TSTP Solution File: ANA003-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ANA003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n026.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 : Thu Jul 14 19:10:16 EDT 2022

% Result   : Unsatisfiable 0.77s 0.97s
% Output   : CNFRefutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  152 (  74 unt;  17 typ;   0 def)
%            Number of atoms       :  674 ( 178 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives : 1478 ( 153   ~; 183   |;   0   &;1142   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   7 con; 0-2 aty)
%            Number of variables   :  234 (   0   ^ 234   !;   0   ?; 234   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $i ).

thf(tp_absolute,type,
    absolute: $i > $i ).

thf(tp_add,type,
    add: $i > $i > $i ).

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

thf(tp_equalish,type,
    equalish: $i > $i > $o ).

thf(tp_f,type,
    f: $i > $i ).

thf(tp_fp31,type,
    fp31: $i > $i ).

thf(tp_fp32,type,
    fp32: $i > $i ).

thf(tp_fp33,type,
    fp33: $i > $i ).

thf(tp_g,type,
    g: $i > $i ).

thf(tp_half,type,
    half: $i > $i ).

thf(tp_l1,type,
    l1: $i ).

thf(tp_l2,type,
    l2: $i ).

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

thf(tp_minimum,type,
    minimum: $i > $i > $i ).

thf(tp_minus,type,
    minus: $i > $i ).

thf(tp_n0,type,
    n0: $i ).

thf(1,axiom,
    ! [Xa: $i] :
      ( ~ ( less_than @ n0 @ Xa )
      | ( less_than @ n0 @ ( half @ Xa ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

thf(2,axiom,
    ! [X: $i,Y: $i,Xa: $i] :
      ( ~ ( less_than @ ( add @ ( absolute @ X ) @ ( absolute @ Y ) ) @ Xa )
      | ( less_than @ ( absolute @ ( add @ X @ Y ) ) @ Xa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_17) ).

thf(3,axiom,
    ! [X: $i,Xa: $i,Y: $i] :
      ( ~ ( less_than @ X @ ( half @ Xa ) )
      | ~ ( less_than @ Y @ ( half @ Xa ) )
      | ( less_than @ ( add @ X @ Y ) @ Xa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(4,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( less_than @ n0 @ X )
      | ~ ( less_than @ n0 @ Y )
      | ( less_than @ ( minimum @ X @ Y ) @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_3) ).

thf(5,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( less_than @ n0 @ X )
      | ~ ( less_than @ n0 @ Y )
      | ( less_than @ ( minimum @ X @ Y ) @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_2) ).

thf(6,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( less_than @ n0 @ X )
      | ~ ( less_than @ n0 @ Y )
      | ( less_than @ n0 @ ( minimum @ X @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_1) ).

thf(7,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( less_than @ X @ Y )
      | ~ ( less_than @ Y @ Z )
      | ( less_than @ X @ Z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_than) ).

thf(8,axiom,
    ! [X: $i] :
      ~ ( less_than @ X @ X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_less_than) ).

thf(9,axiom,
    ! [X: $i] : ( equalish @ ( add @ n0 @ X ) @ X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

thf(10,axiom,
    ! [X: $i] : ( equalish @ ( add @ X @ n0 ) @ X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).

thf(11,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(12,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[11]) ).

thf(13,negated_conjecture,
    ! [X: $i] :
      ( ~ ( less_than @ n0 @ X )
      | ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ X ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ X ) ) @ ( minus @ l2 ) ) ) ) @ b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).

thf(14,negated_conjecture,
    ! [X: $i] :
      ( ~ ( less_than @ n0 @ X )
      | ( less_than @ ( absolute @ ( add @ ( fp33 @ X ) @ ( minus @ a ) ) ) @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).

thf(15,negated_conjecture,
    less_than @ n0 @ b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).

thf(16,negated_conjecture,
    ! [X: $i,Y: $i] :
      ( ~ ( less_than @ n0 @ X )
      | ~ ( less_than @ ( absolute @ ( add @ Y @ ( minus @ a ) ) ) @ ( fp32 @ X ) )
      | ( less_than @ ( absolute @ ( add @ ( g @ Y ) @ ( minus @ l2 ) ) ) @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).

