TSTP Solution File: NUM025-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM025-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 11:46:28 EDT 2022

% Result   : Unsatisfiable 0.23s 0.44s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  113 (  77 unt;   9 typ;   0 def)
%            Number of atoms       :  404 ( 110 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  680 (  75   ~;  80   |;   0   &; 525   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  188 (   0   ^ 188   !;   0   ?; 188   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $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_less,type,
    less: $i > $i > $o ).

thf(tp_multiply,type,
    multiply: $i > $i > $i ).

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

thf(tp_predecessor_of_1st_minus_2nd,type,
    predecessor_of_1st_minus_2nd: $i > $i > $i ).

thf(tp_successor,type,
    successor: $i > $i ).

thf(1,axiom,
    ! [A: $i] :
      ~ ( less @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_number_less_than_itself) ).

thf(2,axiom,
    ! [A: $i] :
      ~ ( equalish @ ( successor @ A ) @ n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_the_first_number) ).

thf(3,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( equalish @ X @ Y )
      | ~ ( equalish @ Y @ Z )
      | ( equalish @ X @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).

thf(4,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( equalish @ X @ Y )
      | ( equalish @ Y @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).

thf(5,axiom,
    ! [X: $i] : ( equalish @ X @ X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( less @ A @ B )
      | ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_lemma) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
      | ( less @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_number) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( less @ A @ B )
      | ~ ( less @ C @ A )
      | ( less @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( equalish @ A @ B )
      | ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_substitution) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
      | ( equalish @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_equality1) ).

thf(11,axiom,
    ! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).

thf(12,axiom,
    ! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).

thf(13,axiom,
    ! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition) ).

thf(14,axiom,
    ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',adding_zero) ).

thf(15,axiom,
    less @ a @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_less_than_b) ).

thf(16,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(17,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[16]) ).

thf(18,negated_conjecture,
    less @ b @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_not_less_than_a) ).

thf(19,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ! [A: $i] :
          ~ ( less @ A @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(21,plain,
    ( ( ! [A: $i] :
          ~ ( equalish @ ( successor @ A ) @ n0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(22,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( equalish @ X @ Y )
          | ~ ( equalish @ Y @ Z )
          | ( equalish @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(23,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ( equalish @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(24,plain,
    ( ( ! [X: $i] : ( equalish @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(25,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( less @ A @ B )
          | ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(26,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
          | ( less @ B @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(27,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( less @ A @ B )
          | ~ ( less @ C @ A )
          | ( less @ C @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(28,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( equalish @ A @ B )
          | ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(29,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
          | ( equalish @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(30,plain,
    ( ( ! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(31,plain,
    ( ( ! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(32,plain,
    ( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(33,plain,
    ( ( ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(34,plain,
    ( ( less @ a @ b )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(35,plain,
    ( ( less @ b @ a )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(36,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[19]) ).

thf(37,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( equalish @ Y @ Z )
              | ( equalish @ X @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[22]) ).

