TSTP Solution File: SWV376+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SWV376+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n024.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 : Wed Jul 20 20:12:11 EDT 2022

% Result   : Theorem 0.50s 0.92s
% Output   : CNFRefutation 0.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   85
% Syntax   : Number of formulae    :  525 ( 331 unt;  41 typ;   0 def)
%            Number of atoms       : 2558 ( 953 equ;   0 cnn)
%            Maximal formula atoms :    6 (   5 avg)
%            Number of connectives : 6690 ( 721   ~; 702   |;  50   &;5137   @)
%                                         (  14 <=>;  66  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   43 (  43   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  41 usr;  18 con; 0-3 aty)
%            Number of variables   : 1732 (   0   ^1732   !;   0   ?;1732   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_bad,type,
    bad: $i ).

thf(tp_bottom,type,
    bottom: $i ).

thf(tp_check_cpq,type,
    check_cpq: $i > $o ).

thf(tp_contains_cpq,type,
    contains_cpq: $i > $i > $o ).

thf(tp_contains_slb,type,
    contains_slb: $i > $i > $o ).

thf(tp_create_slb,type,
    create_slb: $i ).

thf(tp_findmin_cpq_eff,type,
    findmin_cpq_eff: $i > $i ).

thf(tp_findmin_cpq_res,type,
    findmin_cpq_res: $i > $i ).

thf(tp_findmin_pqp_res,type,
    findmin_pqp_res: $i > $i ).

thf(tp_im_succ_cpq,type,
    im_succ_cpq: $i > $i ).

thf(tp_insert_cpq,type,
    insert_cpq: $i > $i > $i ).

thf(tp_insert_pqp,type,
    insert_pqp: $i > $i > $i ).

thf(tp_insert_slb,type,
    insert_slb: $i > $i > $i ).

thf(tp_isnonempty_slb,type,
    isnonempty_slb: $i > $o ).

thf(tp_less_than,type,
    less_than: $i > $i > $o ).

thf(tp_lookup_slb,type,
    lookup_slb: $i > $i > $i ).

thf(tp_ok,type,
    ok: $i > $o ).

thf(tp_pair,type,
    pair: $i > $i > $i ).

thf(tp_pair_in_list,type,
    pair_in_list: $i > $i > $i > $o ).

thf(tp_remove_cpq,type,
    remove_cpq: $i > $i > $i ).

thf(tp_remove_pqp,type,
    remove_pqp: $i > $i > $i ).

thf(tp_remove_slb,type,
    remove_slb: $i > $i > $i ).

thf(tp_removemin_cpq_eff,type,
    removemin_cpq_eff: $i > $i ).

thf(tp_removemin_cpq_res,type,
    removemin_cpq_res: $i > $i ).

thf(tp_sK10_SY162,type,
    sK10_SY162: $i ).

thf(tp_sK11_SY165,type,
    sK11_SY165: $i ).

thf(tp_sK12_SY167,type,
    sK12_SY167: $i ).

thf(tp_sK13_REN,type,
    sK13_REN: $o ).

thf(tp_sK1_U,type,
    sK1_U: $i ).

thf(tp_sK2_SY138,type,
    sK2_SY138: $i ).

thf(tp_sK3_SY143,type,
    sK3_SY143: $i ).

thf(tp_sK4_SY147,type,
    sK4_SY147: $i ).

thf(tp_sK5_SY150,type,
    sK5_SY150: $i ).

thf(tp_sK6_SY152,type,
    sK6_SY152: $i ).

thf(tp_sK7_U,type,
    sK7_U: $i ).

thf(tp_sK8_SY153,type,
    sK8_SY153: $i ).

thf(tp_sK9_SY158,type,
    sK9_SY158: $i ).

thf(tp_strictly_less_than,type,
    strictly_less_than: $i > $i > $o ).

thf(tp_succ_cpq,type,
    succ_cpq: $i > $i > $o ).

thf(tp_triple,type,
    triple: $i > $i > $i > $i ).

thf(tp_update_slb,type,
    update_slb: $i > $i > $i ).

thf(1,axiom,
    ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
        ( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
       => ( ~ ( ok @ ( triple @ X @ Y @ Z ) )
         => ~ ( ok @ ( im_succ_cpq @ ( triple @ X @ Y @ Z ) ) ) ) )
   => ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ok @ ( triple @ X1 @ X2 @ X3 ) )
       => ! [X4: $i,X5: $i,X6: $i] :
            ( ( succ_cpq @ ( triple @ X1 @ X2 @ X3 ) @ ( triple @ X4 @ X5 @ X6 ) )
           => ~ ( ok @ ( triple @ X4 @ X5 @ X6 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_induction) ).

thf(2,axiom,
    ! [U: $i] :
      ( ( removemin_cpq_res @ U )
      = ( findmin_cpq_res @ U ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).

thf(3,axiom,
    ! [U: $i] :
      ( ( removemin_cpq_eff @ U )
      = ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).

thf(4,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( V != create_slb )
     => ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
        = ( findmin_pqp_res @ U ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).

thf(5,axiom,
    ! [U: $i,V: $i] :
      ( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
      = bottom ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).

thf(6,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( ( V != create_slb )
        & ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
        & ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) )
     => ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
        = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).

thf(7,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( ( V != create_slb )
        & ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
        & ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) ) )
     => ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
        = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).

thf(8,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( ( V != create_slb )
        & ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) ) )
     => ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
        = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).

thf(9,axiom,
    ! [U: $i,V: $i] :
      ( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
      = ( triple @ U @ create_slb @ bad ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).

thf(10,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( ( contains_slb @ V @ X )
        & ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) ) )
     => ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
        = ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).

thf(11,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( ( contains_slb @ V @ X )
        & ( less_than @ ( lookup_slb @ V @ X ) @ X ) )
     => ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
        = ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).

thf(12,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ~ ( contains_slb @ V @ X )
     => ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
        = ( triple @ U @ V @ bad ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).

thf(13,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
      = ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).

thf(14,axiom,
    ! [U: $i,V: $i,W: $i] :
      ( ~ ( ok @ ( triple @ U @ V @ W ) )
     => ( W = bad ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).

thf(15,axiom,
    ! [U: $i,V: $i] :
      ( ( ok @ ( triple @ U @ V @ bad ) )
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).

thf(16,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
    <=> ( contains_slb @ V @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).

thf(17,axiom,
    ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
      ( ( strictly_less_than @ X @ Y )
     => ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
      <=> $false ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).

thf(18,axiom,
    ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
      ( ( less_than @ Y @ X )
     => ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
      <=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).

thf(19,axiom,
    ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).

thf(20,axiom,
    ! [U: $i,V: $i] :
      ( ( succ_cpq @ U @ V )
     => ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).

thf(21,axiom,
    ! [U: $i,V: $i] :
      ( ( succ_cpq @ U @ V )
     => ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).

thf(22,axiom,
    ! [U: $i,V: $i,W: $i] :
      ( ( succ_cpq @ U @ V )
     => ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).

thf(23,axiom,
    ! [U: $i,V: $i,W: $i] :
      ( ( succ_cpq @ U @ V )
     => ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).

thf(24,axiom,
    ! [U: $i] : ( succ_cpq @ U @ U ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).

thf(25,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( less_than @ W @ X )
     => ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
        = ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).

thf(26,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( strictly_less_than @ X @ W )
     => ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
        = ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).

thf(27,axiom,
    ! [U: $i] :
      ( ( update_slb @ create_slb @ U )
      = create_slb ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).

thf(28,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( ( V != W )
        & ( contains_slb @ U @ W ) )
     => ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
        = ( lookup_slb @ U @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).

thf(29,axiom,
    ! [U: $i,V: $i,W: $i] :
      ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
      = W ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).

thf(30,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( ( V != W )
        & ( contains_slb @ U @ W ) )
     => ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
        = ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).

thf(31,axiom,
    ! [U: $i,V: $i,W: $i] :
      ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
      = U ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).

thf(32,axiom,
    ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
      ( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
    <=> ( ( pair_in_list @ U @ W @ Y )
        | ( ( V = W )
          & ( X = Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).

thf(33,axiom,
    ! [U: $i,V: $i] :
      ~ ( pair_in_list @ create_slb @ U @ V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).

thf(34,axiom,
    ! [U: $i,V: $i,W: $i,X: $i] :
      ( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
    <=> ( ( contains_slb @ U @ W )
        | ( V = W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).

thf(35,axiom,
    ! [U: $i] :
      ~ ( contains_slb @ create_slb @ U ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).

thf(36,axiom,
    ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).

thf(37,axiom,
    ~ ( isnonempty_slb @ create_slb ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).

thf(38,axiom,
    ! [U: $i] : ( less_than @ bottom @ U ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).

thf(39,axiom,
    ! [U: $i,V: $i] :
      ( ( strictly_less_than @ U @ V )
    <=> ( ( less_than @ U @ V )
        & ~ ( less_than @ V @ U ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).

thf(40,axiom,
    ! [U: $i] : ( less_than @ U @ U ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

thf(41,axiom,
    ! [U: $i,V: $i] :
      ( ( less_than @ U @ V )
      | ( less_than @ V @ U ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).

thf(42,axiom,
    ! [U: $i,V: $i,W: $i] :
      ( ( ( less_than @ U @ V )
        & ( less_than @ V @ W ) )
     => ( less_than @ U @ W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).

thf(43,axiom,
    ! [U: $i,V: $i,W: $i] :
      ( ~ ( ok @ ( triple @ U @ V @ W ) )
     => ~ ( ok @ ( im_succ_cpq @ ( triple @ U @ V @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_l13) ).

thf(44,conjecture,
    ! [U: $i,V: $i,W: $i] :
      ( ~ ( ok @ ( triple @ U @ V @ W ) )
     => ! [X: $i,Y: $i,Z: $i] :
          ( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
         => ~ ( ok @ ( triple @ X @ Y @ Z ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_co) ).

thf(45,negated_conjecture,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( ok @ ( triple @ U @ V @ W ) )
         => ! [X: $i,Y: $i,Z: $i] :
              ( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
             => ~ ( ok @ ( triple @ X @ Y @ Z ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[44]) ).

thf(46,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( ok @ ( triple @ U @ V @ W ) )
         => ! [X: $i,Y: $i,Z: $i] :
              ( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
             => ~ ( ok @ ( triple @ X @ Y @ Z ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[45]) ).

thf(47,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
          ( ( succ_cpq @ ( triple @ U @ V @ W ) @ ( triple @ X @ Y @ Z ) )
         => ( ~ ( ok @ ( triple @ X @ Y @ Z ) )
           => ~ ( ok @ ( im_succ_cpq @ ( triple @ X @ Y @ Z ) ) ) ) )
     => ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( ok @ ( triple @ X1 @ X2 @ X3 ) )
         => ! [X4: $i,X5: $i,X6: $i] :
              ( ( succ_cpq @ ( triple @ X1 @ X2 @ X3 ) @ ( triple @ X4 @ X5 @ X6 ) )
             => ~ ( ok @ ( triple @ X4 @ X5 @ X6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(48,plain,
    ( ( ! [U: $i] :
          ( ( removemin_cpq_res @ U )
          = ( findmin_cpq_res @ U ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(49,plain,
    ( ( ! [U: $i] :
          ( ( removemin_cpq_eff @ U )
          = ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(50,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( V != create_slb )
         => ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
            = ( findmin_pqp_res @ U ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(51,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
          = bottom ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(52,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( ( V != create_slb )
            & ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
            & ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) )
         => ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
            = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(53,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( ( V != create_slb )
            & ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
            & ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) ) )
         => ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
            = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(54,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( ( V != create_slb )
            & ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) ) )
         => ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
            = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(55,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
          = ( triple @ U @ create_slb @ bad ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(56,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( ( contains_slb @ V @ X )
            & ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) ) )
         => ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
            = ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(57,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( ( contains_slb @ V @ X )
            & ( less_than @ ( lookup_slb @ V @ X ) @ X ) )
         => ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
            = ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(58,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( contains_slb @ V @ X )
         => ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
            = ( triple @ U @ V @ bad ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(59,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
          = ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(60,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( ok @ ( triple @ U @ V @ W ) )
         => ( W = bad ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(61,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( ok @ ( triple @ U @ V @ bad ) )
        <=> $false ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(62,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
        <=> ( contains_slb @ V @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(63,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
          ( ( strictly_less_than @ X @ Y )
         => ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
          <=> $false ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(64,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
          ( ( less_than @ Y @ X )
         => ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
          <=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(65,plain,
    ( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(66,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( succ_cpq @ U @ V )
         => ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(67,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( succ_cpq @ U @ V )
         => ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(68,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( succ_cpq @ U @ V )
         => ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(69,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( succ_cpq @ U @ V )
         => ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(70,plain,
    ( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(71,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( less_than @ W @ X )
         => ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
            = ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(72,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( strictly_less_than @ X @ W )
         => ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
            = ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(73,plain,
    ( ( ! [U: $i] :
          ( ( update_slb @ create_slb @ U )
          = create_slb ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(74,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( ( V != W )
            & ( contains_slb @ U @ W ) )
         => ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
            = ( lookup_slb @ U @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(75,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
          = W ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(76,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( ( V != W )
            & ( contains_slb @ U @ W ) )
         => ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
            = ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(77,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
          = U ) )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(78,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
          ( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
        <=> ( ( pair_in_list @ U @ W @ Y )
            | ( ( V = W )
              & ( X = Y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(79,plain,
    ( ( ! [U: $i,V: $i] :
          ~ ( pair_in_list @ create_slb @ U @ V ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(80,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
        <=> ( ( contains_slb @ U @ W )
            | ( V = W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(81,plain,
    ( ( ! [U: $i] :
          ~ ( contains_slb @ create_slb @ U ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(82,plain,
    ( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(83,plain,
    ( ( ~ ( isnonempty_slb @ create_slb ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(84,plain,
    ( ( ! [U: $i] : ( less_than @ bottom @ U ) )
    = $true ),
    inference(unfold_def,[status(thm)],[38]) ).

thf(85,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( strictly_less_than @ U @ V )
        <=> ( ( less_than @ U @ V )
            & ~ ( less_than @ V @ U ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(86,plain,
    ( ( ! [U: $i] : ( less_than @ U @ U ) )
    = $true ),
    inference(unfold_def,[status(thm)],[40]) ).

thf(87,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( less_than @ U @ V )
          | ( less_than @ V @ U ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[41]) ).

thf(88,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( ( less_than @ U @ V )
            & ( less_than @ V @ W ) )
         => ( less_than @ U @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[42]) ).

thf(89,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( ok @ ( triple @ U @ V @ W ) )
         => ~ ( ok @ ( im_succ_cpq @ ( triple @ U @ V @ W ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[43]) ).

thf(90,plain,
    ( ( ! [SY138: $i,SY139: $i] :
          ( ~ ( ok @ ( triple @ sK1_U @ SY138 @ SY139 ) )
         => ! [SY140: $i,SY141: $i,SY142: $i] :
              ( ( succ_cpq @ ( triple @ sK1_U @ SY138 @ SY139 ) @ ( triple @ SY140 @ SY141 @ SY142 ) )
             => ~ ( ok @ ( triple @ SY140 @ SY141 @ SY142 ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[46]) ).

thf(91,plain,
    ( ( ! [SY143: $i] :
          ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY138 @ SY143 ) )
         => ! [SY144: $i,SY145: $i,SY146: $i] :
              ( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ SY143 ) @ ( triple @ SY144 @ SY145 @ SY146 ) )
             => ~ ( ok @ ( triple @ SY144 @ SY145 @ SY146 ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[90]) ).

thf(92,plain,
    ( ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) )
     => ! [SY147: $i,SY148: $i,SY149: $i] :
          ( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) @ ( triple @ SY147 @ SY148 @ SY149 ) )
         => ~ ( ok @ ( triple @ SY147 @ SY148 @ SY149 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[91]) ).

thf(93,plain,
    ( ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[92]) ).

thf(94,plain,
    ( ( ! [SY147: $i,SY148: $i,SY149: $i] :
          ( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) @ ( triple @ SY147 @ SY148 @ SY149 ) )
         => ~ ( ok @ ( triple @ SY147 @ SY148 @ SY149 ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[92]) ).

thf(95,plain,
    ( ( ~ ! [SY147: $i,SY148: $i,SY149: $i] :
            ( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) @ ( triple @ SY147 @ SY148 @ SY149 ) )
           => ~ ( ok @ ( triple @ SY147 @ SY148 @ SY149 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[94]) ).

thf(96,plain,
    ( ( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) )
      & ( ok @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[95]) ).

thf(97,plain,
    ( ( ( sK13_REN
        | ! [X1: $i,X2: $i,X3: $i] :
            ( ( ok @ ( triple @ X1 @ X2 @ X3 ) )
            | ! [X4: $i,X5: $i,X6: $i] :
                ( ~ ( succ_cpq @ ( triple @ X1 @ X2 @ X3 ) @ ( triple @ X4 @ X5 @ X6 ) )
                | ~ ( ok @ ( triple @ X4 @ X5 @ X6 ) ) ) ) )
      & ( sK13_REN
       => ( ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
          & ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
          & ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[47]) ).

thf(98,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( V = create_slb )
          | ! [W: $i] :
              ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
              = ( findmin_pqp_res @ U ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[50]) ).