thf(17,negated_conjecture,
    ! [X: $i] :
      ( ~ ( less_than @ n0 @ X )
      | ( less_than @ n0 @ ( fp32 @ X ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).

thf(18,negated_conjecture,
    ! [X: $i,Y: $i] :
      ( ~ ( less_than @ n0 @ X )
      | ~ ( less_than @ ( absolute @ ( add @ Y @ ( minus @ a ) ) ) @ ( fp31 @ X ) )
      | ( less_than @ ( absolute @ ( add @ ( f @ Y ) @ ( minus @ l1 ) ) ) @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).

thf(19,negated_conjecture,
    ! [X: $i] :
      ( ~ ( less_than @ n0 @ X )
      | ( less_than @ n0 @ ( fp31 @ X ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).

thf(20,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[12]) ).

thf(21,plain,
    ( ( ! [Xa: $i] :
          ( ~ ( less_than @ n0 @ Xa )
          | ( less_than @ n0 @ ( half @ Xa ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(22,plain,
    ( ( ! [X: $i,Y: $i,Xa: $i] :
          ( ~ ( less_than @ ( add @ ( absolute @ X ) @ ( absolute @ Y ) ) @ Xa )
          | ( less_than @ ( absolute @ ( add @ X @ Y ) ) @ Xa ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(23,plain,
    ( ( ! [X: $i,Xa: $i,Y: $i] :
          ( ~ ( less_than @ X @ ( half @ Xa ) )
          | ~ ( less_than @ Y @ ( half @ Xa ) )
          | ( less_than @ ( add @ X @ Y ) @ Xa ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(24,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ~ ( less_than @ n0 @ Y )
          | ( less_than @ ( minimum @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(25,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ~ ( less_than @ n0 @ Y )
          | ( less_than @ ( minimum @ X @ Y ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(26,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ~ ( less_than @ n0 @ Y )
          | ( less_than @ n0 @ ( minimum @ X @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(27,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( less_than @ X @ Y )
          | ~ ( less_than @ Y @ Z )
          | ( less_than @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(28,plain,
    ( ( ! [X: $i] :
          ~ ( less_than @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(29,plain,
    ( ( ! [X: $i] : ( equalish @ ( add @ n0 @ X ) @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(30,plain,
    ( ( ! [X: $i] : ( equalish @ ( add @ X @ n0 ) @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(31,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ X ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ X ) ) @ ( minus @ l2 ) ) ) ) @ b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(32,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ( less_than @ ( absolute @ ( add @ ( fp33 @ X ) @ ( minus @ a ) ) ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(33,plain,
    ( ( less_than @ n0 @ b )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(34,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ~ ( less_than @ ( absolute @ ( add @ Y @ ( minus @ a ) ) ) @ ( fp32 @ X ) )
          | ( less_than @ ( absolute @ ( add @ ( g @ Y ) @ ( minus @ l2 ) ) ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(35,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ( less_than @ n0 @ ( fp32 @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(36,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ~ ( less_than @ ( absolute @ ( add @ Y @ ( minus @ a ) ) ) @ ( fp31 @ X ) )
          | ( less_than @ ( absolute @ ( add @ ( f @ Y ) @ ( minus @ l1 ) ) ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(37,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ( less_than @ n0 @ ( fp31 @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(38,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[20]) ).

thf(39,plain,
    ( ( ! [X: $i,Xa: $i] :
          ( ~ ( less_than @ X @ ( half @ Xa ) )
          | ! [Y: $i] :
              ( ~ ( less_than @ Y @ ( half @ Xa ) )
              | ( less_than @ ( add @ X @ Y ) @ Xa ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[23]) ).

thf(40,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ n0 @ Y )
              | ( less_than @ ( minimum @ X @ Y ) @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[24]) ).

thf(41,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ n0 @ Y )
              | ( less_than @ ( minimum @ X @ Y ) @ X ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[25]) ).

thf(42,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ n0 @ Y )
              | ( less_than @ n0 @ ( minimum @ X @ Y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[26]) ).

