TSTP Solution File: ITP209^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ITP209^1 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n022.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 : Sat Jul 16 23:45:04 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  144 (  60 unt;  16 typ;   0 def)
%            Number of atoms       :  730 ( 426 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives : 2069 ( 186   ~; 163   |;   3   &;1705   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  235 ( 235   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   5 con; 0-2 aty)
%            Number of variables   :  507 (   5   ^ 502   !;   0   ?; 507   :)

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

thf(tp_a2,type,
    a2: a ).

thf(tp_b,type,
    b: a ).

thf(tp_c,type,
    c: a ).

thf(tp_f,type,
    f: a > a > a ).

thf(tp_sK10_SY84,type,
    sK10_SY84: ( a > a > a ) > a ).

thf(tp_sK1_A2,type,
    sK1_A2: ( a > a > a ) > a ).

thf(tp_sK2_SY35,type,
    sK2_SY35: ( a > a > a ) > a ).

thf(tp_sK3_A2,type,
    sK3_A2: ( a > a > a ) > a ).

thf(tp_sK4_SY36,type,
    sK4_SY36: ( a > a > a ) > a ).

thf(tp_sK5_SY38,type,
    sK5_SY38: ( a > a > a ) > a ).

thf(tp_sK6_SY68,type,
    sK6_SY68: ( a > a > a ) > a ).

thf(tp_sK7_SY77,type,
    sK7_SY77: ( a > a > a ) > a ).

thf(tp_sK8_SY79,type,
    sK8_SY79: ( a > a > a ) > a ).

thf(tp_sK9_SY71,type,
    sK9_SY71: ( a > a > a ) > a ).

thf(tp_syntax_ac_operator_a,type,
    syntax_ac_operator_a: ( a > a > a ) > $o ).

thf(1,axiom,
    ( syntax_ac_operator_a
    = ( ^ [F2: a > a > a] :
          ( ! [A3: a,B3: a,C3: a] :
              ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
              = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) )
          & ! [A3: a,B3: a] :
              ( ( F2 @ A3 @ B3 )
              = ( F2 @ B3 @ A3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_ac__operator__def) ).

thf(2,axiom,
    ! [F: a > a > a,A: a,B: a,C: a] :
      ( ( syntax_ac_operator_a @ F )
     => ( ( F @ A @ ( F @ B @ C ) )
        = ( F @ B @ ( F @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_ac__operator_Oleft__commute) ).

thf(3,axiom,
    ! [F: a > a > a,A: a,B: a,C: a] :
      ( ( syntax_ac_operator_a @ F )
     => ( ( F @ ( F @ A @ B ) @ C )
        = ( F @ A @ ( F @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_ac__operator_Oright__assoc) ).

thf(4,axiom,
    ! [F: a > a > a,A: a,B: a,C: a] :
      ( ( syntax_ac_operator_a @ F )
     => ( ( F @ A @ ( F @ B @ C ) )
        = ( F @ ( F @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_ac__operator_Oleft__assoc) ).

thf(5,axiom,
    ! [F: a > a > a,A: a,B: a] :
      ( ( syntax_ac_operator_a @ F )
     => ( ( F @ A @ B )
        = ( F @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_ac__operator_Ocommute) ).

thf(6,axiom,
    ! [F: a > a > a] :
      ( ! [A2: a,B2: a,C2: a] :
          ( ( F @ ( F @ A2 @ B2 ) @ C2 )
          = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
     => ( ! [A2: a,B2: a] :
            ( ( F @ A2 @ B2 )
            = ( F @ B2 @ A2 ) )
       => ( syntax_ac_operator_a @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ac__operator_Ointro) ).

thf(7,axiom,
    ! [A: a,B: a,C: a] :
      ( ( f @ ( f @ A @ B ) @ C )
      = ( f @ A @ ( f @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_right__assoc) ).

thf(8,axiom,
    ! [A: a,B: a,C: a] :
      ( ( f @ A @ ( f @ B @ C ) )
      = ( f @ B @ ( f @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_left__commute) ).

thf(9,axiom,
    ! [A: a,B: a] :
      ( ( f @ A @ B )
      = ( f @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_commute) ).

thf(10,axiom,
    syntax_ac_operator_a @ f,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ac__operator__axioms) ).

thf(11,conjecture,
    ( ( f @ ( f @ a2 @ b ) @ c )
    = ( f @ ( f @ a2 @ c ) @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(12,negated_conjecture,
    ( ( ( f @ ( f @ a2 @ b ) @ c )
      = ( f @ ( f @ a2 @ c ) @ b ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[11]) ).