thf(38,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( less @ A @ B )
          | ! [C: $i] :
              ( ~ ( less @ C @ A )
              | ( less @ C @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(39,plain,
    ( ( less @ b @ a )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(40,plain,
    ( ( less @ a @ b )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(41,plain,
    ( ( ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(42,plain,
    ( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(43,plain,
    ( ( ! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(44,plain,
    ( ( ! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(45,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
          | ( equalish @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(46,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( equalish @ A @ B )
          | ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(47,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( less @ A @ B )
          | ! [C: $i] :
              ( ~ ( less @ C @ A )
              | ( less @ C @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(48,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
          | ( less @ B @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(49,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( less @ A @ B )
          | ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(50,plain,
    ( ( ! [X: $i] : ( equalish @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(51,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ( equalish @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(52,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( equalish @ Y @ Z )
              | ( equalish @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(53,plain,
    ( ( ! [A: $i] :
          ~ ( equalish @ ( successor @ A ) @ n0 ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(54,plain,
    ( ( ! [A: $i] :
          ~ ( less @ A @ A ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(55,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(56,plain,
    ! [SV1: $i] :
      ( ( equalish @ ( add @ SV1 @ n0 ) @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(57,plain,
    ! [SV2: $i] :
      ( ( ! [SY26: $i] : ( equalish @ ( add @ SV2 @ ( successor @ SY26 ) ) @ ( successor @ ( add @ SV2 @ SY26 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(58,plain,
    ! [SV3: $i] :
      ( ( equalish @ ( multiply @ SV3 @ n0 ) @ n0 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(59,plain,
    ! [SV4: $i] :
      ( ( ! [SY27: $i] : ( equalish @ ( multiply @ SV4 @ ( successor @ SY27 ) ) @ ( add @ ( multiply @ SV4 @ SY27 ) @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(60,plain,
    ! [SV5: $i] :
      ( ( ! [SY28: $i] :
            ( ~ ( equalish @ ( successor @ SV5 ) @ ( successor @ SY28 ) )
            | ( equalish @ SV5 @ SY28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(61,plain,
    ! [SV6: $i] :
      ( ( ! [SY29: $i] :
            ( ~ ( equalish @ SV6 @ SY29 )
            | ( equalish @ ( successor @ SV6 ) @ ( successor @ SY29 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(62,plain,
    ! [SV7: $i] :
      ( ( ! [SY30: $i] :
            ( ~ ( less @ SV7 @ SY30 )
            | ! [SY31: $i] :
                ( ~ ( less @ SY31 @ SV7 )
                | ( less @ SY31 @ SY30 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(63,plain,
    ! [SV8: $i] :
      ( ( ! [SY32: $i,SY33: $i] :
            ( ~ ( equalish @ ( add @ ( successor @ SV8 ) @ SY32 ) @ SY33 )
            | ( less @ SY32 @ SY33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(64,plain,
    ! [SV9: $i] :
      ( ( ! [SY34: $i] :
            ( ~ ( less @ SV9 @ SY34 )
            | ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ SY34 @ SV9 ) ) @ SV9 ) @ SY34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(65,plain,
    ! [SV10: $i] :
      ( ( equalish @ SV10 @ SV10 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(66,plain,
    ! [SV11: $i] :
      ( ( ! [SY35: $i] :
            ( ~ ( equalish @ SV11 @ SY35 )
            | ( equalish @ SY35 @ SV11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(67,plain,
    ! [SV12: $i] :
      ( ( ! [SY36: $i] :
            ( ~ ( equalish @ SV12 @ SY36 )
            | ! [SY37: $i] :
                ( ~ ( equalish @ SY36 @ SY37 )
                | ( equalish @ SV12 @ SY37 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(68,plain,
    ! [SV13: $i] :
      ( ( ~ ( equalish @ ( successor @ SV13 ) @ n0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(69,plain,
    ! [SV14: $i] :
      ( ( ~ ( less @ SV14 @ SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(70,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(71,plain,
    ! [SV15: $i,SV2: $i] :
      ( ( equalish @ ( add @ SV2 @ ( successor @ SV15 ) ) @ ( successor @ ( add @ SV2 @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(72,plain,
    ! [SV16: $i,SV4: $i] :
      ( ( equalish @ ( multiply @ SV4 @ ( successor @ SV16 ) ) @ ( add @ ( multiply @ SV4 @ SV16 ) @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(73,plain,
    ! [SV17: $i,SV5: $i] :
      ( ( ~ ( equalish @ ( successor @ SV5 ) @ ( successor @ SV17 ) )
        | ( equalish @ SV5 @ SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(74,plain,
    ! [SV18: $i,SV6: $i] :
      ( ( ~ ( equalish @ SV6 @ SV18 )
        | ( equalish @ ( successor @ SV6 ) @ ( successor @ SV18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(75,plain,
    ! [SV19: $i,SV7: $i] :
      ( ( ~ ( less @ SV7 @ SV19 )
        | ! [SY38: $i] :
            ( ~ ( less @ SY38 @ SV7 )
            | ( less @ SY38 @ SV19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(76,plain,
    ! [SV20: $i,SV8: $i] :
      ( ( ! [SY39: $i] :
            ( ~ ( equalish @ ( add @ ( successor @ SV8 ) @ SV20 ) @ SY39 )
            | ( less @ SV20 @ SY39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(77,plain,
    ! [SV21: $i,SV9: $i] :
      ( ( ~ ( less @ SV9 @ SV21 )
        | ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ SV21 @ SV9 ) ) @ SV9 ) @ SV21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(78,plain,
    ! [SV22: $i,SV11: $i] :
      ( ( ~ ( equalish @ SV11 @ SV22 )
        | ( equalish @ SV22 @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(79,plain,
    ! [SV23: $i,SV12: $i] :
      ( ( ~ ( equalish @ SV12 @ SV23 )
        | ! [SY40: $i] :
            ( ~ ( equalish @ SV23 @ SY40 )
            | ( equalish @ SV12 @ SY40 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(80,plain,
    ! [SV13: $i] :
      ( ( equalish @ ( successor @ SV13 ) @ n0 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(81,plain,
    ! [SV14: $i] :
      ( ( less @ SV14 @ SV14 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(82,plain,
    ! [SV17: $i,SV5: $i] :
      ( ( ( ~ ( equalish @ ( successor @ SV5 ) @ ( successor @ SV17 ) ) )
        = $true )
      | ( ( equalish @ SV5 @ SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(83,plain,
    ! [SV18: $i,SV6: $i] :
      ( ( ( ~ ( equalish @ SV6 @ SV18 ) )
        = $true )
      | ( ( equalish @ ( successor @ SV6 ) @ ( successor @ SV18 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[74]) ).