thf(43,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( less_than @ Y @ Z )
              | ( less_than @ X @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(44,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ ( absolute @ ( add @ Y @ ( minus @ a ) ) ) @ ( fp32 @ X ) )
              | ( less_than @ ( absolute @ ( add @ ( g @ Y ) @ ( minus @ l2 ) ) ) @ X ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[34]) ).

thf(45,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ ( absolute @ ( add @ Y @ ( minus @ a ) ) ) @ ( fp31 @ X ) )
              | ( less_than @ ( absolute @ ( add @ ( f @ Y ) @ ( minus @ l1 ) ) ) @ X ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[36]) ).

thf(46,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ( less_than @ n0 @ ( fp31 @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(47,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ ( absolute @ ( add @ Y @ ( minus @ a ) ) ) @ ( fp31 @ X ) )
              | ( less_than @ ( absolute @ ( add @ ( f @ Y ) @ ( minus @ l1 ) ) ) @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(48,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ( less_than @ n0 @ ( fp32 @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(49,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ ( absolute @ ( add @ Y @ ( minus @ a ) ) ) @ ( fp32 @ X ) )
              | ( less_than @ ( absolute @ ( add @ ( g @ Y ) @ ( minus @ l2 ) ) ) @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(50,plain,
    ( ( less_than @ n0 @ b )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(51,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ( less_than @ ( absolute @ ( add @ ( fp33 @ X ) @ ( minus @ a ) ) ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(52,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ X ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ X ) ) @ ( minus @ l2 ) ) ) ) @ b ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(53,plain,
    ( ( ! [X: $i] : ( equalish @ ( add @ X @ n0 ) @ X ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(54,plain,
    ( ( ! [X: $i] : ( equalish @ ( add @ n0 @ X ) @ X ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(55,plain,
    ( ( ! [X: $i] :
          ~ ( less_than @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(56,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( less_than @ Y @ Z )
              | ( less_than @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(57,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ n0 @ Y )
              | ( less_than @ n0 @ ( minimum @ X @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(58,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ n0 @ Y )
              | ( less_than @ ( minimum @ X @ Y ) @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(59,plain,
    ( ( ! [X: $i] :
          ( ~ ( less_than @ n0 @ X )
          | ! [Y: $i] :
              ( ~ ( less_than @ n0 @ Y )
              | ( less_than @ ( minimum @ X @ Y ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(60,plain,
    ( ( ! [X: $i,Xa: $i] :
          ( ~ ( less_than @ X @ ( half @ Xa ) )
          | ! [Y: $i] :
              ( ~ ( less_than @ Y @ ( half @ Xa ) )
              | ( less_than @ ( add @ X @ Y ) @ Xa ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(61,plain,
    ( ( ! [X: $i,Y: $i,Xa: $i] :
          ( ~ ( less_than @ ( add @ ( absolute @ X ) @ ( absolute @ Y ) ) @ Xa )
          | ( less_than @ ( absolute @ ( add @ X @ Y ) ) @ Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(62,plain,
    ( ( ! [Xa: $i] :
          ( ~ ( less_than @ n0 @ Xa )
          | ( less_than @ n0 @ ( half @ Xa ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(63,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(64,plain,
    ! [SV1: $i] :
      ( ( ~ ( less_than @ n0 @ SV1 )
        | ( less_than @ n0 @ ( fp31 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(65,plain,
    ! [SV2: $i] :
      ( ( ~ ( less_than @ n0 @ SV2 )
        | ! [SY27: $i] :
            ( ~ ( less_than @ ( absolute @ ( add @ SY27 @ ( minus @ a ) ) ) @ ( fp31 @ SV2 ) )
            | ( less_than @ ( absolute @ ( add @ ( f @ SY27 ) @ ( minus @ l1 ) ) ) @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(66,plain,
    ! [SV3: $i] :
      ( ( ~ ( less_than @ n0 @ SV3 )