thf(13,plain,
    ( ( ( f @ ( f @ a2 @ b ) @ c )
      = ( f @ ( f @ a2 @ c ) @ b ) )
    = $false ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(14,plain,
    ( ( syntax_ac_operator_a
      = ( ^ [F2: a > a > a] :
            ( ! [A3: a,B3: a,C3: a] :
                ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
                = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) )
            & ! [A3: a,B3: a] :
                ( ( F2 @ A3 @ B3 )
                = ( F2 @ B3 @ A3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(15,plain,
    ( ( ! [F: a > a > a,A: a,B: a,C: a] :
          ( ( syntax_ac_operator_a @ F )
         => ( ( F @ A @ ( F @ B @ C ) )
            = ( F @ B @ ( F @ A @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(16,plain,
    ( ( ! [F: a > a > a,A: a,B: a,C: a] :
          ( ( syntax_ac_operator_a @ F )
         => ( ( F @ ( F @ A @ B ) @ C )
            = ( F @ A @ ( F @ B @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(17,plain,
    ( ( ! [F: a > a > a,A: a,B: a,C: a] :
          ( ( syntax_ac_operator_a @ F )
         => ( ( F @ A @ ( F @ B @ C ) )
            = ( F @ ( F @ A @ B ) @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(18,plain,
    ( ( ! [F: a > a > a,A: a,B: a] :
          ( ( syntax_ac_operator_a @ F )
         => ( ( F @ A @ B )
            = ( F @ B @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(19,plain,
    ( ( ! [F: a > a > a] :
          ( ! [A2: a,B2: a,C2: a] :
              ( ( F @ ( F @ A2 @ B2 ) @ C2 )
              = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
         => ( ! [A2: a,B2: a] :
                ( ( F @ A2 @ B2 )
                = ( F @ B2 @ A2 ) )
           => ( syntax_ac_operator_a @ F ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(20,plain,
    ( ( ! [A: a,B: a,C: a] :
          ( ( f @ ( f @ A @ B ) @ C )
          = ( f @ A @ ( f @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(21,plain,
    ( ( ! [A: a,B: a,C: a] :
          ( ( f @ A @ ( f @ B @ C ) )
          = ( f @ B @ ( f @ A @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(22,plain,
    ( ( ! [A: a,B: a] :
          ( ( f @ A @ B )
          = ( f @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(23,plain,
    ( ( syntax_ac_operator_a @ f )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(24,plain,
    ( ( ( ( f @ ( f @ a2 @ b ) @ c )
       != ( f @ ( f @ a2 @ c ) @ b ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[13]) ).

thf(25,plain,
    ( ( ! [F: a > a > a,A: a] :
          ( ~ ( syntax_ac_operator_a @ F )
          | ! [B: a,C: a] :
              ( ( F @ A @ ( F @ B @ C ) )
              = ( F @ B @ ( F @ A @ C ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(26,plain,
    ( ( ! [F: a > a > a,A: a] :
          ( ~ ( syntax_ac_operator_a @ F )
          | ! [B: a,C: a] :
              ( ( F @ ( F @ A @ B ) @ C )
              = ( F @ A @ ( F @ B @ C ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[16]) ).

thf(27,plain,
    ( ( ! [F: a > a > a,A: a] :
          ( ~ ( syntax_ac_operator_a @ F )
          | ! [B: a,C: a] :
              ( ( F @ A @ ( F @ B @ C ) )
              = ( F @ ( F @ A @ B ) @ C ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[17]) ).