thf(99,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( V = create_slb )
          | ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
          | ~ ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) )
          | ! [W: $i] :
              ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
              = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[52]) ).

thf(100,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( V = create_slb )
          | ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
          | ~ ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) )
          | ! [W: $i] :
              ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
              = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[53]) ).

thf(101,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( V = create_slb )
          | ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
          | ! [W: $i] :
              ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
              = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[54]) ).

thf(102,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( contains_slb @ V @ X )
          | ~ ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) )
          | ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
            = ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[56]) ).

thf(103,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( contains_slb @ V @ X )
          | ~ ( less_than @ ( lookup_slb @ V @ X ) @ X )
          | ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
            = ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[57]) ).

thf(104,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( contains_slb @ V @ X )
          | ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
            = ( triple @ U @ V @ bad ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[58]) ).

thf(105,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( ok @ ( triple @ U @ V @ W ) )
          | ( W = bad ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[60]) ).

thf(106,plain,
    ( ( ! [U: $i,V: $i] :
          ~ ( ok @ ( triple @ U @ V @ bad ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[61]) ).

thf(107,plain,
    ( ( ! [U: $i,V: $i] :
          ( ! [W: $i,X: $i] :
              ( ~ ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
              | ( contains_slb @ V @ X ) )
          & ! [W: $i,X: $i] :
              ( ~ ( contains_slb @ V @ X )
              | ( contains_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[62]) ).

thf(108,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
          ( ~ ( strictly_less_than @ X @ Y )
          | ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[63]) ).

thf(109,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ! [X: $i,Y: $i] :
              ( ~ ( less_than @ Y @ X )
              | ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
              | ( check_cpq @ ( triple @ U @ V @ W ) ) )
          & ! [X: $i,Y: $i] :
              ( ~ ( less_than @ Y @ X )
              | ~ ( check_cpq @ ( triple @ U @ V @ W ) )
              | ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[64]) ).

thf(110,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( succ_cpq @ U @ V )
          | ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[66]) ).

thf(111,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( succ_cpq @ U @ V )
          | ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[67]) ).

thf(112,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( succ_cpq @ U @ V )
          | ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[68]) ).

thf(113,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( succ_cpq @ U @ V )
          | ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[69]) ).

thf(114,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( less_than @ W @ X )
          | ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
            = ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[71]) ).

thf(115,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( strictly_less_than @ X @ W )
          | ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
            = ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[72]) ).

thf(116,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( V = W )
          | ~ ( contains_slb @ U @ W )
          | ! [X: $i] :
              ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
              = ( lookup_slb @ U @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[74]) ).

thf(117,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( V = W )
          | ~ ( contains_slb @ U @ W )
          | ! [X: $i] :
              ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
              = ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[76]) ).

thf(118,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ! [X: $i,Y: $i] :
              ( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
              | ( V = W )
              | ( pair_in_list @ U @ W @ Y ) )
          & ! [X: $i,Y: $i] :
              ( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
              | ( X = Y )
              | ( pair_in_list @ U @ W @ Y ) )
          & ! [X: $i,Y: $i] :
              ( ( V != W )
              | ( X != Y )
              | ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
          & ! [X: $i,Y: $i] :
              ( ~ ( pair_in_list @ U @ W @ Y )
              | ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[78]) ).

thf(119,plain,
    ( ( ! [U: $i,V: $i] :
          ( ! [W: $i] :
              ( ! [X: $i] :
                  ~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
              | ( V = W )
              | ( contains_slb @ U @ W ) )
          & ! [W: $i] :
              ( ( V != W )
              | ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
          & ! [W: $i] :
              ( ~ ( contains_slb @ U @ W )
              | ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[80]) ).

thf(120,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( less_than @ U @ V )
          | ( less_than @ V @ U )
          | ( strictly_less_than @ U @ V ) )
      & ! [U: $i,V: $i] :
          ( ~ ( strictly_less_than @ U @ V )
          | ( less_than @ U @ V ) )
      & ! [U: $i,V: $i] :
          ( ~ ( strictly_less_than @ U @ V )
          | ~ ( less_than @ V @ U ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[85]) ).

thf(121,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( less_than @ U @ V )
          | ~ ( less_than @ V @ W )
          | ( less_than @ U @ W ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[88]) ).

thf(122,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( ok @ ( triple @ U @ V @ W ) )
          | ~ ( ok @ ( im_succ_cpq @ ( triple @ U @ V @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[89]) ).

thf(123,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( ok @ ( triple @ U @ V @ W ) )
          | ~ ( ok @ ( im_succ_cpq @ ( triple @ U @ V @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[122]) ).

thf(124,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ~ ( less_than @ U @ V )
          | ~ ( less_than @ V @ W )
          | ( less_than @ U @ W ) ) )
    = $true ),
    inference(copy,[status(thm)],[121]) ).

thf(125,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( less_than @ U @ V )
          | ( less_than @ V @ U ) ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(126,plain,
    ( ( ! [U: $i] : ( less_than @ U @ U ) )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(127,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( less_than @ U @ V )
          | ( less_than @ V @ U )
          | ( strictly_less_than @ U @ V ) )
      & ! [U: $i,V: $i] :
          ( ~ ( strictly_less_than @ U @ V )
          | ( less_than @ U @ V ) )
      & ! [U: $i,V: $i] :
          ( ~ ( strictly_less_than @ U @ V )
          | ~ ( less_than @ V @ U ) ) )
    = $true ),
    inference(copy,[status(thm)],[120]) ).

thf(128,plain,
    ( ( ! [U: $i] : ( less_than @ bottom @ U ) )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(129,plain,
    ( ( ~ ( isnonempty_slb @ create_slb ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(130,plain,
    ( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(131,plain,
    ( ( ! [U: $i] :
          ~ ( contains_slb @ create_slb @ U ) )
    = $true ),
    inference(copy,[status(thm)],[81]) ).

thf(132,plain,
    ( ( ! [U: $i,V: $i] :
          ( ! [W: $i] :
              ( ! [X: $i] :
                  ~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
              | ( V = W )
              | ( contains_slb @ U @ W ) )
          & ! [W: $i] :
              ( ( V != W )
              | ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
          & ! [W: $i] :
              ( ~ ( contains_slb @ U @ W )
              | ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[119]) ).

thf(133,plain,
    ( ( ! [U: $i,V: $i] :
          ~ ( pair_in_list @ create_slb @ U @ V ) )
    = $true ),
    inference(copy,[status(thm)],[79]) ).

thf(134,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ! [X: $i,Y: $i] :
              ( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
              | ( V = W )
              | ( pair_in_list @ U @ W @ Y ) )
          & ! [X: $i,Y: $i] :
              ( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
              | ( X = Y )
              | ( pair_in_list @ U @ W @ Y ) )
          & ! [X: $i,Y: $i] :
              ( ( V != W )
              | ( X != Y )
              | ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
          & ! [X: $i,Y: $i] :
              ( ~ ( pair_in_list @ U @ W @ Y )
              | ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[118]) ).

thf(135,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
          = U ) )
    = $true ),
    inference(copy,[status(thm)],[77]) ).

thf(136,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( V = W )
          | ~ ( contains_slb @ U @ W )
          | ! [X: $i] :
              ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
              = ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[117]) ).

thf(137,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
          = W ) )
    = $true ),
    inference(copy,[status(thm)],[75]) ).

thf(138,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( V = W )
          | ~ ( contains_slb @ U @ W )
          | ! [X: $i] :
              ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
              = ( lookup_slb @ U @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[116]) ).

thf(139,plain,
    ( ( ! [U: $i] :
          ( ( update_slb @ create_slb @ U )
          = create_slb ) )
    = $true ),
    inference(copy,[status(thm)],[73]) ).

thf(140,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( strictly_less_than @ X @ W )
          | ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
            = ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[115]) ).

thf(141,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( less_than @ W @ X )
          | ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
            = ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[114]) ).

thf(142,plain,
    ( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(143,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( succ_cpq @ U @ V )
          | ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[113]) ).

thf(144,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( succ_cpq @ U @ V )
          | ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[112]) ).

thf(145,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( succ_cpq @ U @ V )
          | ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[111]) ).

thf(146,plain,
    ( ( ! [U: $i,V: $i] :
          ( ~ ( succ_cpq @ U @ V )
          | ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[110]) ).

thf(147,plain,
    ( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
    = $true ),
    inference(copy,[status(thm)],[65]) ).

thf(148,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ! [X: $i,Y: $i] :
              ( ~ ( less_than @ Y @ X )
              | ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
              | ( check_cpq @ ( triple @ U @ V @ W ) ) )
          & ! [X: $i,Y: $i] :
              ( ~ ( less_than @ Y @ X )
              | ~ ( check_cpq @ ( triple @ U @ V @ W ) )
              | ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[109]) ).

thf(149,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
          ( ~ ( strictly_less_than @ X @ Y )
          | ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(150,plain,
    ( ( ! [U: $i,V: $i] :
          ( ! [W: $i,X: $i] :
              ( ~ ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
              | ( contains_slb @ V @ X ) )
          & ! [W: $i,X: $i] :
              ( ~ ( contains_slb @ V @ X )
              | ( contains_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(151,plain,
    ( ( ! [U: $i,V: $i] :
          ~ ( ok @ ( triple @ U @ V @ bad ) ) )
    = $true ),
    inference(copy,[status(thm)],[106]) ).

thf(152,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( ok @ ( triple @ U @ V @ W ) )
          | ( W = bad ) ) )
    = $true ),
    inference(copy,[status(thm)],[105]) ).

thf(153,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
          = ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(154,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( contains_slb @ V @ X )
          | ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
            = ( triple @ U @ V @ bad ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(155,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( contains_slb @ V @ X )
          | ~ ( less_than @ ( lookup_slb @ V @ X ) @ X )
          | ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
            = ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(156,plain,
    ( ( ! [U: $i,V: $i,W: $i,X: $i] :
          ( ~ ( contains_slb @ V @ X )
          | ~ ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) )
          | ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
            = ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(157,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
          = ( triple @ U @ create_slb @ bad ) ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(158,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( V = create_slb )
          | ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
          | ! [W: $i] :
              ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
              = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(159,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( V = create_slb )
          | ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
          | ~ ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) )
          | ! [W: $i] :
              ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
              = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(160,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( V = create_slb )
          | ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
          | ~ ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) )
          | ! [W: $i] :
              ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
              = ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(161,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
          = bottom ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(162,plain,
    ( ( ! [U: $i,V: $i] :
          ( ( V = create_slb )
          | ! [W: $i] :
              ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
              = ( findmin_pqp_res @ U ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(163,plain,
    ( ( ! [U: $i] :
          ( ( removemin_cpq_eff @ U )
          = ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(164,plain,
    ( ( ! [U: $i] :
          ( ( removemin_cpq_res @ U )
          = ( findmin_cpq_res @ U ) ) )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(165,plain,
    ( ( ( sK13_REN
        | ! [X1: $i,X2: $i,X3: $i] :
            ( ( ok @ ( triple @ X1 @ X2 @ X3 ) )
            | ! [X4: $i,X5: $i,X6: $i] :
                ( ~ ( succ_cpq @ ( triple @ X1 @ X2 @ X3 ) @ ( triple @ X4 @ X5 @ X6 ) )
                | ~ ( ok @ ( triple @ X4 @ X5 @ X6 ) ) ) ) )
      & ( sK13_REN
       => ( ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
          & ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
          & ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(166,plain,
    ( ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(167,plain,
    ( ( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) )
      & ( ok @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(168,plain,
    ( ( ~ ( ~ ( sK13_REN
              | ! [SX0: $i,SX1: $i,SX2: $i] :
                  ( ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
                  | ! [SX3: $i,SX4: $i,SX5: $i] :
                      ( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
                      | ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
          | ~ ( ~ sK13_REN
              | ~ ( ~ ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
                  | ~ ~ ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
                        | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[165]) ).

thf(169,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i] :
                  ( ! [SX3: $i] :
                      ~ ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
                  | ( SX1 = SX2 )
                  | ( contains_slb @ SX0 @ SX2 ) )
            | ~ ~ ( ~ ! [SX2: $i] :
                        ( ( SX1 != SX2 )
                        | ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) )
                  | ~ ! [SX2: $i] :
                        ( ~ ( contains_slb @ SX0 @ SX2 )
                        | ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[132]) ).

thf(170,plain,
    ( ( ~ ( ~ ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) )
          | ~ ( ok @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[167]) ).

thf(171,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
                        | ( SX1 = SX2 )
                        | ( pair_in_list @ SX0 @ SX2 @ SX4 ) )
                  | ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
                        | ( SX3 = SX4 )
                        | ( pair_in_list @ SX0 @ SX2 @ SX4 ) ) )
            | ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
                        ( ( SX1 != SX2 )
                        | ( SX3 != SX4 )
                        | ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) )
                  | ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( pair_in_list @ SX0 @ SX2 @ SX4 )
                        | ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[134]) ).

thf(172,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( less_than @ SX4 @ SX3 )
                  | ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
                  | ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) ) )
            | ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( less_than @ SX4 @ SX3 )
                  | ~ ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) )
                  | ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[148]) ).

thf(173,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( less_than @ SX0 @ SX1 )
                | ( less_than @ SX1 @ SX0 )
                | ( strictly_less_than @ SX0 @ SX1 ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( strictly_less_than @ SX0 @ SX1 )
                      | ( less_than @ SX0 @ SX1 ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( strictly_less_than @ SX0 @ SX1 )
                      | ~ ( less_than @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[127]) ).

thf(174,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
                  | ( contains_slb @ SX1 @ SX3 ) )
            | ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( contains_slb @ SX1 @ SX3 )
                  | ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[150]) ).

thf(175,plain,
    ! [SV1: $i] :
      ( ( ! [SY168: $i,SY169: $i] :
            ( ( ok @ ( triple @ SV1 @ SY168 @ SY169 ) )
            | ~ ( ok @ ( im_succ_cpq @ ( triple @ SV1 @ SY168 @ SY169 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(176,plain,
    ! [SV2: $i] :
      ( ( ! [SY170: $i,SY171: $i] :
            ( ~ ( less_than @ SV2 @ SY170 )
            | ~ ( less_than @ SY170 @ SY171 )
            | ( less_than @ SV2 @ SY171 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(177,plain,
    ! [SV3: $i] :
      ( ( ! [SY172: $i] :
            ( ( less_than @ SV3 @ SY172 )
            | ( less_than @ SY172 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[125]) ).

thf(178,plain,
    ! [SV4: $i] :
      ( ( less_than @ SV4 @ SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(179,plain,
    ! [SV5: $i] :
      ( ( less_than @ bottom @ SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(180,plain,
    ( ( isnonempty_slb @ create_slb )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[129]) ).

thf(181,plain,
    ! [SV6: $i] :
      ( ( ! [SY173: $i,SY174: $i] : ( isnonempty_slb @ ( insert_slb @ SV6 @ ( pair @ SY173 @ SY174 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[130]) ).

thf(182,plain,
    ! [SV7: $i] :
      ( ( ~ ( contains_slb @ create_slb @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[131]) ).

thf(183,plain,
    ! [SV8: $i] :
      ( ( ! [SY175: $i] :
            ~ ( pair_in_list @ create_slb @ SV8 @ SY175 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(184,plain,
    ! [SV9: $i] :
      ( ( ! [SY176: $i,SY177: $i] :
            ( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SY176 @ SY177 ) ) @ SY176 )
            = SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(185,plain,
    ! [SV10: $i] :
      ( ( ! [SY178: $i,SY179: $i] :
            ( ( SY178 = SY179 )
            | ~ ( contains_slb @ SV10 @ SY179 )
            | ! [SY180: $i] :
                ( ( remove_slb @ ( insert_slb @ SV10 @ ( pair @ SY178 @ SY180 ) ) @ SY179 )
                = ( insert_slb @ ( remove_slb @ SV10 @ SY179 ) @ ( pair @ SY178 @ SY180 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(186,plain,
    ! [SV11: $i] :
      ( ( ! [SY181: $i,SY182: $i] :
            ( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SY181 @ SY182 ) ) @ SY181 )
            = SY182 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[137]) ).

thf(187,plain,
    ! [SV12: $i] :
      ( ( ! [SY183: $i,SY184: $i] :
            ( ( SY183 = SY184 )
            | ~ ( contains_slb @ SV12 @ SY184 )
            | ! [SY185: $i] :
                ( ( lookup_slb @ ( insert_slb @ SV12 @ ( pair @ SY183 @ SY185 ) ) @ SY184 )
                = ( lookup_slb @ SV12 @ SY184 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[138]) ).

thf(188,plain,
    ! [SV13: $i] :
      ( ( ( update_slb @ create_slb @ SV13 )
        = create_slb )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(189,plain,
    ! [SV14: $i] :
      ( ( ! [SY186: $i,SY187: $i,SY188: $i] :
            ( ~ ( strictly_less_than @ SY188 @ SY187 )
            | ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SY186 @ SY188 ) ) @ SY187 )
              = ( insert_slb @ ( update_slb @ SV14 @ SY187 ) @ ( pair @ SY186 @ SY187 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(190,plain,
    ! [SV15: $i] :
      ( ( ! [SY189: $i,SY190: $i,SY191: $i] :
            ( ~ ( less_than @ SY190 @ SY191 )
            | ( ( update_slb @ ( insert_slb @ SV15 @ ( pair @ SY189 @ SY191 ) ) @ SY190 )
              = ( insert_slb @ ( update_slb @ SV15 @ SY190 ) @ ( pair @ SY189 @ SY191 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(191,plain,
    ! [SV16: $i] :
      ( ( succ_cpq @ SV16 @ SV16 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[142]) ).