        | ( less_than @ n0 @ ( fp32 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(67,plain,
    ! [SV4: $i] :
      ( ( ~ ( less_than @ n0 @ SV4 )
        | ! [SY28: $i] :
            ( ~ ( less_than @ ( absolute @ ( add @ SY28 @ ( minus @ a ) ) ) @ ( fp32 @ SV4 ) )
            | ( less_than @ ( absolute @ ( add @ ( g @ SY28 ) @ ( minus @ l2 ) ) ) @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(68,plain,
    ! [SV5: $i] :
      ( ( ~ ( less_than @ n0 @ SV5 )
        | ( less_than @ ( absolute @ ( add @ ( fp33 @ SV5 ) @ ( minus @ a ) ) ) @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(69,plain,
    ! [SV6: $i] :
      ( ( ~ ( less_than @ n0 @ SV6 )
        | ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ SV6 ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ SV6 ) ) @ ( minus @ l2 ) ) ) ) @ b ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(70,plain,
    ! [SV7: $i] :
      ( ( equalish @ ( add @ SV7 @ n0 ) @ SV7 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(71,plain,
    ! [SV8: $i] :
      ( ( equalish @ ( add @ n0 @ SV8 ) @ SV8 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(72,plain,
    ! [SV9: $i] :
      ( ( ~ ( less_than @ SV9 @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(73,plain,
    ! [SV10: $i] :
      ( ( ! [SY29: $i] :
            ( ~ ( less_than @ SV10 @ SY29 )
            | ! [SY30: $i] :
                ( ~ ( less_than @ SY29 @ SY30 )
                | ( less_than @ SV10 @ SY30 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(74,plain,
    ! [SV11: $i] :
      ( ( ~ ( less_than @ n0 @ SV11 )
        | ! [SY31: $i] :
            ( ~ ( less_than @ n0 @ SY31 )
            | ( less_than @ n0 @ ( minimum @ SV11 @ SY31 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(75,plain,
    ! [SV12: $i] :
      ( ( ~ ( less_than @ n0 @ SV12 )
        | ! [SY32: $i] :
            ( ~ ( less_than @ n0 @ SY32 )
            | ( less_than @ ( minimum @ SV12 @ SY32 ) @ SV12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(76,plain,
    ! [SV13: $i] :
      ( ( ~ ( less_than @ n0 @ SV13 )
        | ! [SY33: $i] :
            ( ~ ( less_than @ n0 @ SY33 )
            | ( less_than @ ( minimum @ SV13 @ SY33 ) @ SY33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(77,plain,
    ! [SV14: $i] :
      ( ( ! [SY34: $i] :
            ( ~ ( less_than @ SV14 @ ( half @ SY34 ) )
            | ! [SY35: $i] :
                ( ~ ( less_than @ SY35 @ ( half @ SY34 ) )
                | ( less_than @ ( add @ SV14 @ SY35 ) @ SY34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(78,plain,
    ! [SV15: $i] :
      ( ( ! [SY36: $i,SY37: $i] :
            ( ~ ( less_than @ ( add @ ( absolute @ SV15 ) @ ( absolute @ SY36 ) ) @ SY37 )
            | ( less_than @ ( absolute @ ( add @ SV15 @ SY36 ) ) @ SY37 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(79,plain,
    ! [SV16: $i] :
      ( ( ~ ( less_than @ n0 @ SV16 )
        | ( less_than @ n0 @ ( half @ SV16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(80,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(81,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV1 ) )
        = $true )
      | ( ( less_than @ n0 @ ( fp31 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(82,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV2 ) )
        = $true )
      | ( ( ! [SY27: $i] :
              ( ~ ( less_than @ ( absolute @ ( add @ SY27 @ ( minus @ a ) ) ) @ ( fp31 @ SV2 ) )
              | ( less_than @ ( absolute @ ( add @ ( f @ SY27 ) @ ( minus @ l1 ) ) ) @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(83,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV3 ) )
        = $true )
      | ( ( less_than @ n0 @ ( fp32 @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(84,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV4 ) )
        = $true )
      | ( ( ! [SY28: $i] :
              ( ~ ( less_than @ ( absolute @ ( add @ SY28 @ ( minus @ a ) ) ) @ ( fp32 @ SV4 ) )
              | ( less_than @ ( absolute @ ( add @ ( g @ SY28 ) @ ( minus @ l2 ) ) ) @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[67]) ).

thf(85,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV5 ) )
        = $true )
      | ( ( less_than @ ( absolute @ ( add @ ( fp33 @ SV5 ) @ ( minus @ a ) ) ) @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[68]) ).