thf(28,plain,
    ( ( ! [F: a > a > a] :
          ( ~ ( syntax_ac_operator_a @ F )
          | ! [A: a,B: a] :
              ( ( F @ A @ B )
              = ( F @ B @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(29,plain,
    ( ( ! [F: a > a > a] :
          ( ( ( F @ ( F @ ( sK3_A2 @ F ) @ ( sK4_SY36 @ F ) ) @ ( sK5_SY38 @ F ) )
           != ( F @ ( sK3_A2 @ F ) @ ( F @ ( sK4_SY36 @ F ) @ ( sK5_SY38 @ F ) ) ) )
          | ( ( F @ ( sK1_A2 @ F ) @ ( sK2_SY35 @ F ) )
           != ( F @ ( sK2_SY35 @ F ) @ ( sK1_A2 @ F ) ) )
          | ( syntax_ac_operator_a @ F ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(30,plain,
    ( ( syntax_ac_operator_a @ f )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(31,plain,
    ( ( ! [A: a,B: a] :
          ( ( f @ A @ B )
          = ( f @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(32,plain,
    ( ( ! [A: a,B: a,C: a] :
          ( ( f @ A @ ( f @ B @ C ) )
          = ( f @ B @ ( f @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(33,plain,
    ( ( ! [A: a,B: a,C: a] :
          ( ( f @ ( f @ A @ B ) @ C )
          = ( f @ A @ ( f @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(34,plain,
    ( ( ! [F: a > a > a] :
          ( ( ( F @ ( F @ ( sK3_A2 @ F ) @ ( sK4_SY36 @ F ) ) @ ( sK5_SY38 @ F ) )
           != ( F @ ( sK3_A2 @ F ) @ ( F @ ( sK4_SY36 @ F ) @ ( sK5_SY38 @ F ) ) ) )
          | ( ( F @ ( sK1_A2 @ F ) @ ( sK2_SY35 @ F ) )
           != ( F @ ( sK2_SY35 @ F ) @ ( sK1_A2 @ F ) ) )
          | ( syntax_ac_operator_a @ F ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(35,plain,
    ( ( ! [F: a > a > a] :
          ( ~ ( syntax_ac_operator_a @ F )
          | ! [A: a,B: a] :
              ( ( F @ A @ B )
              = ( F @ B @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(36,plain,
    ( ( ! [F: a > a > a,A: a] :
          ( ~ ( syntax_ac_operator_a @ F )
          | ! [B: a,C: a] :
              ( ( F @ A @ ( F @ B @ C ) )
              = ( F @ ( F @ A @ B ) @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(37,plain,
    ( ( ! [F: a > a > a,A: a] :
          ( ~ ( syntax_ac_operator_a @ F )
          | ! [B: a,C: a] :
              ( ( F @ ( F @ A @ B ) @ C )
              = ( F @ A @ ( F @ B @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(38,plain,
    ( ( ! [F: a > a > a,A: a] :
          ( ~ ( syntax_ac_operator_a @ F )
          | ! [B: a,C: a] :
              ( ( F @ A @ ( F @ B @ C ) )
              = ( F @ B @ ( F @ A @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(39,plain,
    ( ( syntax_ac_operator_a
      = ( ^ [F2: a > a > a] :
            ( ! [A3: a,B3: a,C3: a] :
                ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
                = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) )
            & ! [A3: a,B3: a] :
                ( ( F2 @ A3 @ B3 )
                = ( F2 @ B3 @ A3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(40,plain,
    ( ( ( ( f @ ( f @ a2 @ b ) @ c )
       != ( f @ ( f @ a2 @ c ) @ b ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(41,plain,
    ( ( syntax_ac_operator_a
      = ( ^ [SX0: a > a > a] :
            ~ ( ~ ! [SX1: a,SX2: a,SX3: a] :
                    ( ( SX0 @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
                    = ( SX0 @ SX1 @ ( SX0 @ SX2 @ SX3 ) ) )
              | ~ ! [SX1: a,SX2: a] :
                    ( ( SX0 @ SX1 @ SX2 )
                    = ( SX0 @ SX2 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(42,plain,
    ! [SV1: a] :
      ( ( ! [SY39: a] :
            ( ( f @ SV1 @ SY39 )
            = ( f @ SY39 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(43,plain,
    ! [SV2: a] :
      ( ( ! [SY40: a,SY41: a] :
            ( ( f @ SV2 @ ( f @ SY40 @ SY41 ) )
            = ( f @ SY40 @ ( f @ SV2 @ SY41 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(44,plain,
    ! [SV3: a] :
      ( ( ! [SY42: a,SY43: a] :
            ( ( f @ ( f @ SV3 @ SY42 ) @ SY43 )
            = ( f @ SV3 @ ( f @ SY42 @ SY43 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(45,plain,
    ! [SV4: a > a > a] :
      ( ( ( ( SV4 @ ( SV4 @ ( sK3_A2 @ SV4 ) @ ( sK4_SY36 @ SV4 ) ) @ ( sK5_SY38 @ SV4 ) )
         != ( SV4 @ ( sK3_A2 @ SV4 ) @ ( SV4 @ ( sK4_SY36 @ SV4 ) @ ( sK5_SY38 @ SV4 ) ) ) )
        | ( ( SV4 @ ( sK1_A2 @ SV4 ) @ ( sK2_SY35 @ SV4 ) )
         != ( SV4 @ ( sK2_SY35 @ SV4 ) @ ( sK1_A2 @ SV4 ) ) )
        | ( syntax_ac_operator_a @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(46,plain,
    ! [SV5: a > a > a] :
      ( ( ~ ( syntax_ac_operator_a @ SV5 )
        | ! [SY44: a,SY45: a] :
            ( ( SV5 @ SY44 @ SY45 )
            = ( SV5 @ SY45 @ SY44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(47,plain,
    ! [SV6: a > a > a] :
      ( ( ! [SY46: a] :
            ( ~ ( syntax_ac_operator_a @ SV6 )
            | ! [SY47: a,SY48: a] :
                ( ( SV6 @ SY46 @ ( SV6 @ SY47 @ SY48 ) )
                = ( SV6 @ ( SV6 @ SY46 @ SY47 ) @ SY48 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(48,plain,
    ! [SV7: a > a > a] :
      ( ( ! [SY49: a] :
            ( ~ ( syntax_ac_operator_a @ SV7 )
            | ! [SY50: a,SY51: a] :
                ( ( SV7 @ ( SV7 @ SY49 @ SY50 ) @ SY51 )
                = ( SV7 @ SY49 @ ( SV7 @ SY50 @ SY51 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(49,plain,
    ! [SV8: a > a > a] :
      ( ( ! [SY52: a] :
            ( ~ ( syntax_ac_operator_a @ SV8 )
            | ! [SY53: a,SY54: a] :
                ( ( SV8 @ SY52 @ ( SV8 @ SY53 @ SY54 ) )
                = ( SV8 @ SY53 @ ( SV8 @ SY52 @ SY54 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(50,plain,
    ( ( ( f @ ( f @ a2 @ b ) @ c )
      = ( f @ ( f @ a2 @ c ) @ b ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(51,plain,
    ( ( ! [SV9: a > a > a] :
          ( ( syntax_ac_operator_a @ SV9 )
          = ( ~ ( ~ ! [SY55: a,SY56: a,SY57: a] :
                      ( ( SV9 @ ( SV9 @ SY55 @ SY56 ) @ SY57 )
                      = ( SV9 @ SY55 @ ( SV9 @ SY56 @ SY57 ) ) )
                | ~ ! [SY58: a,SY59: a] :
                      ( ( SV9 @ SY58 @ SY59 )
                      = ( SV9 @ SY59 @ SY58 ) ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[41]) ).