thf(192,plain,
    ! [SV17: $i] :
      ( ( ! [SY192: $i] :
            ( ~ ( succ_cpq @ SV17 @ SY192 )
            | ! [SY193: $i] : ( succ_cpq @ SV17 @ ( insert_cpq @ SY192 @ SY193 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(193,plain,
    ! [SV18: $i] :
      ( ( ! [SY194: $i] :
            ( ~ ( succ_cpq @ SV18 @ SY194 )
            | ! [SY195: $i] : ( succ_cpq @ SV18 @ ( remove_cpq @ SY194 @ SY195 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[144]) ).

thf(194,plain,
    ! [SV19: $i] :
      ( ( ! [SY196: $i] :
            ( ~ ( succ_cpq @ SV19 @ SY196 )
            | ( succ_cpq @ SV19 @ ( findmin_cpq_eff @ SY196 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[145]) ).

thf(195,plain,
    ! [SV20: $i] :
      ( ( ! [SY197: $i] :
            ( ~ ( succ_cpq @ SV20 @ SY197 )
            | ( succ_cpq @ SV20 @ ( removemin_cpq_eff @ SY197 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[146]) ).

thf(196,plain,
    ! [SV21: $i] :
      ( ( ! [SY198: $i] : ( check_cpq @ ( triple @ SV21 @ create_slb @ SY198 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[147]) ).

thf(197,plain,
    ! [SV22: $i] :
      ( ( ! [SY199: $i,SY200: $i,SY201: $i,SY202: $i] :
            ( ~ ( strictly_less_than @ SY201 @ SY202 )
            | ~ ( check_cpq @ ( triple @ SV22 @ ( insert_slb @ SY199 @ ( pair @ SY201 @ SY202 ) ) @ SY200 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[149]) ).

thf(198,plain,
    ! [SV23: $i] :
      ( ( ! [SY203: $i] :
            ~ ( ok @ ( triple @ SV23 @ SY203 @ bad ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[151]) ).

thf(199,plain,
    ! [SV24: $i] :
      ( ( ! [SY204: $i,SY205: $i] :
            ( ( ok @ ( triple @ SV24 @ SY204 @ SY205 ) )
            | ( SY205 = bad ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[152]) ).

thf(200,plain,
    ! [SV25: $i] :
      ( ( ! [SY206: $i,SY207: $i,SY208: $i] :
            ( ( insert_cpq @ ( triple @ SV25 @ SY206 @ SY207 ) @ SY208 )
            = ( triple @ ( insert_pqp @ SV25 @ SY208 ) @ ( insert_slb @ SY206 @ ( pair @ SY208 @ bottom ) ) @ SY207 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[153]) ).

thf(201,plain,
    ! [SV26: $i] :
      ( ( ! [SY209: $i,SY210: $i,SY211: $i] :
            ( ( contains_slb @ SY209 @ SY211 )
            | ( ( remove_cpq @ ( triple @ SV26 @ SY209 @ SY210 ) @ SY211 )
              = ( triple @ SV26 @ SY209 @ bad ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[154]) ).

thf(202,plain,
    ! [SV27: $i] :
      ( ( ! [SY212: $i,SY213: $i,SY214: $i] :
            ( ~ ( contains_slb @ SY212 @ SY214 )
            | ~ ( less_than @ ( lookup_slb @ SY212 @ SY214 ) @ SY214 )
            | ( ( remove_cpq @ ( triple @ SV27 @ SY212 @ SY213 ) @ SY214 )
              = ( triple @ ( remove_pqp @ SV27 @ SY214 ) @ ( remove_slb @ SY212 @ SY214 ) @ SY213 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[155]) ).

thf(203,plain,
    ! [SV28: $i] :
      ( ( ! [SY215: $i,SY216: $i,SY217: $i] :
            ( ~ ( contains_slb @ SY215 @ SY217 )
            | ~ ( strictly_less_than @ SY217 @ ( lookup_slb @ SY215 @ SY217 ) )
            | ( ( remove_cpq @ ( triple @ SV28 @ SY215 @ SY216 ) @ SY217 )
              = ( triple @ ( remove_pqp @ SV28 @ SY217 ) @ ( remove_slb @ SY215 @ SY217 ) @ bad ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[156]) ).

thf(204,plain,
    ! [SV29: $i] :
      ( ( ! [SY218: $i] :
            ( ( findmin_cpq_eff @ ( triple @ SV29 @ create_slb @ SY218 ) )
            = ( triple @ SV29 @ create_slb @ bad ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[157]) ).

thf(205,plain,
    ! [SV30: $i] :
      ( ( ! [SY219: $i] :
            ( ( SY219 = create_slb )
            | ( contains_slb @ SY219 @ ( findmin_pqp_res @ SV30 ) )
            | ! [SY220: $i] :
                ( ( findmin_cpq_eff @ ( triple @ SV30 @ SY219 @ SY220 ) )
                = ( triple @ SV30 @ ( update_slb @ SY219 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[158]) ).

thf(206,plain,
    ! [SV31: $i] :
      ( ( ! [SY221: $i] :
            ( ( SY221 = create_slb )
            | ~ ( contains_slb @ SY221 @ ( findmin_pqp_res @ SV31 ) )
            | ~ ( strictly_less_than @ ( findmin_pqp_res @ SV31 ) @ ( lookup_slb @ SY221 @ ( findmin_pqp_res @ SV31 ) ) )
            | ! [SY222: $i] :
                ( ( findmin_cpq_eff @ ( triple @ SV31 @ SY221 @ SY222 ) )
                = ( triple @ SV31 @ ( update_slb @ SY221 @ ( findmin_pqp_res @ SV31 ) ) @ bad ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[159]) ).

thf(207,plain,
    ! [SV32: $i] :
      ( ( ! [SY223: $i] :
            ( ( SY223 = create_slb )
            | ~ ( contains_slb @ SY223 @ ( findmin_pqp_res @ SV32 ) )
            | ~ ( less_than @ ( lookup_slb @ SY223 @ ( findmin_pqp_res @ SV32 ) ) @ ( findmin_pqp_res @ SV32 ) )
            | ! [SY224: $i] :
                ( ( findmin_cpq_eff @ ( triple @ SV32 @ SY223 @ SY224 ) )
                = ( triple @ SV32 @ ( update_slb @ SY223 @ ( findmin_pqp_res @ SV32 ) ) @ SY224 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[160]) ).

thf(208,plain,
    ! [SV33: $i] :
      ( ( ! [SY225: $i] :
            ( ( findmin_cpq_res @ ( triple @ SV33 @ create_slb @ SY225 ) )
            = bottom ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[161]) ).

thf(209,plain,
    ! [SV34: $i] :
      ( ( ! [SY226: $i] :
            ( ( SY226 = create_slb )
            | ! [SY227: $i] :
                ( ( findmin_cpq_res @ ( triple @ SV34 @ SY226 @ SY227 ) )
                = ( findmin_pqp_res @ SV34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[162]) ).

thf(210,plain,
    ! [SV35: $i] :
      ( ( ( removemin_cpq_eff @ SV35 )
        = ( remove_cpq @ ( findmin_cpq_eff @ SV35 ) @ ( findmin_cpq_res @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[163]) ).

thf(211,plain,
    ! [SV36: $i] :
      ( ( ( removemin_cpq_res @ SV36 )
        = ( findmin_cpq_res @ SV36 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(212,plain,
    ( ( ok @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[166]) ).

thf(213,plain,
    ( ( ~ ( sK13_REN
          | ! [SX0: $i,SX1: $i,SX2: $i] :
              ( ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
              | ! [SX3: $i,SX4: $i,SX5: $i] :
                  ( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
                  | ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
      | ~ ( ~ sK13_REN
          | ~ ( ~ ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
              | ~ ~ ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
                    | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[168]) ).

thf(214,plain,
    ! [SV37: $i] :
      ( ( ! [SY228: $i] :
            ~ ( ~ ! [SY229: $i] :
                    ( ! [SY230: $i] :
                        ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY228 @ SY230 ) ) @ SY229 )
                    | ( SY228 = SY229 )
                    | ( contains_slb @ SV37 @ SY229 ) )
              | ~ ~ ( ~ ! [SY231: $i] :
                          ( ( SY228 != SY231 )
                          | ! [SY232: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY228 @ SY232 ) ) @ SY231 ) )
                    | ~ ! [SY233: $i] :
                          ( ~ ( contains_slb @ SV37 @ SY233 )
                          | ! [SY234: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY228 @ SY234 ) ) @ SY233 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[169]) ).

thf(215,plain,
    ( ( ~ ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) )
      | ~ ( ok @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[170]) ).

thf(216,plain,
    ! [SV38: $i] :
      ( ( ! [SY235: $i,SY236: $i] :
            ~ ( ~ ~ ( ~ ! [SY237: $i,SY238: $i] :
                          ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SY235 @ SY237 ) ) @ SY236 @ SY238 )
                          | ( SY235 = SY236 )
                          | ( pair_in_list @ SV38 @ SY236 @ SY238 ) )
                    | ~ ! [SY239: $i,SY240: $i] :
                          ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SY235 @ SY239 ) ) @ SY236 @ SY240 )
                          | ( SY239 = SY240 )
                          | ( pair_in_list @ SV38 @ SY236 @ SY240 ) ) )
              | ~ ~ ( ~ ! [SY241: $i,SY242: $i] :
                          ( ( SY235 != SY236 )
                          | ( SY241 != SY242 )
                          | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SY235 @ SY241 ) ) @ SY236 @ SY242 ) )
                    | ~ ! [SY243: $i,SY244: $i] :
                          ( ~ ( pair_in_list @ SV38 @ SY236 @ SY244 )
                          | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SY235 @ SY243 ) ) @ SY236 @ SY244 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[171]) ).

thf(217,plain,
    ! [SV39: $i] :
      ( ( ! [SY245: $i,SY246: $i] :
            ~ ( ~ ! [SY247: $i,SY248: $i] :
                    ( ~ ( less_than @ SY248 @ SY247 )
                    | ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SY245 @ ( pair @ SY247 @ SY248 ) ) @ SY246 ) )
                    | ( check_cpq @ ( triple @ SV39 @ SY245 @ SY246 ) ) )
              | ~ ! [SY249: $i,SY250: $i] :
                    ( ~ ( less_than @ SY250 @ SY249 )
                    | ~ ( check_cpq @ ( triple @ SV39 @ SY245 @ SY246 ) )
                    | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SY245 @ ( pair @ SY249 @ SY250 ) ) @ SY246 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[172]) ).

thf(218,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less_than @ SX0 @ SX1 )
            | ( less_than @ SX1 @ SX0 )
            | ( strictly_less_than @ SX0 @ SX1 ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( strictly_less_than @ SX0 @ SX1 )
                  | ( less_than @ SX0 @ SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( strictly_less_than @ SX0 @ SX1 )
                  | ~ ( less_than @ SX1 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[173]) ).

thf(219,plain,
    ! [SV40: $i] :
      ( ( ! [SY251: $i] :
            ~ ( ~ ! [SY252: $i,SY253: $i] :
                    ( ~ ( contains_cpq @ ( triple @ SV40 @ SY251 @ SY252 ) @ SY253 )
                    | ( contains_slb @ SY251 @ SY253 ) )
              | ~ ! [SY254: $i,SY255: $i] :
                    ( ~ ( contains_slb @ SY251 @ SY255 )
                    | ( contains_cpq @ ( triple @ SV40 @ SY251 @ SY254 ) @ SY255 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[174]) ).

thf(220,plain,
    ! [SV41: $i,SV1: $i] :
      ( ( ! [SY256: $i] :
            ( ( ok @ ( triple @ SV1 @ SV41 @ SY256 ) )
            | ~ ( ok @ ( im_succ_cpq @ ( triple @ SV1 @ SV41 @ SY256 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[175]) ).

thf(221,plain,
    ! [SV42: $i,SV2: $i] :
      ( ( ! [SY257: $i] :
            ( ~ ( less_than @ SV2 @ SV42 )
            | ~ ( less_than @ SV42 @ SY257 )
            | ( less_than @ SV2 @ SY257 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[176]) ).

thf(222,plain,
    ! [SV43: $i,SV3: $i] :
      ( ( ( less_than @ SV3 @ SV43 )
        | ( less_than @ SV43 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[177]) ).

thf(223,plain,
    ! [SV44: $i,SV6: $i] :
      ( ( ! [SY258: $i] : ( isnonempty_slb @ ( insert_slb @ SV6 @ ( pair @ SV44 @ SY258 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[181]) ).

thf(224,plain,
    ! [SV7: $i] :
      ( ( contains_slb @ create_slb @ SV7 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[182]) ).

thf(225,plain,
    ! [SV45: $i,SV8: $i] :
      ( ( ~ ( pair_in_list @ create_slb @ SV8 @ SV45 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[183]) ).

thf(226,plain,
    ! [SV46: $i,SV9: $i] :
      ( ( ! [SY259: $i] :
            ( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV46 @ SY259 ) ) @ SV46 )
            = SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[184]) ).

thf(227,plain,
    ! [SV10: $i,SV47: $i] :
      ( ( ! [SY260: $i] :
            ( ( SV47 = SY260 )
            | ~ ( contains_slb @ SV10 @ SY260 )
            | ! [SY261: $i] :
                ( ( remove_slb @ ( insert_slb @ SV10 @ ( pair @ SV47 @ SY261 ) ) @ SY260 )
                = ( insert_slb @ ( remove_slb @ SV10 @ SY260 ) @ ( pair @ SV47 @ SY261 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[185]) ).

thf(228,plain,
    ! [SV48: $i,SV11: $i] :
      ( ( ! [SY262: $i] :
            ( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV48 @ SY262 ) ) @ SV48 )
            = SY262 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[186]) ).

thf(229,plain,
    ! [SV12: $i,SV49: $i] :
      ( ( ! [SY263: $i] :
            ( ( SV49 = SY263 )
            | ~ ( contains_slb @ SV12 @ SY263 )
            | ! [SY264: $i] :
                ( ( lookup_slb @ ( insert_slb @ SV12 @ ( pair @ SV49 @ SY264 ) ) @ SY263 )
                = ( lookup_slb @ SV12 @ SY263 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[187]) ).

thf(230,plain,
    ! [SV50: $i,SV14: $i] :
      ( ( ! [SY265: $i,SY266: $i] :
            ( ~ ( strictly_less_than @ SY266 @ SY265 )
            | ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SY266 ) ) @ SY265 )
              = ( insert_slb @ ( update_slb @ SV14 @ SY265 ) @ ( pair @ SV50 @ SY265 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[189]) ).

thf(231,plain,
    ! [SV51: $i,SV15: $i] :
      ( ( ! [SY267: $i,SY268: $i] :
            ( ~ ( less_than @ SY267 @ SY268 )
            | ( ( update_slb @ ( insert_slb @ SV15 @ ( pair @ SV51 @ SY268 ) ) @ SY267 )
              = ( insert_slb @ ( update_slb @ SV15 @ SY267 ) @ ( pair @ SV51 @ SY268 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[190]) ).

thf(232,plain,
    ! [SV52: $i,SV17: $i] :
      ( ( ~ ( succ_cpq @ SV17 @ SV52 )
        | ! [SY269: $i] : ( succ_cpq @ SV17 @ ( insert_cpq @ SV52 @ SY269 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[192]) ).

thf(233,plain,
    ! [SV53: $i,SV18: $i] :
      ( ( ~ ( succ_cpq @ SV18 @ SV53 )
        | ! [SY270: $i] : ( succ_cpq @ SV18 @ ( remove_cpq @ SV53 @ SY270 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[193]) ).

thf(234,plain,
    ! [SV54: $i,SV19: $i] :
      ( ( ~ ( succ_cpq @ SV19 @ SV54 )
        | ( succ_cpq @ SV19 @ ( findmin_cpq_eff @ SV54 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[194]) ).

thf(235,plain,
    ! [SV55: $i,SV20: $i] :
      ( ( ~ ( succ_cpq @ SV20 @ SV55 )
        | ( succ_cpq @ SV20 @ ( removemin_cpq_eff @ SV55 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[195]) ).

thf(236,plain,
    ! [SV56: $i,SV21: $i] :
      ( ( check_cpq @ ( triple @ SV21 @ create_slb @ SV56 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[196]) ).

thf(237,plain,
    ! [SV57: $i,SV22: $i] :
      ( ( ! [SY271: $i,SY272: $i,SY273: $i] :
            ( ~ ( strictly_less_than @ SY272 @ SY273 )
            | ~ ( check_cpq @ ( triple @ SV22 @ ( insert_slb @ SV57 @ ( pair @ SY272 @ SY273 ) ) @ SY271 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[197]) ).

thf(238,plain,
    ! [SV58: $i,SV23: $i] :
      ( ( ~ ( ok @ ( triple @ SV23 @ SV58 @ bad ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[198]) ).