thf(86,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV6 ) )
        = $true )
      | ( ( ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ SV6 ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ SV6 ) ) @ ( minus @ l2 ) ) ) ) @ b ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[69]) ).

thf(87,plain,
    ! [SV9: $i] :
      ( ( less_than @ SV9 @ SV9 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(88,plain,
    ! [SV17: $i,SV10: $i] :
      ( ( ~ ( less_than @ SV10 @ SV17 )
        | ! [SY38: $i] :
            ( ~ ( less_than @ SV17 @ SY38 )
            | ( less_than @ SV10 @ SY38 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(89,plain,
    ! [SV11: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV11 ) )
        = $true )
      | ( ( ! [SY31: $i] :
              ( ~ ( less_than @ n0 @ SY31 )
              | ( less_than @ n0 @ ( minimum @ SV11 @ SY31 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[74]) ).

thf(90,plain,
    ! [SV12: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV12 ) )
        = $true )
      | ( ( ! [SY32: $i] :
              ( ~ ( less_than @ n0 @ SY32 )
              | ( less_than @ ( minimum @ SV12 @ SY32 ) @ SV12 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[75]) ).

thf(91,plain,
    ! [SV13: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV13 ) )
        = $true )
      | ( ( ! [SY33: $i] :
              ( ~ ( less_than @ n0 @ SY33 )
              | ( less_than @ ( minimum @ SV13 @ SY33 ) @ SY33 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[76]) ).

thf(92,plain,
    ! [SV18: $i,SV14: $i] :
      ( ( ~ ( less_than @ SV14 @ ( half @ SV18 ) )
        | ! [SY39: $i] :
            ( ~ ( less_than @ SY39 @ ( half @ SV18 ) )
            | ( less_than @ ( add @ SV14 @ SY39 ) @ SV18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(93,plain,
    ! [SV19: $i,SV15: $i] :
      ( ( ! [SY40: $i] :
            ( ~ ( less_than @ ( add @ ( absolute @ SV15 ) @ ( absolute @ SV19 ) ) @ SY40 )
            | ( less_than @ ( absolute @ ( add @ SV15 @ SV19 ) ) @ SY40 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(94,plain,
    ! [SV16: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV16 ) )
        = $true )
      | ( ( less_than @ n0 @ ( half @ SV16 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[79]) ).

thf(95,plain,
    ! [SV1: $i] :
      ( ( ( less_than @ n0 @ SV1 )
        = $false )
      | ( ( less_than @ n0 @ ( fp31 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[81]) ).

thf(96,plain,
    ! [SV2: $i] :
      ( ( ( less_than @ n0 @ SV2 )
        = $false )
      | ( ( ! [SY27: $i] :
              ( ~ ( less_than @ ( absolute @ ( add @ SY27 @ ( minus @ a ) ) ) @ ( fp31 @ SV2 ) )
              | ( less_than @ ( absolute @ ( add @ ( f @ SY27 ) @ ( minus @ l1 ) ) ) @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(97,plain,
    ! [SV3: $i] :
      ( ( ( less_than @ n0 @ SV3 )
        = $false )
      | ( ( less_than @ n0 @ ( fp32 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[83]) ).

thf(98,plain,
    ! [SV4: $i] :
      ( ( ( less_than @ n0 @ SV4 )
        = $false )
      | ( ( ! [SY28: $i] :
              ( ~ ( less_than @ ( absolute @ ( add @ SY28 @ ( minus @ a ) ) ) @ ( fp32 @ SV4 ) )
              | ( less_than @ ( absolute @ ( add @ ( g @ SY28 ) @ ( minus @ l2 ) ) ) @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(99,plain,
    ! [SV5: $i] :
      ( ( ( less_than @ n0 @ SV5 )
        = $false )
      | ( ( less_than @ ( absolute @ ( add @ ( fp33 @ SV5 ) @ ( minus @ a ) ) ) @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(100,plain,
    ! [SV6: $i] :
      ( ( ( less_than @ n0 @ SV6 )
        = $false )
      | ( ( ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ SV6 ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ SV6 ) ) @ ( minus @ l2 ) ) ) ) @ b ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[86]) ).