thf(52,plain,
    ( ( syntax_ac_operator_a
      = ( ^ [SX0: a > a > a] :
            ~ ( ~ ! [SX1: a,SX2: a,SX3: a] :
                    ( ( SX0 @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
                    = ( SX0 @ SX1 @ ( SX0 @ SX2 @ SX3 ) ) )
              | ~ ! [SX1: a,SX2: a] :
                    ( ( SX0 @ SX1 @ SX2 )
                    = ( SX0 @ SX2 @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[41]) ).

thf(53,plain,
    ! [SV10: a,SV1: a] :
      ( ( ( f @ SV1 @ SV10 )
        = ( f @ SV10 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(54,plain,
    ! [SV11: a,SV2: a] :
      ( ( ! [SY60: a] :
            ( ( f @ SV2 @ ( f @ SV11 @ SY60 ) )
            = ( f @ SV11 @ ( f @ SV2 @ SY60 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(55,plain,
    ! [SV12: a,SV3: a] :
      ( ( ! [SY61: a] :
            ( ( f @ ( f @ SV3 @ SV12 ) @ SY61 )
            = ( f @ SV3 @ ( f @ SV12 @ SY61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(56,plain,
    ! [SV4: a > a > a] :
      ( ( ( ( ( SV4 @ ( SV4 @ ( sK3_A2 @ SV4 ) @ ( sK4_SY36 @ SV4 ) ) @ ( sK5_SY38 @ SV4 ) )
           != ( SV4 @ ( sK3_A2 @ SV4 ) @ ( SV4 @ ( sK4_SY36 @ SV4 ) @ ( sK5_SY38 @ SV4 ) ) ) ) )
        = $true )
      | ( ( ( ( SV4 @ ( sK1_A2 @ SV4 ) @ ( sK2_SY35 @ SV4 ) )
           != ( SV4 @ ( sK2_SY35 @ SV4 ) @ ( sK1_A2 @ SV4 ) ) )
          | ( syntax_ac_operator_a @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(57,plain,
    ! [SV5: a > a > a] :
      ( ( ( ~ ( syntax_ac_operator_a @ SV5 ) )
        = $true )
      | ( ( ! [SY44: a,SY45: a] :
              ( ( SV5 @ SY44 @ SY45 )
              = ( SV5 @ SY45 @ SY44 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(58,plain,
    ! [SV13: a,SV6: a > a > a] :
      ( ( ~ ( syntax_ac_operator_a @ SV6 )
        | ! [SY62: a,SY63: a] :
            ( ( SV6 @ SV13 @ ( SV6 @ SY62 @ SY63 ) )
            = ( SV6 @ ( SV6 @ SV13 @ SY62 ) @ SY63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(59,plain,
    ! [SV14: a,SV7: a > a > a] :
      ( ( ~ ( syntax_ac_operator_a @ SV7 )
        | ! [SY64: a,SY65: a] :
            ( ( SV7 @ ( SV7 @ SV14 @ SY64 ) @ SY65 )
            = ( SV7 @ SV14 @ ( SV7 @ SY64 @ SY65 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(60,plain,
    ! [SV15: a,SV8: a > a > a] :
      ( ( ~ ( syntax_ac_operator_a @ SV8 )
        | ! [SY66: a,SY67: a] :
            ( ( SV8 @ SV15 @ ( SV8 @ SY66 @ SY67 ) )
            = ( SV8 @ SY66 @ ( SV8 @ SV15 @ SY67 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(61,plain,
    ! [SV16: a > a > a] :
      ( ( ( syntax_ac_operator_a @ SV16 )
        = ( ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                    ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                    = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
              | ~ ! [SY71: a,SY72: a] :
                    ( ( SV16 @ SY71 @ SY72 )
                    = ( SV16 @ SY72 @ SY71 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(62,plain,
    ! [SV17: a,SV11: a,SV2: a] :
      ( ( ( f @ SV2 @ ( f @ SV11 @ SV17 ) )
        = ( f @ SV11 @ ( f @ SV2 @ SV17 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(63,plain,
    ! [SV18: a,SV12: a,SV3: a] :
      ( ( ( f @ ( f @ SV3 @ SV12 ) @ SV18 )
        = ( f @ SV3 @ ( f @ SV12 @ SV18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(64,plain,
    ! [SV4: a > a > a] :
      ( ( ( ( SV4 @ ( SV4 @ ( sK3_A2 @ SV4 ) @ ( sK4_SY36 @ SV4 ) ) @ ( sK5_SY38 @ SV4 ) )
          = ( SV4 @ ( sK3_A2 @ SV4 ) @ ( SV4 @ ( sK4_SY36 @ SV4 ) @ ( sK5_SY38 @ SV4 ) ) ) )
        = $false )
      | ( ( ( ( SV4 @ ( sK1_A2 @ SV4 ) @ ( sK2_SY35 @ SV4 ) )
           != ( SV4 @ ( sK2_SY35 @ SV4 ) @ ( sK1_A2 @ SV4 ) ) )
          | ( syntax_ac_operator_a @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(65,plain,
    ! [SV5: a > a > a] :
      ( ( ( syntax_ac_operator_a @ SV5 )
        = $false )
      | ( ( ! [SY44: a,SY45: a] :
              ( ( SV5 @ SY44 @ SY45 )
              = ( SV5 @ SY45 @ SY44 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(66,plain,
    ! [SV13: a,SV6: a > a > a] :
      ( ( ( ~ ( syntax_ac_operator_a @ SV6 ) )
        = $true )
      | ( ( ! [SY62: a,SY63: a] :
              ( ( SV6 @ SV13 @ ( SV6 @ SY62 @ SY63 ) )
              = ( SV6 @ ( SV6 @ SV13 @ SY62 ) @ SY63 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(67,plain,
    ! [SV14: a,SV7: a > a > a] :
      ( ( ( ~ ( syntax_ac_operator_a @ SV7 ) )
        = $true )
      | ( ( ! [SY64: a,SY65: a] :
              ( ( SV7 @ ( SV7 @ SV14 @ SY64 ) @ SY65 )
              = ( SV7 @ SV14 @ ( SV7 @ SY64 @ SY65 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(68,plain,
    ! [SV15: a,SV8: a > a > a] :
      ( ( ( ~ ( syntax_ac_operator_a @ SV8 ) )
        = $true )
      | ( ( ! [SY66: a,SY67: a] :
              ( ( SV8 @ SV15 @ ( SV8 @ SY66 @ SY67 ) )
              = ( SV8 @ SY66 @ ( SV8 @ SV15 @ SY67 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[60]) ).