thf(239,plain,
    ! [SV59: $i,SV24: $i] :
      ( ( ! [SY274: $i] :
            ( ( ok @ ( triple @ SV24 @ SV59 @ SY274 ) )
            | ( SY274 = bad ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[199]) ).

thf(240,plain,
    ! [SV60: $i,SV25: $i] :
      ( ( ! [SY275: $i,SY276: $i] :
            ( ( insert_cpq @ ( triple @ SV25 @ SV60 @ SY275 ) @ SY276 )
            = ( triple @ ( insert_pqp @ SV25 @ SY276 ) @ ( insert_slb @ SV60 @ ( pair @ SY276 @ bottom ) ) @ SY275 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[200]) ).

thf(241,plain,
    ! [SV26: $i,SV61: $i] :
      ( ( ! [SY277: $i,SY278: $i] :
            ( ( contains_slb @ SV61 @ SY278 )
            | ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SY277 ) @ SY278 )
              = ( triple @ SV26 @ SV61 @ bad ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[201]) ).

thf(242,plain,
    ! [SV27: $i,SV62: $i] :
      ( ( ! [SY279: $i,SY280: $i] :
            ( ~ ( contains_slb @ SV62 @ SY280 )
            | ~ ( less_than @ ( lookup_slb @ SV62 @ SY280 ) @ SY280 )
            | ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SY279 ) @ SY280 )
              = ( triple @ ( remove_pqp @ SV27 @ SY280 ) @ ( remove_slb @ SV62 @ SY280 ) @ SY279 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[202]) ).

thf(243,plain,
    ! [SV28: $i,SV63: $i] :
      ( ( ! [SY281: $i,SY282: $i] :
            ( ~ ( contains_slb @ SV63 @ SY282 )
            | ~ ( strictly_less_than @ SY282 @ ( lookup_slb @ SV63 @ SY282 ) )
            | ( ( remove_cpq @ ( triple @ SV28 @ SV63 @ SY281 ) @ SY282 )
              = ( triple @ ( remove_pqp @ SV28 @ SY282 ) @ ( remove_slb @ SV63 @ SY282 ) @ bad ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[203]) ).

thf(244,plain,
    ! [SV64: $i,SV29: $i] :
      ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ create_slb @ SV64 ) )
        = ( triple @ SV29 @ create_slb @ bad ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[204]) ).

thf(245,plain,
    ! [SV30: $i,SV65: $i] :
      ( ( ( SV65 = create_slb )
        | ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) )
        | ! [SY283: $i] :
            ( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SY283 ) )
            = ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[205]) ).

thf(246,plain,
    ! [SV31: $i,SV66: $i] :
      ( ( ( SV66 = create_slb )
        | ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
        | ~ ( strictly_less_than @ ( findmin_pqp_res @ SV31 ) @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) )
        | ! [SY284: $i] :
            ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY284 ) )
            = ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ bad ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[206]) ).

thf(247,plain,
    ! [SV32: $i,SV67: $i] :
      ( ( ( SV67 = create_slb )
        | ~ ( contains_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) )
        | ~ ( less_than @ ( lookup_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ ( findmin_pqp_res @ SV32 ) )
        | ! [SY285: $i] :
            ( ( findmin_cpq_eff @ ( triple @ SV32 @ SV67 @ SY285 ) )
            = ( triple @ SV32 @ ( update_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ SY285 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[207]) ).

thf(248,plain,
    ! [SV68: $i,SV33: $i] :
      ( ( ( findmin_cpq_res @ ( triple @ SV33 @ create_slb @ SV68 ) )
        = bottom )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[208]) ).

thf(249,plain,
    ! [SV34: $i,SV69: $i] :
      ( ( ( SV69 = create_slb )
        | ! [SY286: $i] :
            ( ( findmin_cpq_res @ ( triple @ SV34 @ SV69 @ SY286 ) )
            = ( findmin_pqp_res @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[209]) ).

thf(250,plain,
    ( ( ~ ( sK13_REN
          | ! [SX0: $i,SX1: $i,SX2: $i] :
              ( ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
              | ! [SX3: $i,SX4: $i,SX5: $i] :
                  ( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
                  | ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[213]) ).

thf(251,plain,
    ( ( ~ ( ~ sK13_REN
          | ~ ( ~ ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
              | ~ ~ ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
                    | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[213]) ).

thf(252,plain,
    ! [SV70: $i,SV37: $i] :
      ( ( ~ ( ~ ! [SY287: $i] :
                  ( ! [SY288: $i] :
                      ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY288 ) ) @ SY287 )
                  | ( SV70 = SY287 )
                  | ( contains_slb @ SV37 @ SY287 ) )
            | ~ ~ ( ~ ! [SY289: $i] :
                        ( ( SV70 != SY289 )
                        | ! [SY290: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY290 ) ) @ SY289 ) )
                  | ~ ! [SY291: $i] :
                        ( ~ ( contains_slb @ SV37 @ SY291 )
                        | ! [SY292: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY292 ) ) @ SY291 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[214]) ).

thf(253,plain,
    ( ( ~ ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[215]) ).

thf(254,plain,
    ( ( ~ ( ok @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[215]) ).

thf(255,plain,
    ! [SV71: $i,SV38: $i] :
      ( ( ! [SY293: $i] :
            ~ ( ~ ~ ( ~ ! [SY294: $i,SY295: $i] :
                          ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY294 ) ) @ SY293 @ SY295 )
                          | ( SV71 = SY293 )
                          | ( pair_in_list @ SV38 @ SY293 @ SY295 ) )
                    | ~ ! [SY296: $i,SY297: $i] :
                          ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY296 ) ) @ SY293 @ SY297 )
                          | ( SY296 = SY297 )
                          | ( pair_in_list @ SV38 @ SY293 @ SY297 ) ) )
              | ~ ~ ( ~ ! [SY298: $i,SY299: $i] :
                          ( ( SV71 != SY293 )
                          | ( SY298 != SY299 )
                          | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY298 ) ) @ SY293 @ SY299 ) )
                    | ~ ! [SY300: $i,SY301: $i] :
                          ( ~ ( pair_in_list @ SV38 @ SY293 @ SY301 )
                          | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY300 ) ) @ SY293 @ SY301 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[216]) ).

thf(256,plain,
    ! [SV72: $i,SV39: $i] :
      ( ( ! [SY302: $i] :
            ~ ( ~ ! [SY303: $i,SY304: $i] :
                    ( ~ ( less_than @ SY304 @ SY303 )
                    | ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY303 @ SY304 ) ) @ SY302 ) )
                    | ( check_cpq @ ( triple @ SV39 @ SV72 @ SY302 ) ) )
              | ~ ! [SY305: $i,SY306: $i] :
                    ( ~ ( less_than @ SY306 @ SY305 )
                    | ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SY302 ) )
                    | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY305 @ SY306 ) ) @ SY302 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[217]) ).

thf(257,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less_than @ SX0 @ SX1 )
            | ( less_than @ SX1 @ SX0 )
            | ( strictly_less_than @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[218]) ).

thf(258,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( strictly_less_than @ SX0 @ SX1 )
                  | ( less_than @ SX0 @ SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( strictly_less_than @ SX0 @ SX1 )
                  | ~ ( less_than @ SX1 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[218]) ).

thf(259,plain,
    ! [SV73: $i,SV40: $i] :
      ( ( ~ ( ~ ! [SY307: $i,SY308: $i] :
                  ( ~ ( contains_cpq @ ( triple @ SV40 @ SV73 @ SY307 ) @ SY308 )
                  | ( contains_slb @ SV73 @ SY308 ) )
            | ~ ! [SY309: $i,SY310: $i] :
                  ( ~ ( contains_slb @ SV73 @ SY310 )
                  | ( contains_cpq @ ( triple @ SV40 @ SV73 @ SY309 ) @ SY310 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[219]) ).

thf(260,plain,
    ! [SV74: $i,SV41: $i,SV1: $i] :
      ( ( ( ok @ ( triple @ SV1 @ SV41 @ SV74 ) )
        | ~ ( ok @ ( im_succ_cpq @ ( triple @ SV1 @ SV41 @ SV74 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[220]) ).

thf(261,plain,
    ! [SV75: $i,SV42: $i,SV2: $i] :
      ( ( ~ ( less_than @ SV2 @ SV42 )
        | ~ ( less_than @ SV42 @ SV75 )
        | ( less_than @ SV2 @ SV75 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[221]) ).

thf(262,plain,
    ! [SV43: $i,SV3: $i] :
      ( ( ( less_than @ SV3 @ SV43 )
        = $true )
      | ( ( less_than @ SV43 @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[222]) ).

thf(263,plain,
    ! [SV76: $i,SV44: $i,SV6: $i] :
      ( ( isnonempty_slb @ ( insert_slb @ SV6 @ ( pair @ SV44 @ SV76 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[223]) ).

thf(264,plain,
    ! [SV45: $i,SV8: $i] :
      ( ( pair_in_list @ create_slb @ SV8 @ SV45 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[225]) ).

thf(265,plain,
    ! [SV77: $i,SV46: $i,SV9: $i] :
      ( ( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV46 @ SV77 ) ) @ SV46 )
        = SV9 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[226]) ).

thf(266,plain,
    ! [SV10: $i,SV78: $i,SV47: $i] :
      ( ( ( SV47 = SV78 )
        | ~ ( contains_slb @ SV10 @ SV78 )
        | ! [SY311: $i] :
            ( ( remove_slb @ ( insert_slb @ SV10 @ ( pair @ SV47 @ SY311 ) ) @ SV78 )
            = ( insert_slb @ ( remove_slb @ SV10 @ SV78 ) @ ( pair @ SV47 @ SY311 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[227]) ).

thf(267,plain,
    ! [SV79: $i,SV48: $i,SV11: $i] :
      ( ( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV48 @ SV79 ) ) @ SV48 )
        = SV79 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[228]) ).

thf(268,plain,
    ! [SV12: $i,SV80: $i,SV49: $i] :
      ( ( ( SV49 = SV80 )
        | ~ ( contains_slb @ SV12 @ SV80 )
        | ! [SY312: $i] :
            ( ( lookup_slb @ ( insert_slb @ SV12 @ ( pair @ SV49 @ SY312 ) ) @ SV80 )
            = ( lookup_slb @ SV12 @ SV80 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[229]) ).

thf(269,plain,
    ! [SV50: $i,SV14: $i,SV81: $i] :
      ( ( ! [SY313: $i] :
            ( ~ ( strictly_less_than @ SY313 @ SV81 )
            | ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SY313 ) ) @ SV81 )
              = ( insert_slb @ ( update_slb @ SV14 @ SV81 ) @ ( pair @ SV50 @ SV81 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[230]) ).

thf(270,plain,
    ! [SV51: $i,SV15: $i,SV82: $i] :
      ( ( ! [SY314: $i] :
            ( ~ ( less_than @ SV82 @ SY314 )
            | ( ( update_slb @ ( insert_slb @ SV15 @ ( pair @ SV51 @ SY314 ) ) @ SV82 )
              = ( insert_slb @ ( update_slb @ SV15 @ SV82 ) @ ( pair @ SV51 @ SY314 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[231]) ).

thf(271,plain,
    ! [SV52: $i,SV17: $i] :
      ( ( ( ~ ( succ_cpq @ SV17 @ SV52 ) )
        = $true )
      | ( ( ! [SY269: $i] : ( succ_cpq @ SV17 @ ( insert_cpq @ SV52 @ SY269 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[232]) ).

thf(272,plain,
    ! [SV53: $i,SV18: $i] :
      ( ( ( ~ ( succ_cpq @ SV18 @ SV53 ) )
        = $true )
      | ( ( ! [SY270: $i] : ( succ_cpq @ SV18 @ ( remove_cpq @ SV53 @ SY270 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[233]) ).

thf(273,plain,
    ! [SV54: $i,SV19: $i] :
      ( ( ( ~ ( succ_cpq @ SV19 @ SV54 ) )
        = $true )
      | ( ( succ_cpq @ SV19 @ ( findmin_cpq_eff @ SV54 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[234]) ).

thf(274,plain,
    ! [SV55: $i,SV20: $i] :
      ( ( ( ~ ( succ_cpq @ SV20 @ SV55 ) )
        = $true )
      | ( ( succ_cpq @ SV20 @ ( removemin_cpq_eff @ SV55 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[235]) ).

thf(275,plain,
    ! [SV83: $i,SV57: $i,SV22: $i] :
      ( ( ! [SY315: $i,SY316: $i] :
            ( ~ ( strictly_less_than @ SY315 @ SY316 )
            | ~ ( check_cpq @ ( triple @ SV22 @ ( insert_slb @ SV57 @ ( pair @ SY315 @ SY316 ) ) @ SV83 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[237]) ).

thf(276,plain,
    ! [SV58: $i,SV23: $i] :
      ( ( ok @ ( triple @ SV23 @ SV58 @ bad ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[238]) ).

thf(277,plain,
    ! [SV84: $i,SV59: $i,SV24: $i] :
      ( ( ( ok @ ( triple @ SV24 @ SV59 @ SV84 ) )
        | ( SV84 = bad ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[239]) ).

thf(278,plain,
    ! [SV85: $i,SV60: $i,SV25: $i] :
      ( ( ! [SY317: $i] :
            ( ( insert_cpq @ ( triple @ SV25 @ SV60 @ SV85 ) @ SY317 )
            = ( triple @ ( insert_pqp @ SV25 @ SY317 ) @ ( insert_slb @ SV60 @ ( pair @ SY317 @ bottom ) ) @ SV85 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[240]) ).

thf(279,plain,
    ! [SV86: $i,SV26: $i,SV61: $i] :
      ( ( ! [SY318: $i] :
            ( ( contains_slb @ SV61 @ SY318 )
            | ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SV86 ) @ SY318 )
              = ( triple @ SV26 @ SV61 @ bad ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[241]) ).

thf(280,plain,
    ! [SV87: $i,SV27: $i,SV62: $i] :
      ( ( ! [SY319: $i] :
            ( ~ ( contains_slb @ SV62 @ SY319 )
            | ~ ( less_than @ ( lookup_slb @ SV62 @ SY319 ) @ SY319 )
            | ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV87 ) @ SY319 )
              = ( triple @ ( remove_pqp @ SV27 @ SY319 ) @ ( remove_slb @ SV62 @ SY319 ) @ SV87 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[242]) ).

thf(281,plain,
    ! [SV88: $i,SV28: $i,SV63: $i] :
      ( ( ! [SY320: $i] :
            ( ~ ( contains_slb @ SV63 @ SY320 )
            | ~ ( strictly_less_than @ SY320 @ ( lookup_slb @ SV63 @ SY320 ) )
            | ( ( remove_cpq @ ( triple @ SV28 @ SV63 @ SV88 ) @ SY320 )
              = ( triple @ ( remove_pqp @ SV28 @ SY320 ) @ ( remove_slb @ SV63 @ SY320 ) @ bad ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[243]) ).

thf(282,plain,
    ! [SV30: $i,SV65: $i] :
      ( ( ( ( SV65 = create_slb )
          | ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) )
        = $true )
      | ( ( ! [SY283: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SY283 ) )
              = ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[245]) ).

thf(283,plain,
    ! [SV31: $i,SV66: $i] :
      ( ( ( ( SV66 = create_slb )
          | ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
          | ~ ( strictly_less_than @ ( findmin_pqp_res @ SV31 ) @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) ) )
        = $true )
      | ( ( ! [SY284: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY284 ) )
              = ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ bad ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[246]) ).

thf(284,plain,
    ! [SV32: $i,SV67: $i] :
      ( ( ( ( SV67 = create_slb )
          | ~ ( contains_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) )
          | ~ ( less_than @ ( lookup_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ ( findmin_pqp_res @ SV32 ) ) )
        = $true )
      | ( ( ! [SY285: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV32 @ SV67 @ SY285 ) )
              = ( triple @ SV32 @ ( update_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ SY285 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[247]) ).

thf(285,plain,
    ! [SV34: $i,SV69: $i] :
      ( ( ( SV69 = create_slb )
        = $true )
      | ( ( ! [SY286: $i] :
              ( ( findmin_cpq_res @ ( triple @ SV34 @ SV69 @ SY286 ) )
              = ( findmin_pqp_res @ SV34 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[249]) ).

thf(286,plain,
    ( ( sK13_REN
      | ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
          | ! [SX3: $i,SX4: $i,SX5: $i] :
              ( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
              | ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[250]) ).

thf(287,plain,
    ( ( ~ sK13_REN
      | ~ ( ~ ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
          | ~ ~ ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
                | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[251]) ).

thf(288,plain,
    ! [SV70: $i,SV37: $i] :
      ( ( ~ ! [SY287: $i] :
              ( ! [SY288: $i] :
                  ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY288 ) ) @ SY287 )
              | ( SV70 = SY287 )
              | ( contains_slb @ SV37 @ SY287 ) )
        | ~ ~ ( ~ ! [SY289: $i] :
                    ( ( SV70 != SY289 )
                    | ! [SY290: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY290 ) ) @ SY289 ) )
              | ~ ! [SY291: $i] :
                    ( ~ ( contains_slb @ SV37 @ SY291 )
                    | ! [SY292: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY292 ) ) @ SY291 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[252]) ).