thf(84,plain,
    ! [SV19: $i,SV7: $i] :
      ( ( ( ~ ( less @ SV7 @ SV19 ) )
        = $true )
      | ( ( ! [SY38: $i] :
              ( ~ ( less @ SY38 @ SV7 )
              | ( less @ SY38 @ SV19 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[75]) ).

thf(85,plain,
    ! [SV24: $i,SV20: $i,SV8: $i] :
      ( ( ~ ( equalish @ ( add @ ( successor @ SV8 ) @ SV20 ) @ SV24 )
        | ( less @ SV20 @ SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(86,plain,
    ! [SV21: $i,SV9: $i] :
      ( ( ( ~ ( less @ SV9 @ SV21 ) )
        = $true )
      | ( ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ SV21 @ SV9 ) ) @ SV9 ) @ SV21 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[77]) ).

thf(87,plain,
    ! [SV22: $i,SV11: $i] :
      ( ( ( ~ ( equalish @ SV11 @ SV22 ) )
        = $true )
      | ( ( equalish @ SV22 @ SV11 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[78]) ).

thf(88,plain,
    ! [SV23: $i,SV12: $i] :
      ( ( ( ~ ( equalish @ SV12 @ SV23 ) )
        = $true )
      | ( ( ! [SY40: $i] :
              ( ~ ( equalish @ SV23 @ SY40 )
              | ( equalish @ SV12 @ SY40 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[79]) ).

thf(89,plain,
    ! [SV17: $i,SV5: $i] :
      ( ( ( equalish @ ( successor @ SV5 ) @ ( successor @ SV17 ) )
        = $false )
      | ( ( equalish @ SV5 @ SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(90,plain,
    ! [SV18: $i,SV6: $i] :
      ( ( ( equalish @ SV6 @ SV18 )
        = $false )
      | ( ( equalish @ ( successor @ SV6 ) @ ( successor @ SV18 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[83]) ).

thf(91,plain,
    ! [SV19: $i,SV7: $i] :
      ( ( ( less @ SV7 @ SV19 )
        = $false )
      | ( ( ! [SY38: $i] :
              ( ~ ( less @ SY38 @ SV7 )
              | ( less @ SY38 @ SV19 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(92,plain,
    ! [SV24: $i,SV20: $i,SV8: $i] :
      ( ( ( ~ ( equalish @ ( add @ ( successor @ SV8 ) @ SV20 ) @ SV24 ) )
        = $true )
      | ( ( less @ SV20 @ SV24 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[85]) ).