thf(69,plain,
    ! [SV16: a > a > a] :
      ( ( ~ ( ( syntax_ac_operator_a @ SV16 )
            | ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                      ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                      = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                | ~ ! [SY71: a,SY72: a] :
                      ( ( SV16 @ SY71 @ SY72 )
                      = ( SV16 @ SY72 @ SY71 ) ) ) )
        | ~ ( ~ ( syntax_ac_operator_a @ SV16 )
            | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                        ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                        = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                  | ~ ! [SY71: a,SY72: a] :
                        ( ( SV16 @ SY71 @ SY72 )
                        = ( SV16 @ SY72 @ SY71 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[61]) ).

thf(70,plain,
    ! [SV16: a > a > a] :
      ( ( ( syntax_ac_operator_a @ SV16 )
        = ( ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                    ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                    = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
              | ~ ! [SY71: a,SY72: a] :
                    ( ( SV16 @ SY71 @ SY72 )
                    = ( SV16 @ SY72 @ SY71 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[61]) ).

thf(71,plain,
    ! [SV4: a > a > a] :
      ( ( ( ( ( SV4 @ ( sK1_A2 @ SV4 ) @ ( sK2_SY35 @ SV4 ) )
           != ( SV4 @ ( sK2_SY35 @ SV4 ) @ ( sK1_A2 @ SV4 ) ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV4 )
        = $true )
      | ( ( ( SV4 @ ( SV4 @ ( sK3_A2 @ SV4 ) @ ( sK4_SY36 @ SV4 ) ) @ ( sK5_SY38 @ SV4 ) )
          = ( SV4 @ ( sK3_A2 @ SV4 ) @ ( SV4 @ ( sK4_SY36 @ SV4 ) @ ( sK5_SY38 @ SV4 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(72,plain,
    ! [SV19: a,SV5: a > a > a] :
      ( ( ( ! [SY73: a] :
              ( ( SV5 @ SV19 @ SY73 )
              = ( SV5 @ SY73 @ SV19 ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(73,plain,
    ! [SV13: a,SV6: a > a > a] :
      ( ( ( syntax_ac_operator_a @ SV6 )
        = $false )
      | ( ( ! [SY62: a,SY63: a] :
              ( ( SV6 @ SV13 @ ( SV6 @ SY62 @ SY63 ) )
              = ( SV6 @ ( SV6 @ SV13 @ SY62 ) @ SY63 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[66]) ).