thf(289,plain,
    ( ( succ_cpq @ ( triple @ sK1_U @ sK2_SY138 @ sK3_SY143 ) @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[253]) ).

thf(290,plain,
    ( ( ok @ ( triple @ sK4_SY147 @ sK5_SY150 @ sK6_SY152 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[254]) ).

thf(291,plain,
    ! [SV89: $i,SV71: $i,SV38: $i] :
      ( ( ~ ( ~ ~ ( ~ ! [SY321: $i,SY322: $i] :
                        ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY321 ) ) @ SV89 @ SY322 )
                        | ( SV71 = SV89 )
                        | ( pair_in_list @ SV38 @ SV89 @ SY322 ) )
                  | ~ ! [SY323: $i,SY324: $i] :
                        ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY323 ) ) @ SV89 @ SY324 )
                        | ( SY323 = SY324 )
                        | ( pair_in_list @ SV38 @ SV89 @ SY324 ) ) )
            | ~ ~ ( ~ ! [SY325: $i,SY326: $i] :
                        ( ( SV71 != SV89 )
                        | ( SY325 != SY326 )
                        | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY325 ) ) @ SV89 @ SY326 ) )
                  | ~ ! [SY327: $i,SY328: $i] :
                        ( ~ ( pair_in_list @ SV38 @ SV89 @ SY328 )
                        | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY327 ) ) @ SV89 @ SY328 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[255]) ).

thf(292,plain,
    ! [SV90: $i,SV72: $i,SV39: $i] :
      ( ( ~ ( ~ ! [SY329: $i,SY330: $i] :
                  ( ~ ( less_than @ SY330 @ SY329 )
                  | ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY329 @ SY330 ) ) @ SV90 ) )
                  | ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) ) )
            | ~ ! [SY331: $i,SY332: $i] :
                  ( ~ ( less_than @ SY332 @ SY331 )
                  | ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
                  | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY331 @ SY332 ) ) @ SV90 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[256]) ).

thf(293,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( less_than @ SX0 @ SX1 )
          | ( less_than @ SX1 @ SX0 )
          | ( strictly_less_than @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[257]) ).

thf(294,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( strictly_less_than @ SX0 @ SX1 )
                | ( less_than @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( strictly_less_than @ SX0 @ SX1 )
                | ~ ( less_than @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[258]) ).

thf(295,plain,
    ! [SV73: $i,SV40: $i] :
      ( ( ~ ! [SY307: $i,SY308: $i] :
              ( ~ ( contains_cpq @ ( triple @ SV40 @ SV73 @ SY307 ) @ SY308 )
              | ( contains_slb @ SV73 @ SY308 ) )
        | ~ ! [SY309: $i,SY310: $i] :
              ( ~ ( contains_slb @ SV73 @ SY310 )
              | ( contains_cpq @ ( triple @ SV40 @ SV73 @ SY309 ) @ SY310 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[259]) ).

thf(296,plain,
    ! [SV74: $i,SV41: $i,SV1: $i] :
      ( ( ( ok @ ( triple @ SV1 @ SV41 @ SV74 ) )
        = $true )
      | ( ( ~ ( ok @ ( im_succ_cpq @ ( triple @ SV1 @ SV41 @ SV74 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[260]) ).

thf(297,plain,
    ! [SV75: $i,SV42: $i,SV2: $i] :
      ( ( ( ~ ( less_than @ SV2 @ SV42 )
          | ~ ( less_than @ SV42 @ SV75 ) )
        = $true )
      | ( ( less_than @ SV2 @ SV75 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[261]) ).

thf(298,plain,
    ! [SV10: $i,SV78: $i,SV47: $i] :
      ( ( ( ( SV47 = SV78 )
          | ~ ( contains_slb @ SV10 @ SV78 ) )
        = $true )
      | ( ( ! [SY311: $i] :
              ( ( remove_slb @ ( insert_slb @ SV10 @ ( pair @ SV47 @ SY311 ) ) @ SV78 )
              = ( insert_slb @ ( remove_slb @ SV10 @ SV78 ) @ ( pair @ SV47 @ SY311 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[266]) ).

thf(299,plain,
    ! [SV12: $i,SV80: $i,SV49: $i] :
      ( ( ( ( SV49 = SV80 )
          | ~ ( contains_slb @ SV12 @ SV80 ) )
        = $true )
      | ( ( ! [SY312: $i] :
              ( ( lookup_slb @ ( insert_slb @ SV12 @ ( pair @ SV49 @ SY312 ) ) @ SV80 )
              = ( lookup_slb @ SV12 @ SV80 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[268]) ).

thf(300,plain,
    ! [SV50: $i,SV14: $i,SV81: $i,SV91: $i] :
      ( ( ~ ( strictly_less_than @ SV91 @ SV81 )
        | ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SV91 ) ) @ SV81 )
          = ( insert_slb @ ( update_slb @ SV14 @ SV81 ) @ ( pair @ SV50 @ SV81 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[269]) ).

thf(301,plain,
    ! [SV51: $i,SV15: $i,SV92: $i,SV82: $i] :
      ( ( ~ ( less_than @ SV82 @ SV92 )
        | ( ( update_slb @ ( insert_slb @ SV15 @ ( pair @ SV51 @ SV92 ) ) @ SV82 )
          = ( insert_slb @ ( update_slb @ SV15 @ SV82 ) @ ( pair @ SV51 @ SV92 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[270]) ).

thf(302,plain,
    ! [SV52: $i,SV17: $i] :
      ( ( ( succ_cpq @ SV17 @ SV52 )
        = $false )
      | ( ( ! [SY269: $i] : ( succ_cpq @ SV17 @ ( insert_cpq @ SV52 @ SY269 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[271]) ).

thf(303,plain,
    ! [SV53: $i,SV18: $i] :
      ( ( ( succ_cpq @ SV18 @ SV53 )
        = $false )
      | ( ( ! [SY270: $i] : ( succ_cpq @ SV18 @ ( remove_cpq @ SV53 @ SY270 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[272]) ).

thf(304,plain,
    ! [SV54: $i,SV19: $i] :
      ( ( ( succ_cpq @ SV19 @ SV54 )
        = $false )
      | ( ( succ_cpq @ SV19 @ ( findmin_cpq_eff @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[273]) ).

thf(305,plain,
    ! [SV55: $i,SV20: $i] :
      ( ( ( succ_cpq @ SV20 @ SV55 )
        = $false )
      | ( ( succ_cpq @ SV20 @ ( removemin_cpq_eff @ SV55 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[274]) ).

thf(306,plain,
    ! [SV83: $i,SV57: $i,SV22: $i,SV93: $i] :
      ( ( ! [SY333: $i] :
            ( ~ ( strictly_less_than @ SV93 @ SY333 )
            | ~ ( check_cpq @ ( triple @ SV22 @ ( insert_slb @ SV57 @ ( pair @ SV93 @ SY333 ) ) @ SV83 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[275]) ).

thf(307,plain,
    ! [SV84: $i,SV59: $i,SV24: $i] :
      ( ( ( ok @ ( triple @ SV24 @ SV59 @ SV84 ) )
        = $true )
      | ( ( SV84 = bad )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[277]) ).

thf(308,plain,
    ! [SV94: $i,SV85: $i,SV60: $i,SV25: $i] :
      ( ( ( insert_cpq @ ( triple @ SV25 @ SV60 @ SV85 ) @ SV94 )
        = ( triple @ ( insert_pqp @ SV25 @ SV94 ) @ ( insert_slb @ SV60 @ ( pair @ SV94 @ bottom ) ) @ SV85 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[278]) ).

thf(309,plain,
    ! [SV86: $i,SV26: $i,SV95: $i,SV61: $i] :
      ( ( ( contains_slb @ SV61 @ SV95 )
        | ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SV86 ) @ SV95 )
          = ( triple @ SV26 @ SV61 @ bad ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[279]) ).

thf(310,plain,
    ! [SV87: $i,SV27: $i,SV96: $i,SV62: $i] :
      ( ( ~ ( contains_slb @ SV62 @ SV96 )
        | ~ ( less_than @ ( lookup_slb @ SV62 @ SV96 ) @ SV96 )
        | ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV87 ) @ SV96 )
          = ( triple @ ( remove_pqp @ SV27 @ SV96 ) @ ( remove_slb @ SV62 @ SV96 ) @ SV87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[280]) ).

thf(311,plain,
    ! [SV88: $i,SV28: $i,SV97: $i,SV63: $i] :
      ( ( ~ ( contains_slb @ SV63 @ SV97 )
        | ~ ( strictly_less_than @ SV97 @ ( lookup_slb @ SV63 @ SV97 ) )
        | ( ( remove_cpq @ ( triple @ SV28 @ SV63 @ SV88 ) @ SV97 )
          = ( triple @ ( remove_pqp @ SV28 @ SV97 ) @ ( remove_slb @ SV63 @ SV97 ) @ bad ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[281]) ).

thf(312,plain,
    ! [SV30: $i,SV65: $i] :
      ( ( ( SV65 = create_slb )
        = $true )
      | ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) )
        = $true )
      | ( ( ! [SY283: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SY283 ) )
              = ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[282]) ).

thf(313,plain,
    ! [SV31: $i,SV66: $i] :
      ( ( ( ( SV66 = create_slb )
          | ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) )
        = $true )
      | ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV31 ) @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) ) )
        = $true )
      | ( ( ! [SY284: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY284 ) )
              = ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ bad ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[283]) ).

thf(314,plain,
    ! [SV32: $i,SV67: $i] :
      ( ( ( ( SV67 = create_slb )
          | ~ ( contains_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) )
        = $true )
      | ( ( ~ ( less_than @ ( lookup_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ ( findmin_pqp_res @ SV32 ) ) )
        = $true )
      | ( ( ! [SY285: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV32 @ SV67 @ SY285 ) )
              = ( triple @ SV32 @ ( update_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ SY285 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[284]) ).

thf(315,plain,
    ! [SV98: $i,SV69: $i,SV34: $i] :
      ( ( ( ( findmin_cpq_res @ ( triple @ SV34 @ SV69 @ SV98 ) )
          = ( findmin_pqp_res @ SV34 ) )
        = $true )
      | ( ( SV69 = create_slb )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[285]) ).

thf(316,plain,
    ( ( sK13_REN = $true )
    | ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
            ( ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
            | ! [SX3: $i,SX4: $i,SX5: $i] :
                ( ~ ( succ_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ ( triple @ SX3 @ SX4 @ SX5 ) )
                | ~ ( ok @ ( triple @ SX3 @ SX4 @ SX5 ) ) ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[286]) ).

thf(317,plain,
    ( ( ( ~ sK13_REN )
      = $true )
    | ( ( ~ ( ~ ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
            | ~ ~ ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
                  | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[287]) ).

thf(318,plain,
    ! [SV70: $i,SV37: $i] :
      ( ( ~ ! [SY287: $i] :
              ( ! [SY288: $i] :
                  ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY288 ) ) @ SY287 )
              | ( SV70 = SY287 )
              | ( contains_slb @ SV37 @ SY287 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[288]) ).

thf(319,plain,
    ! [SV37: $i,SV70: $i] :
      ( ( ~ ~ ( ~ ! [SY289: $i] :
                    ( ( SV70 != SY289 )
                    | ! [SY290: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY290 ) ) @ SY289 ) )
              | ~ ! [SY291: $i] :
                    ( ~ ( contains_slb @ SV37 @ SY291 )
                    | ! [SY292: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY292 ) ) @ SY291 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[288]) ).

thf(320,plain,
    ! [SV89: $i,SV71: $i,SV38: $i] :
      ( ( ~ ~ ( ~ ! [SY321: $i,SY322: $i] :
                    ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY321 ) ) @ SV89 @ SY322 )
                    | ( SV71 = SV89 )
                    | ( pair_in_list @ SV38 @ SV89 @ SY322 ) )
              | ~ ! [SY323: $i,SY324: $i] :
                    ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY323 ) ) @ SV89 @ SY324 )
                    | ( SY323 = SY324 )
                    | ( pair_in_list @ SV38 @ SV89 @ SY324 ) ) )
        | ~ ~ ( ~ ! [SY325: $i,SY326: $i] :
                    ( ( SV71 != SV89 )
                    | ( SY325 != SY326 )
                    | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY325 ) ) @ SV89 @ SY326 ) )
              | ~ ! [SY327: $i,SY328: $i] :
                    ( ~ ( pair_in_list @ SV38 @ SV89 @ SY328 )
                    | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY327 ) ) @ SV89 @ SY328 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[291]) ).

thf(321,plain,
    ! [SV90: $i,SV72: $i,SV39: $i] :
      ( ( ~ ! [SY329: $i,SY330: $i] :
              ( ~ ( less_than @ SY330 @ SY329 )
              | ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY329 @ SY330 ) ) @ SV90 ) )
              | ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) ) )
        | ~ ! [SY331: $i,SY332: $i] :
              ( ~ ( less_than @ SY332 @ SY331 )
              | ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
              | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY331 @ SY332 ) ) @ SV90 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[292]) ).

thf(322,plain,
    ! [SV99: $i] :
      ( ( ! [SY334: $i] :
            ( ~ ( less_than @ SV99 @ SY334 )
            | ( less_than @ SY334 @ SV99 )
            | ( strictly_less_than @ SV99 @ SY334 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[293]) ).

thf(323,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( strictly_less_than @ SX0 @ SX1 )
            | ( less_than @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( strictly_less_than @ SX0 @ SX1 )
            | ~ ( less_than @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[294]) ).

thf(324,plain,
    ! [SV73: $i,SV40: $i] :
      ( ( ~ ! [SY307: $i,SY308: $i] :
              ( ~ ( contains_cpq @ ( triple @ SV40 @ SV73 @ SY307 ) @ SY308 )
              | ( contains_slb @ SV73 @ SY308 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[295]) ).

thf(325,plain,
    ! [SV40: $i,SV73: $i] :
      ( ( ~ ! [SY309: $i,SY310: $i] :
              ( ~ ( contains_slb @ SV73 @ SY310 )
              | ( contains_cpq @ ( triple @ SV40 @ SV73 @ SY309 ) @ SY310 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[295]) ).

thf(326,plain,
    ! [SV74: $i,SV41: $i,SV1: $i] :
      ( ( ( ok @ ( im_succ_cpq @ ( triple @ SV1 @ SV41 @ SV74 ) ) )
        = $false )
      | ( ( ok @ ( triple @ SV1 @ SV41 @ SV74 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[296]) ).

thf(327,plain,
    ! [SV75: $i,SV42: $i,SV2: $i] :
      ( ( ( ~ ( less_than @ SV2 @ SV42 ) )
        = $true )
      | ( ( ~ ( less_than @ SV42 @ SV75 ) )
        = $true )
      | ( ( less_than @ SV2 @ SV75 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[297]) ).

thf(328,plain,
    ! [SV10: $i,SV78: $i,SV47: $i] :
      ( ( ( SV47 = SV78 )
        = $true )
      | ( ( ~ ( contains_slb @ SV10 @ SV78 ) )
        = $true )
      | ( ( ! [SY311: $i] :
              ( ( remove_slb @ ( insert_slb @ SV10 @ ( pair @ SV47 @ SY311 ) ) @ SV78 )
              = ( insert_slb @ ( remove_slb @ SV10 @ SV78 ) @ ( pair @ SV47 @ SY311 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[298]) ).

thf(329,plain,
    ! [SV12: $i,SV80: $i,SV49: $i] :
      ( ( ( SV49 = SV80 )
        = $true )
      | ( ( ~ ( contains_slb @ SV12 @ SV80 ) )
        = $true )
      | ( ( ! [SY312: $i] :
              ( ( lookup_slb @ ( insert_slb @ SV12 @ ( pair @ SV49 @ SY312 ) ) @ SV80 )
              = ( lookup_slb @ SV12 @ SV80 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[299]) ).

thf(330,plain,
    ! [SV50: $i,SV14: $i,SV81: $i,SV91: $i] :
      ( ( ( ~ ( strictly_less_than @ SV91 @ SV81 ) )
        = $true )
      | ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SV91 ) ) @ SV81 )
          = ( insert_slb @ ( update_slb @ SV14 @ SV81 ) @ ( pair @ SV50 @ SV81 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[300]) ).

thf(331,plain,
    ! [SV51: $i,SV15: $i,SV92: $i,SV82: $i] :
      ( ( ( ~ ( less_than @ SV82 @ SV92 ) )
        = $true )
      | ( ( ( update_slb @ ( insert_slb @ SV15 @ ( pair @ SV51 @ SV92 ) ) @ SV82 )
          = ( insert_slb @ ( update_slb @ SV15 @ SV82 ) @ ( pair @ SV51 @ SV92 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[301]) ).

thf(332,plain,
    ! [SV100: $i,SV52: $i,SV17: $i] :
      ( ( ( succ_cpq @ SV17 @ ( insert_cpq @ SV52 @ SV100 ) )
        = $true )
      | ( ( succ_cpq @ SV17 @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[302]) ).