thf(101,plain,
    ! [SV17: $i,SV10: $i] :
      ( ( ( ~ ( less_than @ SV10 @ SV17 ) )
        = $true )
      | ( ( ! [SY38: $i] :
              ( ~ ( less_than @ SV17 @ SY38 )
              | ( less_than @ SV10 @ SY38 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(102,plain,
    ! [SV11: $i] :
      ( ( ( less_than @ n0 @ SV11 )
        = $false )
      | ( ( ! [SY31: $i] :
              ( ~ ( less_than @ n0 @ SY31 )
              | ( less_than @ n0 @ ( minimum @ SV11 @ SY31 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[89]) ).

thf(103,plain,
    ! [SV12: $i] :
      ( ( ( less_than @ n0 @ SV12 )
        = $false )
      | ( ( ! [SY32: $i] :
              ( ~ ( less_than @ n0 @ SY32 )
              | ( less_than @ ( minimum @ SV12 @ SY32 ) @ SV12 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(104,plain,
    ! [SV13: $i] :
      ( ( ( less_than @ n0 @ SV13 )
        = $false )
      | ( ( ! [SY33: $i] :
              ( ~ ( less_than @ n0 @ SY33 )
              | ( less_than @ ( minimum @ SV13 @ SY33 ) @ SY33 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[91]) ).

thf(105,plain,
    ! [SV18: $i,SV14: $i] :
      ( ( ( ~ ( less_than @ SV14 @ ( half @ SV18 ) ) )
        = $true )
      | ( ( ! [SY39: $i] :
              ( ~ ( less_than @ SY39 @ ( half @ SV18 ) )
              | ( less_than @ ( add @ SV14 @ SY39 ) @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[92]) ).

thf(106,plain,
    ! [SV20: $i,SV19: $i,SV15: $i] :
      ( ( ~ ( less_than @ ( add @ ( absolute @ SV15 ) @ ( absolute @ SV19 ) ) @ SV20 )
        | ( less_than @ ( absolute @ ( add @ SV15 @ SV19 ) ) @ SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(107,plain,
    ! [SV16: $i] :
      ( ( ( less_than @ n0 @ SV16 )
        = $false )
      | ( ( less_than @ n0 @ ( half @ SV16 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(108,plain,
    ! [SV2: $i,SV21: $i] :
      ( ( ( ~ ( less_than @ ( absolute @ ( add @ SV21 @ ( minus @ a ) ) ) @ ( fp31 @ SV2 ) )
          | ( less_than @ ( absolute @ ( add @ ( f @ SV21 ) @ ( minus @ l1 ) ) ) @ SV2 ) )
        = $true )
      | ( ( less_than @ n0 @ SV2 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(109,plain,
    ! [SV4: $i,SV22: $i] :
      ( ( ( ~ ( less_than @ ( absolute @ ( add @ SV22 @ ( minus @ a ) ) ) @ ( fp32 @ SV4 ) )
          | ( less_than @ ( absolute @ ( add @ ( g @ SV22 ) @ ( minus @ l2 ) ) ) @ SV4 ) )
        = $true )
      | ( ( less_than @ n0 @ SV4 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(110,plain,
    ! [SV6: $i] :
      ( ( ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ SV6 ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ SV6 ) ) @ ( minus @ l2 ) ) ) ) @ b )
        = $false )
      | ( ( less_than @ n0 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(111,plain,
    ! [SV17: $i,SV10: $i] :
      ( ( ( less_than @ SV10 @ SV17 )
        = $false )
      | ( ( ! [SY38: $i] :
              ( ~ ( less_than @ SV17 @ SY38 )
              | ( less_than @ SV10 @ SY38 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[101]) ).

thf(112,plain,
    ! [SV11: $i,SV23: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV23 )
          | ( less_than @ n0 @ ( minimum @ SV11 @ SV23 ) ) )
        = $true )
      | ( ( less_than @ n0 @ SV11 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[102]) ).

thf(113,plain,
    ! [SV12: $i,SV24: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV24 )
          | ( less_than @ ( minimum @ SV12 @ SV24 ) @ SV12 ) )
        = $true )
      | ( ( less_than @ n0 @ SV12 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(114,plain,
    ! [SV13: $i,SV25: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV25 )
          | ( less_than @ ( minimum @ SV13 @ SV25 ) @ SV25 ) )
        = $true )
      | ( ( less_than @ n0 @ SV13 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[104]) ).