thf(74,plain,
    ! [SV14: a,SV7: a > a > a] :
      ( ( ( syntax_ac_operator_a @ SV7 )
        = $false )
      | ( ( ! [SY64: a,SY65: a] :
              ( ( SV7 @ ( SV7 @ SV14 @ SY64 ) @ SY65 )
              = ( SV7 @ SV14 @ ( SV7 @ SY64 @ SY65 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(75,plain,
    ! [SV15: a,SV8: a > a > a] :
      ( ( ( syntax_ac_operator_a @ SV8 )
        = $false )
      | ( ( ! [SY66: a,SY67: a] :
              ( ( SV8 @ SV15 @ ( SV8 @ SY66 @ SY67 ) )
              = ( SV8 @ SY66 @ ( SV8 @ SV15 @ SY67 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(76,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ( ( syntax_ac_operator_a @ SV16 )
              | ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                        ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                        = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                  | ~ ! [SY71: a,SY72: a] :
                        ( ( SV16 @ SY71 @ SY72 )
                        = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[69]) ).

thf(77,plain,
    ! [SV4: a > a > a] :
      ( ( ( ( SV4 @ ( sK1_A2 @ SV4 ) @ ( sK2_SY35 @ SV4 ) )
          = ( SV4 @ ( sK2_SY35 @ SV4 ) @ ( sK1_A2 @ SV4 ) ) )
        = $false )
      | ( ( syntax_ac_operator_a @ SV4 )
        = $true )
      | ( ( ( SV4 @ ( SV4 @ ( sK3_A2 @ SV4 ) @ ( sK4_SY36 @ SV4 ) ) @ ( sK5_SY38 @ SV4 ) )
          = ( SV4 @ ( sK3_A2 @ SV4 ) @ ( SV4 @ ( sK4_SY36 @ SV4 ) @ ( sK5_SY38 @ SV4 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(78,plain,
    ! [SV20: a,SV19: a,SV5: a > a > a] :
      ( ( ( ( SV5 @ SV19 @ SV20 )
          = ( SV5 @ SV20 @ SV19 ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(79,plain,
    ! [SV21: a,SV13: a,SV6: a > a > a] :
      ( ( ( ! [SY74: a] :
              ( ( SV6 @ SV13 @ ( SV6 @ SV21 @ SY74 ) )
              = ( SV6 @ ( SV6 @ SV13 @ SV21 ) @ SY74 ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(80,plain,
    ! [SV22: a,SV14: a,SV7: a > a > a] :
      ( ( ( ! [SY75: a] :
              ( ( SV7 @ ( SV7 @ SV14 @ SV22 ) @ SY75 )
              = ( SV7 @ SV14 @ ( SV7 @ SV22 @ SY75 ) ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(81,plain,
    ! [SV23: a,SV15: a,SV8: a > a > a] :
      ( ( ( ! [SY76: a] :
              ( ( SV8 @ SV15 @ ( SV8 @ SV23 @ SY76 ) )
              = ( SV8 @ SV23 @ ( SV8 @ SV15 @ SY76 ) ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV8 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(82,plain,
    ! [SV16: a > a > a] :
      ( ( ( ( syntax_ac_operator_a @ SV16 )
          | ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                    ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                    = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
              | ~ ! [SY71: a,SY72: a] :
                    ( ( SV16 @ SY71 @ SY72 )
                    = ( SV16 @ SY72 @ SY71 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(83,plain,
    ! [SV24: a,SV21: a,SV13: a,SV6: a > a > a] :
      ( ( ( ( SV6 @ SV13 @ ( SV6 @ SV21 @ SV24 ) )
          = ( SV6 @ ( SV6 @ SV13 @ SV21 ) @ SV24 ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(84,plain,
    ! [SV25: a,SV22: a,SV14: a,SV7: a > a > a] :
      ( ( ( ( SV7 @ ( SV7 @ SV14 @ SV22 ) @ SV25 )
          = ( SV7 @ SV14 @ ( SV7 @ SV22 @ SV25 ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(85,plain,
    ! [SV26: a,SV23: a,SV15: a,SV8: a > a > a] :
      ( ( ( ( SV8 @ SV15 @ ( SV8 @ SV23 @ SV26 ) )
          = ( SV8 @ SV23 @ ( SV8 @ SV15 @ SV26 ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV8 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(86,plain,
    ! [SV16: a > a > a] :
      ( ( ( syntax_ac_operator_a @ SV16 )
        = $false )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[82]) ).

thf(87,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                    ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                    = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
              | ~ ! [SY71: a,SY72: a] :
                    ( ( SV16 @ SY71 @ SY72 )
                    = ( SV16 @ SY72 @ SY71 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[82]) ).

thf(88,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ( syntax_ac_operator_a @ SV16 )
          | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                      ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                      = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                | ~ ! [SY71: a,SY72: a] :
                      ( ( SV16 @ SY71 @ SY72 )
                      = ( SV16 @ SY72 @ SY71 ) ) ) )
        = $false )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[86]) ).

thf(89,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ! [SY68: a,SY69: a,SY70: a] :
                ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
          | ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $true )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[87]) ).

thf(90,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ( syntax_ac_operator_a @ SV16 ) )
        = $false )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[88]) ).