thf(333,plain,
    ! [SV101: $i,SV53: $i,SV18: $i] :
      ( ( ( succ_cpq @ SV18 @ ( remove_cpq @ SV53 @ SV101 ) )
        = $true )
      | ( ( succ_cpq @ SV18 @ SV53 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[303]) ).

thf(334,plain,
    ! [SV83: $i,SV57: $i,SV22: $i,SV102: $i,SV93: $i] :
      ( ( ~ ( strictly_less_than @ SV93 @ SV102 )
        | ~ ( check_cpq @ ( triple @ SV22 @ ( insert_slb @ SV57 @ ( pair @ SV93 @ SV102 ) ) @ SV83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[306]) ).

thf(335,plain,
    ! [SV86: $i,SV26: $i,SV95: $i,SV61: $i] :
      ( ( ( contains_slb @ SV61 @ SV95 )
        = $true )
      | ( ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SV86 ) @ SV95 )
          = ( triple @ SV26 @ SV61 @ bad ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[309]) ).

thf(336,plain,
    ! [SV87: $i,SV27: $i,SV96: $i,SV62: $i] :
      ( ( ( ~ ( contains_slb @ SV62 @ SV96 )
          | ~ ( less_than @ ( lookup_slb @ SV62 @ SV96 ) @ SV96 ) )
        = $true )
      | ( ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV87 ) @ SV96 )
          = ( triple @ ( remove_pqp @ SV27 @ SV96 ) @ ( remove_slb @ SV62 @ SV96 ) @ SV87 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[310]) ).

thf(337,plain,
    ! [SV88: $i,SV28: $i,SV97: $i,SV63: $i] :
      ( ( ( ~ ( contains_slb @ SV63 @ SV97 )
          | ~ ( strictly_less_than @ SV97 @ ( lookup_slb @ SV63 @ SV97 ) ) )
        = $true )
      | ( ( ( remove_cpq @ ( triple @ SV28 @ SV63 @ SV88 ) @ SV97 )
          = ( triple @ ( remove_pqp @ SV28 @ SV97 ) @ ( remove_slb @ SV63 @ SV97 ) @ bad ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[311]) ).

thf(338,plain,
    ! [SV103: $i,SV65: $i,SV30: $i] :
      ( ( ( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SV103 ) )
          = ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) )
        = $true )
      | ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) )
        = $true )
      | ( ( SV65 = create_slb )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[312]) ).

thf(339,plain,
    ! [SV31: $i,SV66: $i] :
      ( ( ( SV66 = create_slb )
        = $true )
      | ( ( ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) )
        = $true )
      | ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV31 ) @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) ) )
        = $true )
      | ( ( ! [SY284: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY284 ) )
              = ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ bad ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[313]) ).

thf(340,plain,
    ! [SV32: $i,SV67: $i] :
      ( ( ( SV67 = create_slb )
        = $true )
      | ( ( ~ ( contains_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) )
        = $true )
      | ( ( ~ ( less_than @ ( lookup_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ ( findmin_pqp_res @ SV32 ) ) )
        = $true )
      | ( ( ! [SY285: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV32 @ SV67 @ SY285 ) )
              = ( triple @ SV32 @ ( update_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ SY285 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[314]) ).

thf(341,plain,
    ! [SV104: $i] :
      ( ( ( ! [SY335: $i,SY336: $i] :
              ( ( ok @ ( triple @ SV104 @ SY335 @ SY336 ) )
              | ! [SY337: $i,SY338: $i,SY339: $i] :
                  ( ~ ( succ_cpq @ ( triple @ SV104 @ SY335 @ SY336 ) @ ( triple @ SY337 @ SY338 @ SY339 ) )
                  | ~ ( ok @ ( triple @ SY337 @ SY338 @ SY339 ) ) ) ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[316]) ).

thf(342,plain,
    ( ( sK13_REN = $false )
    | ( ( ~ ( ~ ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
            | ~ ~ ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
                  | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[317]) ).

thf(343,plain,
    ! [SV70: $i,SV37: $i] :
      ( ( ! [SY287: $i] :
            ( ! [SY288: $i] :
                ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY288 ) ) @ SY287 )
            | ( SV70 = SY287 )
            | ( contains_slb @ SV37 @ SY287 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[318]) ).

thf(344,plain,
    ! [SV37: $i,SV70: $i] :
      ( ( ~ ( ~ ! [SY289: $i] :
                  ( ( SV70 != SY289 )
                  | ! [SY290: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY290 ) ) @ SY289 ) )
            | ~ ! [SY291: $i] :
                  ( ~ ( contains_slb @ SV37 @ SY291 )
                  | ! [SY292: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY292 ) ) @ SY291 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[319]) ).

thf(345,plain,
    ! [SV89: $i,SV71: $i,SV38: $i] :
      ( ( ~ ~ ( ~ ! [SY321: $i,SY322: $i] :
                    ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY321 ) ) @ SV89 @ SY322 )
                    | ( SV71 = SV89 )
                    | ( pair_in_list @ SV38 @ SV89 @ SY322 ) )
              | ~ ! [SY323: $i,SY324: $i] :
                    ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY323 ) ) @ SV89 @ SY324 )
                    | ( SY323 = SY324 )
                    | ( pair_in_list @ SV38 @ SV89 @ SY324 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[320]) ).

thf(346,plain,
    ! [SV38: $i,SV89: $i,SV71: $i] :
      ( ( ~ ~ ( ~ ! [SY325: $i,SY326: $i] :
                    ( ( SV71 != SV89 )
                    | ( SY325 != SY326 )
                    | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY325 ) ) @ SV89 @ SY326 ) )
              | ~ ! [SY327: $i,SY328: $i] :
                    ( ~ ( pair_in_list @ SV38 @ SV89 @ SY328 )
                    | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY327 ) ) @ SV89 @ SY328 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[320]) ).

thf(347,plain,
    ! [SV90: $i,SV72: $i,SV39: $i] :
      ( ( ~ ! [SY329: $i,SY330: $i] :
              ( ~ ( less_than @ SY330 @ SY329 )
              | ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY329 @ SY330 ) ) @ SV90 ) )
              | ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[321]) ).

thf(348,plain,
    ! [SV90: $i,SV72: $i,SV39: $i] :
      ( ( ~ ! [SY331: $i,SY332: $i] :
              ( ~ ( less_than @ SY332 @ SY331 )
              | ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
              | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY331 @ SY332 ) ) @ SV90 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[321]) ).

thf(349,plain,
    ! [SV105: $i,SV99: $i] :
      ( ( ~ ( less_than @ SV99 @ SV105 )
        | ( less_than @ SV105 @ SV99 )
        | ( strictly_less_than @ SV99 @ SV105 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[322]) ).

thf(350,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( strictly_less_than @ SX0 @ SX1 )
            | ( less_than @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[323]) ).

thf(351,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( strictly_less_than @ SX0 @ SX1 )
            | ~ ( less_than @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[323]) ).

thf(352,plain,
    ! [SV73: $i,SV40: $i] :
      ( ( ! [SY307: $i,SY308: $i] :
            ( ~ ( contains_cpq @ ( triple @ SV40 @ SV73 @ SY307 ) @ SY308 )
            | ( contains_slb @ SV73 @ SY308 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[324]) ).

thf(353,plain,
    ! [SV40: $i,SV73: $i] :
      ( ( ! [SY309: $i,SY310: $i] :
            ( ~ ( contains_slb @ SV73 @ SY310 )
            | ( contains_cpq @ ( triple @ SV40 @ SV73 @ SY309 ) @ SY310 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[325]) ).

thf(354,plain,
    ! [SV75: $i,SV42: $i,SV2: $i] :
      ( ( ( less_than @ SV2 @ SV42 )
        = $false )
      | ( ( ~ ( less_than @ SV42 @ SV75 ) )
        = $true )
      | ( ( less_than @ SV2 @ SV75 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[327]) ).

thf(355,plain,
    ! [SV47: $i,SV78: $i,SV10: $i] :
      ( ( ( contains_slb @ SV10 @ SV78 )
        = $false )
      | ( ( SV47 = SV78 )
        = $true )
      | ( ( ! [SY311: $i] :
              ( ( remove_slb @ ( insert_slb @ SV10 @ ( pair @ SV47 @ SY311 ) ) @ SV78 )
              = ( insert_slb @ ( remove_slb @ SV10 @ SV78 ) @ ( pair @ SV47 @ SY311 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[328]) ).

thf(356,plain,
    ! [SV49: $i,SV80: $i,SV12: $i] :
      ( ( ( contains_slb @ SV12 @ SV80 )
        = $false )
      | ( ( SV49 = SV80 )
        = $true )
      | ( ( ! [SY312: $i] :
              ( ( lookup_slb @ ( insert_slb @ SV12 @ ( pair @ SV49 @ SY312 ) ) @ SV80 )
              = ( lookup_slb @ SV12 @ SV80 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[329]) ).

thf(357,plain,
    ! [SV50: $i,SV14: $i,SV81: $i,SV91: $i] :
      ( ( ( strictly_less_than @ SV91 @ SV81 )
        = $false )
      | ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SV91 ) ) @ SV81 )
          = ( insert_slb @ ( update_slb @ SV14 @ SV81 ) @ ( pair @ SV50 @ SV81 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[330]) ).

thf(358,plain,
    ! [SV51: $i,SV15: $i,SV92: $i,SV82: $i] :
      ( ( ( less_than @ SV82 @ SV92 )
        = $false )
      | ( ( ( update_slb @ ( insert_slb @ SV15 @ ( pair @ SV51 @ SV92 ) ) @ SV82 )
          = ( insert_slb @ ( update_slb @ SV15 @ SV82 ) @ ( pair @ SV51 @ SV92 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[331]) ).

thf(359,plain,
    ! [SV83: $i,SV57: $i,SV22: $i,SV102: $i,SV93: $i] :
      ( ( ( ~ ( strictly_less_than @ SV93 @ SV102 ) )
        = $true )
      | ( ( ~ ( check_cpq @ ( triple @ SV22 @ ( insert_slb @ SV57 @ ( pair @ SV93 @ SV102 ) ) @ SV83 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[334]) ).

thf(360,plain,
    ! [SV87: $i,SV27: $i,SV96: $i,SV62: $i] :
      ( ( ( ~ ( contains_slb @ SV62 @ SV96 ) )
        = $true )
      | ( ( ~ ( less_than @ ( lookup_slb @ SV62 @ SV96 ) @ SV96 ) )
        = $true )
      | ( ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV87 ) @ SV96 )
          = ( triple @ ( remove_pqp @ SV27 @ SV96 ) @ ( remove_slb @ SV62 @ SV96 ) @ SV87 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[336]) ).

thf(361,plain,
    ! [SV88: $i,SV28: $i,SV97: $i,SV63: $i] :
      ( ( ( ~ ( contains_slb @ SV63 @ SV97 ) )
        = $true )
      | ( ( ~ ( strictly_less_than @ SV97 @ ( lookup_slb @ SV63 @ SV97 ) ) )
        = $true )
      | ( ( ( remove_cpq @ ( triple @ SV28 @ SV63 @ SV88 ) @ SV97 )
          = ( triple @ ( remove_pqp @ SV28 @ SV97 ) @ ( remove_slb @ SV63 @ SV97 ) @ bad ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[337]) ).

thf(362,plain,
    ! [SV31: $i,SV66: $i] :
      ( ( ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
        = $false )
      | ( ( SV66 = create_slb )
        = $true )
      | ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV31 ) @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) ) )
        = $true )
      | ( ( ! [SY284: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY284 ) )
              = ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ bad ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[339]) ).

thf(363,plain,
    ! [SV32: $i,SV67: $i] :
      ( ( ( contains_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) )
        = $false )
      | ( ( SV67 = create_slb )
        = $true )
      | ( ( ~ ( less_than @ ( lookup_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ ( findmin_pqp_res @ SV32 ) ) )
        = $true )
      | ( ( ! [SY285: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV32 @ SV67 @ SY285 ) )
              = ( triple @ SV32 @ ( update_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ SY285 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[340]) ).

thf(364,plain,
    ! [SV106: $i,SV104: $i] :
      ( ( ( ! [SY340: $i] :
              ( ( ok @ ( triple @ SV104 @ SV106 @ SY340 ) )
              | ! [SY341: $i,SY342: $i,SY343: $i] :
                  ( ~ ( succ_cpq @ ( triple @ SV104 @ SV106 @ SY340 ) @ ( triple @ SY341 @ SY342 @ SY343 ) )
                  | ~ ( ok @ ( triple @ SY341 @ SY342 @ SY343 ) ) ) ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[341]) ).

thf(365,plain,
    ( ( ( ~ ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
        | ~ ~ ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
              | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[342]) ).

thf(366,plain,
    ! [SV107: $i,SV70: $i,SV37: $i] :
      ( ( ! [SY344: $i] :
            ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY344 ) ) @ SV107 )
        | ( SV70 = SV107 )
        | ( contains_slb @ SV37 @ SV107 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[343]) ).

thf(367,plain,
    ! [SV37: $i,SV70: $i] :
      ( ( ~ ! [SY289: $i] :
              ( ( SV70 != SY289 )
              | ! [SY290: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY290 ) ) @ SY289 ) )
        | ~ ! [SY291: $i] :
              ( ~ ( contains_slb @ SV37 @ SY291 )
              | ! [SY292: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY292 ) ) @ SY291 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[344]) ).

thf(368,plain,
    ! [SV89: $i,SV71: $i,SV38: $i] :
      ( ( ~ ( ~ ! [SY321: $i,SY322: $i] :
                  ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY321 ) ) @ SV89 @ SY322 )
                  | ( SV71 = SV89 )
                  | ( pair_in_list @ SV38 @ SV89 @ SY322 ) )
            | ~ ! [SY323: $i,SY324: $i] :
                  ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY323 ) ) @ SV89 @ SY324 )
                  | ( SY323 = SY324 )
                  | ( pair_in_list @ SV38 @ SV89 @ SY324 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[345]) ).

thf(369,plain,
    ! [SV38: $i,SV89: $i,SV71: $i] :
      ( ( ~ ( ~ ! [SY325: $i,SY326: $i] :
                  ( ( SV71 != SV89 )
                  | ( SY325 != SY326 )
                  | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY325 ) ) @ SV89 @ SY326 ) )
            | ~ ! [SY327: $i,SY328: $i] :
                  ( ~ ( pair_in_list @ SV38 @ SV89 @ SY328 )
                  | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY327 ) ) @ SV89 @ SY328 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[346]) ).

thf(370,plain,
    ! [SV90: $i,SV72: $i,SV39: $i] :
      ( ( ! [SY329: $i,SY330: $i] :
            ( ~ ( less_than @ SY330 @ SY329 )
            | ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY329 @ SY330 ) ) @ SV90 ) )
            | ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[347]) ).

thf(371,plain,
    ! [SV90: $i,SV72: $i,SV39: $i] :
      ( ( ! [SY331: $i,SY332: $i] :
            ( ~ ( less_than @ SY332 @ SY331 )
            | ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
            | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SY331 @ SY332 ) ) @ SV90 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[348]) ).

thf(372,plain,
    ! [SV105: $i,SV99: $i] :
      ( ( ( ~ ( less_than @ SV99 @ SV105 )
          | ( less_than @ SV105 @ SV99 ) )
        = $true )
      | ( ( strictly_less_than @ SV99 @ SV105 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[349]) ).

thf(373,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( strictly_less_than @ SX0 @ SX1 )
          | ( less_than @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[350]) ).

thf(374,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( strictly_less_than @ SX0 @ SX1 )
          | ~ ( less_than @ SX1 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[351]) ).

thf(375,plain,
    ! [SV108: $i,SV73: $i,SV40: $i] :
      ( ( ! [SY345: $i] :
            ( ~ ( contains_cpq @ ( triple @ SV40 @ SV73 @ SV108 ) @ SY345 )
            | ( contains_slb @ SV73 @ SY345 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[352]) ).

thf(376,plain,
    ! [SV109: $i,SV40: $i,SV73: $i] :
      ( ( ! [SY346: $i] :
            ( ~ ( contains_slb @ SV73 @ SY346 )
            | ( contains_cpq @ ( triple @ SV40 @ SV73 @ SV109 ) @ SY346 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[353]) ).

thf(377,plain,
    ! [SV2: $i,SV75: $i,SV42: $i] :
      ( ( ( less_than @ SV42 @ SV75 )
        = $false )
      | ( ( less_than @ SV2 @ SV42 )
        = $false )
      | ( ( less_than @ SV2 @ SV75 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[354]) ).

thf(378,plain,
    ! [SV78: $i,SV110: $i,SV47: $i,SV10: $i] :
      ( ( ( ( remove_slb @ ( insert_slb @ SV10 @ ( pair @ SV47 @ SV110 ) ) @ SV78 )
          = ( insert_slb @ ( remove_slb @ SV10 @ SV78 ) @ ( pair @ SV47 @ SV110 ) ) )
        = $true )
      | ( ( SV47 = SV78 )
        = $true )
      | ( ( contains_slb @ SV10 @ SV78 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[355]) ).