thf(115,plain,
    ! [SV18: $i,SV14: $i] :
      ( ( ( less_than @ SV14 @ ( half @ SV18 ) )
        = $false )
      | ( ( ! [SY39: $i] :
              ( ~ ( less_than @ SY39 @ ( half @ SV18 ) )
              | ( less_than @ ( add @ SV14 @ SY39 ) @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[105]) ).

thf(116,plain,
    ! [SV20: $i,SV19: $i,SV15: $i] :
      ( ( ( ~ ( less_than @ ( add @ ( absolute @ SV15 ) @ ( absolute @ SV19 ) ) @ SV20 ) )
        = $true )
      | ( ( less_than @ ( absolute @ ( add @ SV15 @ SV19 ) ) @ SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[106]) ).

thf(117,plain,
    ! [SV2: $i,SV21: $i] :
      ( ( ( ~ ( less_than @ ( absolute @ ( add @ SV21 @ ( minus @ a ) ) ) @ ( fp31 @ SV2 ) ) )
        = $true )
      | ( ( less_than @ ( absolute @ ( add @ ( f @ SV21 ) @ ( minus @ l1 ) ) ) @ SV2 )
        = $true )
      | ( ( less_than @ n0 @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[108]) ).

thf(118,plain,
    ! [SV4: $i,SV22: $i] :
      ( ( ( ~ ( less_than @ ( absolute @ ( add @ SV22 @ ( minus @ a ) ) ) @ ( fp32 @ SV4 ) ) )
        = $true )
      | ( ( less_than @ ( absolute @ ( add @ ( g @ SV22 ) @ ( minus @ l2 ) ) ) @ SV4 )
        = $true )
      | ( ( less_than @ n0 @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[109]) ).

thf(119,plain,
    ! [SV10: $i,SV26: $i,SV17: $i] :
      ( ( ( ~ ( less_than @ SV17 @ SV26 )
          | ( less_than @ SV10 @ SV26 ) )
        = $true )
      | ( ( less_than @ SV10 @ SV17 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[111]) ).

thf(120,plain,
    ! [SV11: $i,SV23: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV23 ) )
        = $true )
      | ( ( less_than @ n0 @ ( minimum @ SV11 @ SV23 ) )
        = $true )
      | ( ( less_than @ n0 @ SV11 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[112]) ).

thf(121,plain,
    ! [SV12: $i,SV24: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV24 ) )
        = $true )
      | ( ( less_than @ ( minimum @ SV12 @ SV24 ) @ SV12 )
        = $true )
      | ( ( less_than @ n0 @ SV12 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[113]) ).

thf(122,plain,
    ! [SV13: $i,SV25: $i] :
      ( ( ( ~ ( less_than @ n0 @ SV25 ) )
        = $true )
      | ( ( less_than @ ( minimum @ SV13 @ SV25 ) @ SV25 )
        = $true )
      | ( ( less_than @ n0 @ SV13 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[114]) ).

thf(123,plain,
    ! [SV14: $i,SV18: $i,SV27: $i] :
      ( ( ( ~ ( less_than @ SV27 @ ( half @ SV18 ) )
          | ( less_than @ ( add @ SV14 @ SV27 ) @ SV18 ) )
        = $true )
      | ( ( less_than @ SV14 @ ( half @ SV18 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(124,plain,
    ! [SV20: $i,SV19: $i,SV15: $i] :
      ( ( ( less_than @ ( add @ ( absolute @ SV15 ) @ ( absolute @ SV19 ) ) @ SV20 )
        = $false )
      | ( ( less_than @ ( absolute @ ( add @ SV15 @ SV19 ) ) @ SV20 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[116]) ).

thf(125,plain,
    ! [SV2: $i,SV21: $i] :
      ( ( ( less_than @ ( absolute @ ( add @ SV21 @ ( minus @ a ) ) ) @ ( fp31 @ SV2 ) )
        = $false )
      | ( ( less_than @ ( absolute @ ( add @ ( f @ SV21 ) @ ( minus @ l1 ) ) ) @ SV2 )
        = $true )
      | ( ( less_than @ n0 @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[117]) ).