thf(91,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                      ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                      = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                | ~ ! [SY71: a,SY72: a] :
                      ( ( SV16 @ SY71 @ SY72 )
                      = ( SV16 @ SY72 @ SY71 ) ) ) )
        = $false )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[88]) ).

thf(92,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ! [SY68: a,SY69: a,SY70: a] :
                ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) ) )
        = $true )
      | ( ( ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $true )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(93,plain,
    ! [SV16: a > a > a] :
      ( ( ( syntax_ac_operator_a @ SV16 )
        = $true )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[90]) ).

thf(94,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                    ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                    = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
              | ~ ! [SY71: a,SY72: a] :
                    ( ( SV16 @ SY71 @ SY72 )
                    = ( SV16 @ SY72 @ SY71 ) ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[91]) ).

thf(95,plain,
    ! [SV16: a > a > a] :
      ( ( ( ! [SY68: a,SY69: a,SY70: a] :
              ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
              = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) ) )
        = $false )
      | ( ( ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $true )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[92]) ).

thf(96,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ! [SY68: a,SY69: a,SY70: a] :
                ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
          | ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $false )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(97,plain,
    ! [SV16: a > a > a] :
      ( ( ( ! [SY77: a,SY78: a] :
              ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ SY77 ) @ SY78 )
              = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ SY77 @ SY78 ) ) ) )
        = $false )
      | ( ( ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $true )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[95]) ).

thf(98,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ! [SY68: a,SY69: a,SY70: a] :
                ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) ) )
        = $false )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[96]) ).

thf(99,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $false )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[96]) ).

thf(100,plain,
    ! [SV16: a > a > a] :
      ( ( ( ! [SY79: a] :
              ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ SY79 )
              = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ SY79 ) ) ) )
        = $false )
      | ( ( ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $true )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[97]) ).

thf(101,plain,
    ! [SV16: a > a > a] :
      ( ( ( ! [SY68: a,SY69: a,SY70: a] :
              ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
              = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[98]) ).

thf(102,plain,
    ! [SV16: a > a > a] :
      ( ( ( ! [SY71: a,SY72: a] :
              ( ( SV16 @ SY71 @ SY72 )
              = ( SV16 @ SY72 @ SY71 ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[99]) ).

thf(103,plain,
    ! [SV16: a > a > a] :
      ( ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $true )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[100]) ).

thf(104,plain,
    ! [SV27: a,SV16: a > a > a] :
      ( ( ( ! [SY80: a,SY81: a] :
              ( ( SV16 @ ( SV16 @ SV27 @ SY80 ) @ SY81 )
              = ( SV16 @ SV27 @ ( SV16 @ SY80 @ SY81 ) ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(105,plain,
    ! [SV28: a,SV16: a > a > a] :
      ( ( ( ! [SY82: a] :
              ( ( SV16 @ SV28 @ SY82 )
              = ( SV16 @ SY82 @ SV28 ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[102]) ).

thf(106,plain,
    ! [SV16: a > a > a] :
      ( ( ( ! [SY71: a,SY72: a] :
              ( ( SV16 @ SY71 @ SY72 )
              = ( SV16 @ SY72 @ SY71 ) ) )
        = $false )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[103]) ).

thf(107,plain,
    ! [SV29: a,SV27: a,SV16: a > a > a] :
      ( ( ( ! [SY83: a] :
              ( ( SV16 @ ( SV16 @ SV27 @ SV29 ) @ SY83 )
              = ( SV16 @ SV27 @ ( SV16 @ SV29 @ SY83 ) ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[104]) ).

thf(108,plain,
    ! [SV30: a,SV28: a,SV16: a > a > a] :
      ( ( ( ( SV16 @ SV28 @ SV30 )
          = ( SV16 @ SV30 @ SV28 ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(109,plain,
    ! [SV16: a > a > a] :
      ( ( ( ! [SY84: a] :
              ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ SY84 )
              = ( SV16 @ SY84 @ ( sK9_SY71 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[106]) ).

thf(110,plain,
    ! [SV31: a,SV29: a,SV27: a,SV16: a > a > a] :
      ( ( ( ( SV16 @ ( SV16 @ SV27 @ SV29 ) @ SV31 )
          = ( SV16 @ SV27 @ ( SV16 @ SV29 @ SV31 ) ) )
        = $true )
      | ( ( syntax_ac_operator_a @ SV16 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(111,plain,
    ! [SV16: a > a > a] :
      ( ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( syntax_ac_operator_a @ SV16 )
              | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                          ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                          = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                    | ~ ! [SY71: a,SY72: a] :
                          ( ( SV16 @ SY71 @ SY72 )
                          = ( SV16 @ SY72 @ SY71 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[109]) ).

thf(112,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ( syntax_ac_operator_a @ SV16 )
          | ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                      ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                      = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                | ~ ! [SY71: a,SY72: a] :
                      ( ( SV16 @ SY71 @ SY72 )
                      = ( SV16 @ SY72 @ SY71 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(113,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ( syntax_ac_operator_a @ SV16 ) )
        = $false )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[112]) ).