thf(379,plain,
    ! [SV80: $i,SV111: $i,SV49: $i,SV12: $i] :
      ( ( ( ( lookup_slb @ ( insert_slb @ SV12 @ ( pair @ SV49 @ SV111 ) ) @ SV80 )
          = ( lookup_slb @ SV12 @ SV80 ) )
        = $true )
      | ( ( SV49 = SV80 )
        = $true )
      | ( ( contains_slb @ SV12 @ SV80 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[356]) ).

thf(380,plain,
    ! [SV83: $i,SV57: $i,SV22: $i,SV102: $i,SV93: $i] :
      ( ( ( strictly_less_than @ SV93 @ SV102 )
        = $false )
      | ( ( ~ ( check_cpq @ ( triple @ SV22 @ ( insert_slb @ SV57 @ ( pair @ SV93 @ SV102 ) ) @ SV83 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[359]) ).

thf(381,plain,
    ! [SV87: $i,SV27: $i,SV96: $i,SV62: $i] :
      ( ( ( contains_slb @ SV62 @ SV96 )
        = $false )
      | ( ( ~ ( less_than @ ( lookup_slb @ SV62 @ SV96 ) @ SV96 ) )
        = $true )
      | ( ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV87 ) @ SV96 )
          = ( triple @ ( remove_pqp @ SV27 @ SV96 ) @ ( remove_slb @ SV62 @ SV96 ) @ SV87 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[360]) ).

thf(382,plain,
    ! [SV88: $i,SV28: $i,SV97: $i,SV63: $i] :
      ( ( ( contains_slb @ SV63 @ SV97 )
        = $false )
      | ( ( ~ ( strictly_less_than @ SV97 @ ( lookup_slb @ SV63 @ SV97 ) ) )
        = $true )
      | ( ( ( remove_cpq @ ( triple @ SV28 @ SV63 @ SV88 ) @ SV97 )
          = ( triple @ ( remove_pqp @ SV28 @ SV97 ) @ ( remove_slb @ SV63 @ SV97 ) @ bad ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[361]) ).

thf(383,plain,
    ! [SV66: $i,SV31: $i] :
      ( ( ( strictly_less_than @ ( findmin_pqp_res @ SV31 ) @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) )
        = $false )
      | ( ( SV66 = create_slb )
        = $true )
      | ( ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
        = $false )
      | ( ( ! [SY284: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY284 ) )
              = ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ bad ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[362]) ).

thf(384,plain,
    ! [SV32: $i,SV67: $i] :
      ( ( ( less_than @ ( lookup_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ ( findmin_pqp_res @ SV32 ) )
        = $false )
      | ( ( SV67 = create_slb )
        = $true )
      | ( ( contains_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) )
        = $false )
      | ( ( ! [SY285: $i] :
              ( ( findmin_cpq_eff @ ( triple @ SV32 @ SV67 @ SY285 ) )
              = ( triple @ SV32 @ ( update_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ SY285 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[363]) ).

thf(385,plain,
    ! [SV112: $i,SV106: $i,SV104: $i] :
      ( ( ( ( ok @ ( triple @ SV104 @ SV106 @ SV112 ) )
          | ! [SY347: $i,SY348: $i,SY349: $i] :
              ( ~ ( succ_cpq @ ( triple @ SV104 @ SV106 @ SV112 ) @ ( triple @ SY347 @ SY348 @ SY349 ) )
              | ~ ( ok @ ( triple @ SY347 @ SY348 @ SY349 ) ) ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[364]) ).

thf(386,plain,
    ( ( ( ~ ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[365]) ).

thf(387,plain,
    ( ( ( ~ ~ ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
              | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[365]) ).

thf(388,plain,
    ! [SV107: $i,SV70: $i,SV37: $i] :
      ( ( ( ! [SY344: $i] :
              ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY344 ) ) @ SV107 ) )
        = $true )
      | ( ( ( SV70 = SV107 )
          | ( contains_slb @ SV37 @ SV107 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[366]) ).

thf(389,plain,
    ! [SV37: $i,SV70: $i] :
      ( ( ~ ! [SY289: $i] :
              ( ( SV70 != SY289 )
              | ! [SY290: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY290 ) ) @ SY289 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[367]) ).

thf(390,plain,
    ! [SV70: $i,SV37: $i] :
      ( ( ~ ! [SY291: $i] :
              ( ~ ( contains_slb @ SV37 @ SY291 )
              | ! [SY292: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY292 ) ) @ SY291 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[367]) ).

thf(391,plain,
    ! [SV89: $i,SV71: $i,SV38: $i] :
      ( ( ~ ! [SY321: $i,SY322: $i] :
              ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY321 ) ) @ SV89 @ SY322 )
              | ( SV71 = SV89 )
              | ( pair_in_list @ SV38 @ SV89 @ SY322 ) )
        | ~ ! [SY323: $i,SY324: $i] :
              ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY323 ) ) @ SV89 @ SY324 )
              | ( SY323 = SY324 )
              | ( pair_in_list @ SV38 @ SV89 @ SY324 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[368]) ).

thf(392,plain,
    ! [SV38: $i,SV89: $i,SV71: $i] :
      ( ( ~ ! [SY325: $i,SY326: $i] :
              ( ( SV71 != SV89 )
              | ( SY325 != SY326 )
              | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY325 ) ) @ SV89 @ SY326 ) )
        | ~ ! [SY327: $i,SY328: $i] :
              ( ~ ( pair_in_list @ SV38 @ SV89 @ SY328 )
              | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY327 ) ) @ SV89 @ SY328 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[369]) ).

thf(393,plain,
    ! [SV90: $i,SV72: $i,SV39: $i,SV113: $i] :
      ( ( ! [SY350: $i] :
            ( ~ ( less_than @ SY350 @ SV113 )
            | ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV113 @ SY350 ) ) @ SV90 ) )
            | ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[370]) ).

thf(394,plain,
    ! [SV90: $i,SV72: $i,SV39: $i,SV114: $i] :
      ( ( ! [SY351: $i] :
            ( ~ ( less_than @ SY351 @ SV114 )
            | ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
            | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV114 @ SY351 ) ) @ SV90 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[371]) ).

thf(395,plain,
    ! [SV105: $i,SV99: $i] :
      ( ( ( ~ ( less_than @ SV99 @ SV105 ) )
        = $true )
      | ( ( less_than @ SV105 @ SV99 )
        = $true )
      | ( ( strictly_less_than @ SV99 @ SV105 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[372]) ).

thf(396,plain,
    ! [SV115: $i] :
      ( ( ! [SY352: $i] :
            ( ~ ( strictly_less_than @ SV115 @ SY352 )
            | ( less_than @ SV115 @ SY352 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[373]) ).

thf(397,plain,
    ! [SV116: $i] :
      ( ( ! [SY353: $i] :
            ( ~ ( strictly_less_than @ SV116 @ SY353 )
            | ~ ( less_than @ SY353 @ SV116 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[374]) ).

thf(398,plain,
    ! [SV117: $i,SV108: $i,SV73: $i,SV40: $i] :
      ( ( ~ ( contains_cpq @ ( triple @ SV40 @ SV73 @ SV108 ) @ SV117 )
        | ( contains_slb @ SV73 @ SV117 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[375]) ).

thf(399,plain,
    ! [SV109: $i,SV40: $i,SV118: $i,SV73: $i] :
      ( ( ~ ( contains_slb @ SV73 @ SV118 )
        | ( contains_cpq @ ( triple @ SV40 @ SV73 @ SV109 ) @ SV118 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[376]) ).

thf(400,plain,
    ! [SV83: $i,SV102: $i,SV93: $i,SV57: $i,SV22: $i] :
      ( ( ( check_cpq @ ( triple @ SV22 @ ( insert_slb @ SV57 @ ( pair @ SV93 @ SV102 ) ) @ SV83 ) )
        = $false )
      | ( ( strictly_less_than @ SV93 @ SV102 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[380]) ).

thf(401,plain,
    ! [SV87: $i,SV27: $i,SV96: $i,SV62: $i] :
      ( ( ( less_than @ ( lookup_slb @ SV62 @ SV96 ) @ SV96 )
        = $false )
      | ( ( contains_slb @ SV62 @ SV96 )
        = $false )
      | ( ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV87 ) @ SV96 )
          = ( triple @ ( remove_pqp @ SV27 @ SV96 ) @ ( remove_slb @ SV62 @ SV96 ) @ SV87 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[381]) ).

thf(402,plain,
    ! [SV88: $i,SV28: $i,SV63: $i,SV97: $i] :
      ( ( ( strictly_less_than @ SV97 @ ( lookup_slb @ SV63 @ SV97 ) )
        = $false )
      | ( ( contains_slb @ SV63 @ SV97 )
        = $false )
      | ( ( ( remove_cpq @ ( triple @ SV28 @ SV63 @ SV88 ) @ SV97 )
          = ( triple @ ( remove_pqp @ SV28 @ SV97 ) @ ( remove_slb @ SV63 @ SV97 ) @ bad ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[382]) ).

thf(403,plain,
    ! [SV119: $i,SV66: $i,SV31: $i] :
      ( ( ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SV119 ) )
          = ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ bad ) )
        = $true )
      | ( ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
        = $false )
      | ( ( SV66 = create_slb )
        = $true )
      | ( ( strictly_less_than @ ( findmin_pqp_res @ SV31 ) @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[383]) ).

thf(404,plain,
    ! [SV120: $i,SV67: $i,SV32: $i] :
      ( ( ( ( findmin_cpq_eff @ ( triple @ SV32 @ SV67 @ SV120 ) )
          = ( triple @ SV32 @ ( update_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ SV120 ) )
        = $true )
      | ( ( contains_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) )
        = $false )
      | ( ( SV67 = create_slb )
        = $true )
      | ( ( less_than @ ( lookup_slb @ SV67 @ ( findmin_pqp_res @ SV32 ) ) @ ( findmin_pqp_res @ SV32 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[384]) ).

thf(405,plain,
    ! [SV112: $i,SV106: $i,SV104: $i] :
      ( ( ( ok @ ( triple @ SV104 @ SV106 @ SV112 ) )
        = $true )
      | ( ( ! [SY347: $i,SY348: $i,SY349: $i] :
              ( ~ ( succ_cpq @ ( triple @ SV104 @ SV106 @ SV112 ) @ ( triple @ SY347 @ SY348 @ SY349 ) )
              | ~ ( ok @ ( triple @ SY347 @ SY348 @ SY349 ) ) ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[385]) ).

thf(406,plain,
    ( ( ( succ_cpq @ ( triple @ sK7_U @ sK8_SY153 @ sK9_SY158 ) @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
      = $true )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[386]) ).

thf(407,plain,
    ( ( ( ~ ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
            | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) ) )
      = $true )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[387]) ).

thf(408,plain,
    ! [SV107: $i,SV121: $i,SV70: $i,SV37: $i] :
      ( ( ( ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV121 ) ) @ SV107 ) )
        = $true )
      | ( ( ( SV70 = SV107 )
          | ( contains_slb @ SV37 @ SV107 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[388]) ).

thf(409,plain,
    ! [SV37: $i,SV70: $i] :
      ( ( ! [SY289: $i] :
            ( ( SV70 != SY289 )
            | ! [SY290: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY290 ) ) @ SY289 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[389]) ).

thf(410,plain,
    ! [SV70: $i,SV37: $i] :
      ( ( ! [SY291: $i] :
            ( ~ ( contains_slb @ SV37 @ SY291 )
            | ! [SY292: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY292 ) ) @ SY291 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[390]) ).

thf(411,plain,
    ! [SV89: $i,SV71: $i,SV38: $i] :
      ( ( ~ ! [SY321: $i,SY322: $i] :
              ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY321 ) ) @ SV89 @ SY322 )
              | ( SV71 = SV89 )
              | ( pair_in_list @ SV38 @ SV89 @ SY322 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[391]) ).

thf(412,plain,
    ! [SV89: $i,SV71: $i,SV38: $i] :
      ( ( ~ ! [SY323: $i,SY324: $i] :
              ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY323 ) ) @ SV89 @ SY324 )
              | ( SY323 = SY324 )
              | ( pair_in_list @ SV38 @ SV89 @ SY324 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[391]) ).

thf(413,plain,
    ! [SV38: $i,SV89: $i,SV71: $i] :
      ( ( ~ ! [SY325: $i,SY326: $i] :
              ( ( SV71 != SV89 )
              | ( SY325 != SY326 )
              | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY325 ) ) @ SV89 @ SY326 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[392]) ).

thf(414,plain,
    ! [SV71: $i,SV89: $i,SV38: $i] :
      ( ( ~ ! [SY327: $i,SY328: $i] :
              ( ~ ( pair_in_list @ SV38 @ SV89 @ SY328 )
              | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY327 ) ) @ SV89 @ SY328 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[392]) ).

thf(415,plain,
    ! [SV90: $i,SV72: $i,SV39: $i,SV113: $i,SV122: $i] :
      ( ( ~ ( less_than @ SV122 @ SV113 )
        | ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV113 @ SV122 ) ) @ SV90 ) )
        | ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[393]) ).

thf(416,plain,
    ! [SV90: $i,SV72: $i,SV39: $i,SV114: $i,SV123: $i] :
      ( ( ~ ( less_than @ SV123 @ SV114 )
        | ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
        | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV114 @ SV123 ) ) @ SV90 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[394]) ).

thf(417,plain,
    ! [SV105: $i,SV99: $i] :
      ( ( ( less_than @ SV99 @ SV105 )
        = $false )
      | ( ( less_than @ SV105 @ SV99 )
        = $true )
      | ( ( strictly_less_than @ SV99 @ SV105 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[395]) ).

thf(418,plain,
    ! [SV124: $i,SV115: $i] :
      ( ( ~ ( strictly_less_than @ SV115 @ SV124 )
        | ( less_than @ SV115 @ SV124 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[396]) ).

thf(419,plain,
    ! [SV125: $i,SV116: $i] :
      ( ( ~ ( strictly_less_than @ SV116 @ SV125 )
        | ~ ( less_than @ SV125 @ SV116 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[397]) ).

thf(420,plain,
    ! [SV117: $i,SV108: $i,SV73: $i,SV40: $i] :
      ( ( ( ~ ( contains_cpq @ ( triple @ SV40 @ SV73 @ SV108 ) @ SV117 ) )
        = $true )
      | ( ( contains_slb @ SV73 @ SV117 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[398]) ).

thf(421,plain,
    ! [SV109: $i,SV40: $i,SV118: $i,SV73: $i] :
      ( ( ( ~ ( contains_slb @ SV73 @ SV118 ) )
        = $true )
      | ( ( contains_cpq @ ( triple @ SV40 @ SV73 @ SV109 ) @ SV118 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[399]) ).

thf(422,plain,
    ! [SV126: $i,SV112: $i,SV106: $i,SV104: $i] :
      ( ( ( ! [SY354: $i,SY355: $i] :
              ( ~ ( succ_cpq @ ( triple @ SV104 @ SV106 @ SV112 ) @ ( triple @ SV126 @ SY354 @ SY355 ) )
              | ~ ( ok @ ( triple @ SV126 @ SY354 @ SY355 ) ) ) )
        = $true )
      | ( ( ok @ ( triple @ SV104 @ SV106 @ SV112 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[405]) ).

thf(423,plain,
    ( ( ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
        | ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[407]) ).

thf(424,plain,
    ! [SV107: $i,SV121: $i,SV70: $i,SV37: $i] :
      ( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV121 ) ) @ SV107 )
        = $false )
      | ( ( ( SV70 = SV107 )
          | ( contains_slb @ SV37 @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[408]) ).

thf(425,plain,
    ! [SV37: $i,SV127: $i,SV70: $i] :
      ( ( ( SV70 != SV127 )
        | ! [SY356: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY356 ) ) @ SV127 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[409]) ).

thf(426,plain,
    ! [SV70: $i,SV128: $i,SV37: $i] :
      ( ( ~ ( contains_slb @ SV37 @ SV128 )
        | ! [SY357: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY357 ) ) @ SV128 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[410]) ).

thf(427,plain,
    ! [SV89: $i,SV71: $i,SV38: $i] :
      ( ( ! [SY321: $i,SY322: $i] :
            ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY321 ) ) @ SV89 @ SY322 )
            | ( SV71 = SV89 )
            | ( pair_in_list @ SV38 @ SV89 @ SY322 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[411]) ).

thf(428,plain,
    ! [SV89: $i,SV71: $i,SV38: $i] :
      ( ( ! [SY323: $i,SY324: $i] :
            ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY323 ) ) @ SV89 @ SY324 )
            | ( SY323 = SY324 )
            | ( pair_in_list @ SV38 @ SV89 @ SY324 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[412]) ).

thf(429,plain,
    ! [SV38: $i,SV89: $i,SV71: $i] :
      ( ( ! [SY325: $i,SY326: $i] :
            ( ( SV71 != SV89 )
            | ( SY325 != SY326 )
            | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY325 ) ) @ SV89 @ SY326 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[413]) ).

thf(430,plain,
    ! [SV71: $i,SV89: $i,SV38: $i] :
      ( ( ! [SY327: $i,SY328: $i] :
            ( ~ ( pair_in_list @ SV38 @ SV89 @ SY328 )
            | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SY327 ) ) @ SV89 @ SY328 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[414]) ).