thf(93,plain,
    ! [SV21: $i,SV9: $i] :
      ( ( ( less @ SV9 @ SV21 )
        = $false )
      | ( ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ SV21 @ SV9 ) ) @ SV9 ) @ SV21 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[86]) ).

thf(94,plain,
    ! [SV22: $i,SV11: $i] :
      ( ( ( equalish @ SV11 @ SV22 )
        = $false )
      | ( ( equalish @ SV22 @ SV11 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[87]) ).

thf(95,plain,
    ! [SV23: $i,SV12: $i] :
      ( ( ( equalish @ SV12 @ SV23 )
        = $false )
      | ( ( ! [SY40: $i] :
              ( ~ ( equalish @ SV23 @ SY40 )
              | ( equalish @ SV12 @ SY40 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[88]) ).

thf(96,plain,
    ! [SV19: $i,SV7: $i,SV25: $i] :
      ( ( ( ~ ( less @ SV25 @ SV7 )
          | ( less @ SV25 @ SV19 ) )
        = $true )
      | ( ( less @ SV7 @ SV19 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(97,plain,
    ! [SV24: $i,SV20: $i,SV8: $i] :
      ( ( ( equalish @ ( add @ ( successor @ SV8 ) @ SV20 ) @ SV24 )
        = $false )
      | ( ( less @ SV20 @ SV24 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[92]) ).

thf(98,plain,
    ! [SV12: $i,SV26: $i,SV23: $i] :
      ( ( ( ~ ( equalish @ SV23 @ SV26 )
          | ( equalish @ SV12 @ SV26 ) )
        = $true )
      | ( ( equalish @ SV12 @ SV23 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(99,plain,
    ! [SV19: $i,SV7: $i,SV25: $i] :
      ( ( ( ~ ( less @ SV25 @ SV7 ) )
        = $true )
      | ( ( less @ SV25 @ SV19 )
        = $true )
      | ( ( less @ SV7 @ SV19 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[96]) ).

thf(100,plain,
    ! [SV12: $i,SV26: $i,SV23: $i] :
      ( ( ( ~ ( equalish @ SV23 @ SV26 ) )
        = $true )
      | ( ( equalish @ SV12 @ SV26 )
        = $true )
      | ( ( equalish @ SV12 @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[98]) ).

thf(101,plain,
    ! [SV19: $i,SV7: $i,SV25: $i] :
      ( ( ( less @ SV25 @ SV7 )
        = $false )
      | ( ( less @ SV25 @ SV19 )
        = $true )
      | ( ( less @ SV7 @ SV19 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(102,plain,
    ! [SV12: $i,SV26: $i,SV23: $i] :
      ( ( ( equalish @ SV23 @ SV26 )
        = $false )
      | ( ( equalish @ SV12 @ SV26 )
        = $true )
      | ( ( equalish @ SV12 @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(103,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[39,102,101,97,94,93,90,89,81,80,72,71,70,65,58,56,40]) ).

thf(104,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[103]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : NUM025-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.08/0.15  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.37  % Computer : n013.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Tue Jul  5 13:55:14 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.15/0.38  
% 0.15/0.38   No.of.Axioms: 16
% 0.15/0.38  
% 0.15/0.38   Length.of.Defs: 0
% 0.15/0.38  
% 0.15/0.38   Contains.Choice.Funs: false
% 0.15/0.38  (rf:0,axioms:16,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:18,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.23/0.44  
% 0.23/0.44  ********************************
% 0.23/0.44  *   All subproblems solved!    *
% 0.23/0.44  ********************************
% 0.23/0.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,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:103,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.23/0.44  
% 0.23/0.44  %**** Beginning of derivation protocol ****
% 0.23/0.44  % SZS output start CNFRefutation
% See solution above
% 0.23/0.44  
% 0.23/0.44  %**** End of derivation protocol ****
% 0.23/0.44  %**** no. of clauses in derivation: 104 ****
% 0.23/0.44  %**** clause counter: 103 ****
% 0.23/0.44  
% 0.23/0.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,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:103,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------