thf(114,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                      ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                      = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
                | ~ ! [SY71: a,SY72: a] :
                      ( ( SV16 @ SY71 @ SY72 )
                      = ( SV16 @ SY72 @ SY71 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[112]) ).

thf(115,plain,
    ! [SV16: a > a > a] :
      ( ( ( syntax_ac_operator_a @ SV16 )
        = $true )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[113]) ).

thf(116,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ( ~ ! [SY68: a,SY69: a,SY70: a] :
                    ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                    = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
              | ~ ! [SY71: a,SY72: a] :
                    ( ( SV16 @ SY71 @ SY72 )
                    = ( SV16 @ SY72 @ SY71 ) ) ) )
        = $true )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[114]) ).

thf(117,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ! [SY68: a,SY69: a,SY70: a] :
                ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) )
          | ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $false )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[116]) ).

thf(118,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ! [SY68: a,SY69: a,SY70: a] :
                ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
                = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[117]) ).

thf(119,plain,
    ! [SV16: a > a > a] :
      ( ( ( ~ ! [SY71: a,SY72: a] :
                ( ( SV16 @ SY71 @ SY72 )
                = ( SV16 @ SY72 @ SY71 ) ) )
        = $false )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[117]) ).

thf(120,plain,
    ! [SV16: a > a > a] :
      ( ( ( ! [SY68: a,SY69: a,SY70: a] :
              ( ( SV16 @ ( SV16 @ SY68 @ SY69 ) @ SY70 )
              = ( SV16 @ SY68 @ ( SV16 @ SY69 @ SY70 ) ) ) )
        = $true )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[118]) ).

thf(121,plain,
    ! [SV16: a > a > a] :
      ( ( ( ! [SY71: a,SY72: a] :
              ( ( SV16 @ SY71 @ SY72 )
              = ( SV16 @ SY72 @ SY71 ) ) )
        = $true )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[119]) ).

thf(122,plain,
    ! [SV32: a,SV16: a > a > a] :
      ( ( ( ! [SY85: a,SY86: a] :
              ( ( SV16 @ ( SV16 @ SV32 @ SY85 ) @ SY86 )
              = ( SV16 @ SV32 @ ( SV16 @ SY85 @ SY86 ) ) ) )
        = $true )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(123,plain,
    ! [SV33: a,SV16: a > a > a] :
      ( ( ( ! [SY87: a] :
              ( ( SV16 @ SV33 @ SY87 )
              = ( SV16 @ SY87 @ SV33 ) ) )
        = $true )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[121]) ).

thf(124,plain,
    ! [SV34: a,SV32: a,SV16: a > a > a] :
      ( ( ( ! [SY88: a] :
              ( ( SV16 @ ( SV16 @ SV32 @ SV34 ) @ SY88 )
              = ( SV16 @ SV32 @ ( SV16 @ SV34 @ SY88 ) ) ) )
        = $true )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(125,plain,
    ! [SV35: a,SV33: a,SV16: a > a > a] :
      ( ( ( ( SV16 @ SV33 @ SV35 )
          = ( SV16 @ SV35 @ SV33 ) )
        = $true )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(126,plain,
    ! [SV36: a,SV34: a,SV32: a,SV16: a > a > a] :
      ( ( ( ( SV16 @ ( SV16 @ SV32 @ SV34 ) @ SV36 )
          = ( SV16 @ SV32 @ ( SV16 @ SV34 @ SV36 ) ) )
        = $true )
      | ( ( ( SV16 @ ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( sK7_SY77 @ SV16 ) ) @ ( sK8_SY79 @ SV16 ) )
          = ( SV16 @ ( sK6_SY68 @ SV16 ) @ ( SV16 @ ( sK7_SY77 @ SV16 ) @ ( sK8_SY79 @ SV16 ) ) ) )
        = $false )
      | ( ( ( SV16 @ ( sK9_SY71 @ SV16 ) @ ( sK10_SY84 @ SV16 ) )
          = ( SV16 @ ( sK10_SY84 @ SV16 ) @ ( sK9_SY71 @ SV16 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(127,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[30,126,125,115,110,108,93,85,84,83,78,77,70,63,62,53,52,50]) ).

thf(128,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[127]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP209^1 : TPTP v8.1.0. Released v8.1.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun  2 20:12:36 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 10
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.36  (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:12,loop_count:0,foatp_calls:0,translation:fof_full).........
% 0.19/0.45  
% 0.19/0.45  ********************************
% 0.19/0.45  *   All subproblems solved!    *
% 0.19/0.45  ********************************
% 0.19/0.45  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:127,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.45  
% 0.19/0.45  %**** Beginning of derivation protocol ****
% 0.19/0.45  % SZS output start CNFRefutation
% See solution above
% 0.19/0.45  
% 0.19/0.45  %**** End of derivation protocol ****
% 0.19/0.45  %**** no. of clauses in derivation: 128 ****
% 0.19/0.45  %**** clause counter: 127 ****
% 0.19/0.45  
% 0.19/0.45  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:127,loop_count:0,foatp_calls:1,translation:fof_full)
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