thf(126,plain,
    ! [SV4: $i,SV22: $i] :
      ( ( ( less_than @ ( absolute @ ( add @ SV22 @ ( minus @ a ) ) ) @ ( fp32 @ SV4 ) )
        = $false )
      | ( ( less_than @ ( absolute @ ( add @ ( g @ SV22 ) @ ( minus @ l2 ) ) ) @ SV4 )
        = $true )
      | ( ( less_than @ n0 @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(127,plain,
    ! [SV10: $i,SV26: $i,SV17: $i] :
      ( ( ( ~ ( less_than @ SV17 @ SV26 ) )
        = $true )
      | ( ( less_than @ SV10 @ SV26 )
        = $true )
      | ( ( less_than @ SV10 @ SV17 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[119]) ).

thf(128,plain,
    ! [SV11: $i,SV23: $i] :
      ( ( ( less_than @ n0 @ SV23 )
        = $false )
      | ( ( less_than @ n0 @ ( minimum @ SV11 @ SV23 ) )
        = $true )
      | ( ( less_than @ n0 @ SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[120]) ).

thf(129,plain,
    ! [SV12: $i,SV24: $i] :
      ( ( ( less_than @ n0 @ SV24 )
        = $false )
      | ( ( less_than @ ( minimum @ SV12 @ SV24 ) @ SV12 )
        = $true )
      | ( ( less_than @ n0 @ SV12 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(130,plain,
    ! [SV13: $i,SV25: $i] :
      ( ( ( less_than @ n0 @ SV25 )
        = $false )
      | ( ( less_than @ ( minimum @ SV13 @ SV25 ) @ SV25 )
        = $true )
      | ( ( less_than @ n0 @ SV13 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[122]) ).

thf(131,plain,
    ! [SV14: $i,SV18: $i,SV27: $i] :
      ( ( ( ~ ( less_than @ SV27 @ ( half @ SV18 ) ) )
        = $true )
      | ( ( less_than @ ( add @ SV14 @ SV27 ) @ SV18 )
        = $true )
      | ( ( less_than @ SV14 @ ( half @ SV18 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[123]) ).

thf(132,plain,
    ! [SV10: $i,SV26: $i,SV17: $i] :
      ( ( ( less_than @ SV17 @ SV26 )
        = $false )
      | ( ( less_than @ SV10 @ SV26 )
        = $true )
      | ( ( less_than @ SV10 @ SV17 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[127]) ).

thf(133,plain,
    ! [SV14: $i,SV18: $i,SV27: $i] :
      ( ( ( less_than @ SV27 @ ( half @ SV18 ) )
        = $false )
      | ( ( less_than @ ( add @ SV14 @ SV27 ) @ SV18 )
        = $true )
      | ( ( less_than @ SV14 @ ( half @ SV18 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[131]) ).

thf(134,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[50,133,132,130,129,128,126,125,124,110,107,99,97,95,87,80,71,70]) ).

thf(135,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[134]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : ANA003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Fri Jul  8 06:46:39 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  
% 0.14/0.36   No.of.Axioms: 17
% 0.14/0.36  
% 0.14/0.36   Length.of.Defs: 0
% 0.14/0.36  
% 0.14/0.36   Contains.Choice.Funs: false
% 0.14/0.37  (rf:0,axioms:17,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:19,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.77/0.97  
% 0.77/0.97  ********************************
% 0.77/0.97  *   All subproblems solved!    *
% 0.77/0.97  ********************************
% 0.77/0.97  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:17,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:134,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.77/0.97  
% 0.77/0.97  %**** Beginning of derivation protocol ****
% 0.77/0.97  % SZS output start CNFRefutation
% See solution above
% 0.77/0.97  
% 0.77/0.97  %**** End of derivation protocol ****
% 0.77/0.97  %**** no. of clauses in derivation: 135 ****
% 0.77/0.97  %**** clause counter: 134 ****
% 0.77/0.97  
% 0.77/0.97  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:17,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:134,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------