $i] :
      ( ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true )
      | ( ( SV5 = one )
        = $true ) ),
    inference(sim,[status(thm)],[144]) ).

thf(182,plain,
    ! [SV5: $i] :
      ( ( ( SV5 = one )
        = $true )
      | ( ( ( sK2_X
            @ ^ [SX0: $i] : ( SX0 = one ) )
          = one )
        = $true ) ),
    inference(sim,[status(thm)],[146]) ).

thf(183,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,182,181,180,179,178,177,175,174,173,172,171,161,160,159,158,82,80,78,76,74,73,72,71,65,43,41,39,37,29,24]) ).

thf(184,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[183]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM636^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jul  5 06:55:33 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 3
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:3,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:5,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.39/0.57  
% 0.39/0.57   Prim_subst applied to clause 
% 0.39/0.57   
% 0.39/0.57  95:[ 0:<SV19@SV18 = $true>-w(1)-i() 1:<SV19@(sK2_X@SV19) = $true>-w(1)-i() 2:<SV19@one = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 37)-o(AXIOM)-fv([ SV18 SV19 ])
% 0.39/0.59  
% 0.39/0.59   Prim_subst applied to clause 
% 0.39/0.59   
% 0.39/0.59  95:[ 0:<SV19@SV18 = $true>-w(1)-i() 1:<SV19@(sK2_X@SV19) = $true>-w(1)-i() 2:<SV19@one = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 37)-o(AXIOM)-fv([ SV18 SV19 ])
% 0.39/0.63  
% 0.39/0.63   Prim_subst applied to clause 
% 0.39/0.63   
% 0.39/0.63  95:[ 0:<SV19@SV18 = $true>-w(1)-i() 1:<SV19@(sK2_X@SV19) = $true>-w(1)-i() 2:<SV19@one = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 37)-o(AXIOM)-fv([ SV18 SV19 ])
% 0.56/0.74  ................
% 75.27/75.49  (rf:0,axioms:3,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:5,loop_count:0,foatp_calls:0,translation:fof_full)...
% 75.44/75.60  
% 75.44/75.60   Prim_subst applied to clause 
% 75.44/75.60   
% 75.44/75.60  86:[ 0:<SV19@SV18 = $true>-w(1)-i() 1:<SV19@(sK2_X@SV19) = $true>-w(1)-i() 2:<SV19@one = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 33)-o(AXIOM)-fv([ SV18 SV19 ])
% 75.44/75.61  
% 75.44/75.61   Prim_subst applied to clause 
% 75.44/75.61   
% 75.44/75.61  86:[ 0:<SV19@SV18 = $true>-w(1)-i() 1:<SV19@(sK2_X@SV19) = $true>-w(1)-i() 2:<SV19@one = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 33)-o(AXIOM)-fv([ SV18 SV19 ])
% 75.44/75.63  
% 75.44/75.63   Prim_subst applied to clause 
% 75.44/75.63   
% 75.44/75.63  86:[ 0:<SV19@SV18 = $true>-w(1)-i() 1:<SV19@(sK2_X@SV19) = $true>-w(1)-i() 2:<SV19@one = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 33)-o(AXIOM)-fv([ SV18 SV19 ])
% 75.63/75.82  ..................................................
% 150.16/150.34  (rf:0,axioms:3,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:5,loop_count:0,foatp_calls:0,translation:fof_full).....
% 150.36/150.59  
% 150.36/150.59  ********************************
% 150.36/150.59  *   All subproblems solved!    *
% 150.36/150.59  ********************************
% 150.36/150.59  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:183,loop_count:0,foatp_calls:3,translation:fof_full)
% 150.36/150.59  
% 150.36/150.59  %**** Beginning of derivation protocol ****
% 150.36/150.59  % SZS output start CNFRefutation
% See solution above
% 150.36/150.59  
% 150.36/150.59  %**** End of derivation protocol ****
% 150.36/150.59  %**** no. of clauses in derivation: 129 ****
% 150.36/150.59  %**** clause counter: 183 ****
% 150.36/150.59  
% 150.36/150.59  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:183,loop_count:0,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------