thf(431,plain,
    ! [SV90: $i,SV72: $i,SV39: $i,SV113: $i,SV122: $i] :
      ( ( ( ~ ( less_than @ SV122 @ SV113 ) )
        = $true )
      | ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV113 @ SV122 ) ) @ SV90 ) )
          | ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[415]) ).

thf(432,plain,
    ! [SV90: $i,SV72: $i,SV39: $i,SV114: $i,SV123: $i] :
      ( ( ( ~ ( less_than @ SV123 @ SV114 ) )
        = $true )
      | ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
          | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV114 @ SV123 ) ) @ SV90 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[416]) ).

thf(433,plain,
    ! [SV124: $i,SV115: $i] :
      ( ( ( ~ ( strictly_less_than @ SV115 @ SV124 ) )
        = $true )
      | ( ( less_than @ SV115 @ SV124 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[418]) ).

thf(434,plain,
    ! [SV125: $i,SV116: $i] :
      ( ( ( ~ ( strictly_less_than @ SV116 @ SV125 ) )
        = $true )
      | ( ( ~ ( less_than @ SV125 @ SV116 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[419]) ).

thf(435,plain,
    ! [SV117: $i,SV108: $i,SV73: $i,SV40: $i] :
      ( ( ( contains_cpq @ ( triple @ SV40 @ SV73 @ SV108 ) @ SV117 )
        = $false )
      | ( ( contains_slb @ SV73 @ SV117 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[420]) ).

thf(436,plain,
    ! [SV109: $i,SV40: $i,SV118: $i,SV73: $i] :
      ( ( ( contains_slb @ SV73 @ SV118 )
        = $false )
      | ( ( contains_cpq @ ( triple @ SV40 @ SV73 @ SV109 ) @ SV118 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[421]) ).

thf(437,plain,
    ! [SV129: $i,SV126: $i,SV112: $i,SV106: $i,SV104: $i] :
      ( ( ( ! [SY358: $i] :
              ( ~ ( succ_cpq @ ( triple @ SV104 @ SV106 @ SV112 ) @ ( triple @ SV126 @ SV129 @ SY358 ) )
              | ~ ( ok @ ( triple @ SV126 @ SV129 @ SY358 ) ) ) )
        = $true )
      | ( ( ok @ ( triple @ SV104 @ SV106 @ SV112 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[422]) ).

thf(438,plain,
    ( ( ( ~ ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[423]) ).

thf(439,plain,
    ( ( ( ~ ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[423]) ).

thf(440,plain,
    ! [SV121: $i,SV37: $i,SV107: $i,SV70: $i] :
      ( ( ( SV70 = SV107 )
        = $true )
      | ( ( contains_slb @ SV37 @ SV107 )
        = $true )
      | ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV121 ) ) @ SV107 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[424]) ).

thf(441,plain,
    ! [SV37: $i,SV127: $i,SV70: $i] :
      ( ( ( ( SV70 != SV127 ) )
        = $true )
      | ( ( ! [SY356: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY356 ) ) @ SV127 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[425]) ).

thf(442,plain,
    ! [SV70: $i,SV128: $i,SV37: $i] :
      ( ( ( ~ ( contains_slb @ SV37 @ SV128 ) )
        = $true )
      | ( ( ! [SY357: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY357 ) ) @ SV128 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[426]) ).

thf(443,plain,
    ! [SV89: $i,SV130: $i,SV71: $i,SV38: $i] :
      ( ( ! [SY359: $i] :
            ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV130 ) ) @ SV89 @ SY359 )
            | ( SV71 = SV89 )
            | ( pair_in_list @ SV38 @ SV89 @ SY359 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[427]) ).

thf(444,plain,
    ! [SV89: $i,SV131: $i,SV71: $i,SV38: $i] :
      ( ( ! [SY360: $i] :
            ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV131 ) ) @ SV89 @ SY360 )
            | ( SV131 = SY360 )
            | ( pair_in_list @ SV38 @ SV89 @ SY360 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[428]) ).

thf(445,plain,
    ! [SV38: $i,SV132: $i,SV89: $i,SV71: $i] :
      ( ( ! [SY361: $i] :
            ( ( SV71 != SV89 )
            | ( SV132 != SY361 )
            | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV132 ) ) @ SV89 @ SY361 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[429]) ).

thf(446,plain,
    ! [SV133: $i,SV71: $i,SV89: $i,SV38: $i] :
      ( ( ! [SY362: $i] :
            ( ~ ( pair_in_list @ SV38 @ SV89 @ SY362 )
            | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV133 ) ) @ SV89 @ SY362 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[430]) ).

thf(447,plain,
    ! [SV90: $i,SV72: $i,SV39: $i,SV113: $i,SV122: $i] :
      ( ( ( less_than @ SV122 @ SV113 )
        = $false )
      | ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV113 @ SV122 ) ) @ SV90 ) )
          | ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[431]) ).

thf(448,plain,
    ! [SV90: $i,SV72: $i,SV39: $i,SV114: $i,SV123: $i] :
      ( ( ( less_than @ SV123 @ SV114 )
        = $false )
      | ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
          | ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV114 @ SV123 ) ) @ SV90 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[432]) ).

thf(449,plain,
    ! [SV124: $i,SV115: $i] :
      ( ( ( strictly_less_than @ SV115 @ SV124 )
        = $false )
      | ( ( less_than @ SV115 @ SV124 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[433]) ).

thf(450,plain,
    ! [SV125: $i,SV116: $i] :
      ( ( ( strictly_less_than @ SV116 @ SV125 )
        = $false )
      | ( ( ~ ( less_than @ SV125 @ SV116 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[434]) ).

thf(451,plain,
    ! [SV134: $i,SV129: $i,SV126: $i,SV112: $i,SV106: $i,SV104: $i] :
      ( ( ( ~ ( succ_cpq @ ( triple @ SV104 @ SV106 @ SV112 ) @ ( triple @ SV126 @ SV129 @ SV134 ) )
          | ~ ( ok @ ( triple @ SV126 @ SV129 @ SV134 ) ) )
        = $true )
      | ( ( ok @ ( triple @ SV104 @ SV106 @ SV112 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[437]) ).

thf(452,plain,
    ( ( ( ~ ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) )
      = $true )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[438]) ).

thf(453,plain,
    ( ( ( ok @ ( im_succ_cpq @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) ) )
      = $true )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[439]) ).

thf(454,plain,
    ! [SV37: $i,SV127: $i,SV70: $i] :
      ( ( ( SV70 = SV127 )
        = $false )
      | ( ( ! [SY356: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY356 ) ) @ SV127 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[441]) ).

thf(455,plain,
    ! [SV70: $i,SV128: $i,SV37: $i] :
      ( ( ( contains_slb @ SV37 @ SV128 )
        = $false )
      | ( ( ! [SY357: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY357 ) ) @ SV128 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[442]) ).

thf(456,plain,
    ! [SV135: $i,SV89: $i,SV130: $i,SV71: $i,SV38: $i] :
      ( ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV130 ) ) @ SV89 @ SV135 )
        | ( SV71 = SV89 )
        | ( pair_in_list @ SV38 @ SV89 @ SV135 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[443]) ).

thf(457,plain,
    ! [SV136: $i,SV89: $i,SV131: $i,SV71: $i,SV38: $i] :
      ( ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV131 ) ) @ SV89 @ SV136 )
        | ( SV131 = SV136 )
        | ( pair_in_list @ SV38 @ SV89 @ SV136 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[444]) ).

thf(458,plain,
    ! [SV38: $i,SV137: $i,SV132: $i,SV89: $i,SV71: $i] :
      ( ( ( SV71 != SV89 )
        | ( SV132 != SV137 )
        | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV132 ) ) @ SV89 @ SV137 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[445]) ).

thf(459,plain,
    ! [SV133: $i,SV71: $i,SV138: $i,SV89: $i,SV38: $i] :
      ( ( ~ ( pair_in_list @ SV38 @ SV89 @ SV138 )
        | ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV133 ) ) @ SV89 @ SV138 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[446]) ).

thf(460,plain,
    ! [SV90: $i,SV122: $i,SV113: $i,SV72: $i,SV39: $i] :
      ( ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV113 @ SV122 ) ) @ SV90 ) ) )
        = $true )
      | ( ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
        = $true )
      | ( ( less_than @ SV122 @ SV113 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[447]) ).

thf(461,plain,
    ! [SV123: $i,SV114: $i,SV90: $i,SV72: $i,SV39: $i] :
      ( ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) ) )
        = $true )
      | ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV114 @ SV123 ) ) @ SV90 ) )
        = $true )
      | ( ( less_than @ SV123 @ SV114 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[448]) ).

thf(462,plain,
    ! [SV116: $i,SV125: $i] :
      ( ( ( less_than @ SV125 @ SV116 )
        = $false )
      | ( ( strictly_less_than @ SV116 @ SV125 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[450]) ).

thf(463,plain,
    ! [SV134: $i,SV129: $i,SV126: $i,SV112: $i,SV106: $i,SV104: $i] :
      ( ( ( ~ ( succ_cpq @ ( triple @ SV104 @ SV106 @ SV112 ) @ ( triple @ SV126 @ SV129 @ SV134 ) ) )
        = $true )
      | ( ( ~ ( ok @ ( triple @ SV126 @ SV129 @ SV134 ) ) )
        = $true )
      | ( ( ok @ ( triple @ SV104 @ SV106 @ SV112 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[451]) ).

thf(464,plain,
    ( ( ( ok @ ( triple @ sK10_SY162 @ sK11_SY165 @ sK12_SY167 ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[452]) ).

thf(465,plain,
    ! [SV127: $i,SV139: $i,SV70: $i,SV37: $i] :
      ( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV139 ) ) @ SV127 )
        = $true )
      | ( ( SV70 = SV127 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[454]) ).

thf(466,plain,
    ! [SV128: $i,SV140: $i,SV70: $i,SV37: $i] :
      ( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV140 ) ) @ SV128 )
        = $true )
      | ( ( contains_slb @ SV37 @ SV128 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[455]) ).

thf(467,plain,
    ! [SV135: $i,SV89: $i,SV130: $i,SV71: $i,SV38: $i] :
      ( ( ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV130 ) ) @ SV89 @ SV135 ) )
        = $true )
      | ( ( ( SV71 = SV89 )
          | ( pair_in_list @ SV38 @ SV89 @ SV135 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[456]) ).

thf(468,plain,
    ! [SV136: $i,SV89: $i,SV131: $i,SV71: $i,SV38: $i] :
      ( ( ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV131 ) ) @ SV89 @ SV136 ) )
        = $true )
      | ( ( ( SV131 = SV136 )
          | ( pair_in_list @ SV38 @ SV89 @ SV136 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[457]) ).

thf(469,plain,
    ! [SV38: $i,SV137: $i,SV132: $i,SV89: $i,SV71: $i] :
      ( ( ( ( SV71 != SV89 )
          | ( SV132 != SV137 ) )
        = $true )
      | ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV132 ) ) @ SV89 @ SV137 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[458]) ).

thf(470,plain,
    ! [SV133: $i,SV71: $i,SV138: $i,SV89: $i,SV38: $i] :
      ( ( ( ~ ( pair_in_list @ SV38 @ SV89 @ SV138 ) )
        = $true )
      | ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV133 ) ) @ SV89 @ SV138 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[459]) ).

thf(471,plain,
    ! [SV90: $i,SV122: $i,SV113: $i,SV72: $i,SV39: $i] :
      ( ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV113 @ SV122 ) ) @ SV90 ) )
        = $false )
      | ( ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
        = $true )
      | ( ( less_than @ SV122 @ SV113 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[460]) ).

thf(472,plain,
    ! [SV123: $i,SV114: $i,SV90: $i,SV72: $i,SV39: $i] :
      ( ( ( check_cpq @ ( triple @ SV39 @ SV72 @ SV90 ) )
        = $false )
      | ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV72 @ ( pair @ SV114 @ SV123 ) ) @ SV90 ) )
        = $true )
      | ( ( less_than @ SV123 @ SV114 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[461]) ).

thf(473,plain,
    ! [SV134: $i,SV129: $i,SV126: $i,SV112: $i,SV106: $i,SV104: $i] :
      ( ( ( succ_cpq @ ( triple @ SV104 @ SV106 @ SV112 ) @ ( triple @ SV126 @ SV129 @ SV134 ) )
        = $false )
      | ( ( ~ ( ok @ ( triple @ SV126 @ SV129 @ SV134 ) ) )
        = $true )
      | ( ( ok @ ( triple @ SV104 @ SV106 @ SV112 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[463]) ).

thf(474,plain,
    ! [SV135: $i,SV89: $i,SV130: $i,SV71: $i,SV38: $i] :
      ( ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV130 ) ) @ SV89 @ SV135 )
        = $false )
      | ( ( ( SV71 = SV89 )
          | ( pair_in_list @ SV38 @ SV89 @ SV135 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[467]) ).

thf(475,plain,
    ! [SV136: $i,SV89: $i,SV131: $i,SV71: $i,SV38: $i] :
      ( ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV131 ) ) @ SV89 @ SV136 )
        = $false )
      | ( ( ( SV131 = SV136 )
          | ( pair_in_list @ SV38 @ SV89 @ SV136 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[468]) ).

thf(476,plain,
    ! [SV38: $i,SV137: $i,SV132: $i,SV89: $i,SV71: $i] :
      ( ( ( ( SV71 != SV89 ) )
        = $true )
      | ( ( ( SV132 != SV137 ) )
        = $true )
      | ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV132 ) ) @ SV89 @ SV137 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[469]) ).

thf(477,plain,
    ! [SV133: $i,SV71: $i,SV138: $i,SV89: $i,SV38: $i] :
      ( ( ( pair_in_list @ SV38 @ SV89 @ SV138 )
        = $false )
      | ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV133 ) ) @ SV89 @ SV138 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[470]) ).

thf(478,plain,
    ! [SV112: $i,SV106: $i,SV104: $i,SV134: $i,SV129: $i,SV126: $i] :
      ( ( ( ok @ ( triple @ SV126 @ SV129 @ SV134 ) )
        = $false )
      | ( ( succ_cpq @ ( triple @ SV104 @ SV106 @ SV112 ) @ ( triple @ SV126 @ SV129 @ SV134 ) )
        = $false )
      | ( ( ok @ ( triple @ SV104 @ SV106 @ SV112 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[473]) ).

thf(479,plain,
    ! [SV130: $i,SV135: $i,SV38: $i,SV89: $i,SV71: $i] :
      ( ( ( SV71 = SV89 )
        = $true )
      | ( ( pair_in_list @ SV38 @ SV89 @ SV135 )
        = $true )
      | ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV130 ) ) @ SV89 @ SV135 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[474]) ).

thf(480,plain,
    ! [SV71: $i,SV89: $i,SV38: $i,SV136: $i,SV131: $i] :
      ( ( ( SV131 = SV136 )
        = $true )
      | ( ( pair_in_list @ SV38 @ SV89 @ SV136 )
        = $true )
      | ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV131 ) ) @ SV89 @ SV136 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[475]) ).

thf(481,plain,
    ! [SV38: $i,SV137: $i,SV132: $i,SV89: $i,SV71: $i] :
      ( ( ( SV71 = SV89 )
        = $false )
      | ( ( ( SV132 != SV137 ) )
        = $true )
      | ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV132 ) ) @ SV89 @ SV137 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[476]) ).

thf(482,plain,
    ! [SV38: $i,SV89: $i,SV71: $i,SV137: $i,SV132: $i] :
      ( ( ( SV132 = SV137 )
        = $false )
      | ( ( SV71 = SV89 )
        = $false )
      | ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV71 @ SV132 ) ) @ SV89 @ SV137 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[481]) ).

thf(483,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[178,482,480,479,478,477,472,471,466,465,464,462,453,449,440,436,435,417,406,404,403,402,401,400,379,378,377,358,357,338,335,333,332,326,315,308,307,305,304,290,289,276,267,265,264,263,262,248,244,236,224,212,211,210,191,188,180,179]) ).

thf(484,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[483]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SWV376+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Wed Jun 15 20:43:03 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.40  .
% 0.13/0.40  
% 0.13/0.40   No.of.Axioms: 43
% 0.13/0.40  
% 0.13/0.40   Length.of.Defs: 0
% 0.13/0.40  
% 0.13/0.40   Contains.Choice.Funs: false
% 0.20/0.45  .
% 0.20/0.46  (rf:0,axioms:43,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:45,loop_count:0,foatp_calls:0,translation:fof_full)...................................
% 0.50/0.92  
% 0.50/0.92  ********************************
% 0.50/0.92  *   All subproblems solved!    *
% 0.50/0.92  ********************************
% 0.50/0.92  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:44,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:483,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.84/1.04  
% 0.84/1.04  %**** Beginning of derivation protocol ****
% 0.84/1.04  % SZS output start CNFRefutation
% See solution above
% 0.84/1.04  
% 0.84/1.04  %**** End of derivation protocol ****
% 0.84/1.04  %**** no. of clauses in derivation: 484 ****
% 0.84/1.04  %**** clause counter: 483 ****
% 0.84/1.04  
% 0.84/1.04  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:44,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:483,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------