TSTP Solution File: SYN014-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN014-2 : 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 : n009.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 21 08:22:39 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  199 ( 100 unt;   8 typ;   0 def)
%            Number of atoms       : 1153 ( 286 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives : 1774 ( 182   ~; 390   |;   0   &;1202   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  259 (   0   ^ 259   !;   0   ?; 259   :)

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

thf(tp_element,type,
    element: $i > $i > $o ).

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

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

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

thf(tp_k,type,
    k: $i ).

thf(tp_m,type,
    m: $i ).

thf(tp_n,type,
    n: $i ).

thf(1,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( element @ A @ B )
      | ~ ( equalish @ A @ C )
      | ( element @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitutionish2) ).

thf(2,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( element @ C @ A )
      | ( element @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitutionish1) ).

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',transitivityish) ).

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

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

thf(6,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(7,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,negated_conjecture,
    equalish @ m @ k,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_23) ).

thf(9,negated_conjecture,
    ~ ( equalish @ k @ a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_22) ).

thf(10,negated_conjecture,
    ~ ( equalish @ m @ a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_21) ).

thf(11,negated_conjecture,
    equalish @ n @ k,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_20) ).

thf(12,negated_conjecture,
    ~ ( equalish @ m @ n ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_19) ).

thf(13,negated_conjecture,
    ~ ( equalish @ n @ a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_18) ).

thf(14,negated_conjecture,
    ! [A: $i] :
      ( ~ ( element @ A @ k )
      | ( equalish @ A @ n )
      | ( equalish @ A @ m )
      | ( equalish @ A @ k ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_17) ).

thf(15,negated_conjecture,
    ! [A: $i] :
      ( ~ ( equalish @ A @ n )
      | ( element @ A @ k )
      | ( equalish @ A @ k ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).

thf(16,negated_conjecture,
    ! [A: $i] :
      ( ~ ( equalish @ A @ m )
      | ( element @ A @ k )
      | ( equalish @ A @ k ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_15) ).

thf(17,negated_conjecture,
    ! [A: $i,B: $i] :
      ( ~ ( element @ A @ B )
      | ~ ( element @ B @ A )
      | ( equalish @ A @ B )
      | ( equalish @ A @ n )
      | ~ ( element @ B @ n )
      | ( equalish @ B @ n ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).

thf(18,negated_conjecture,
    ! [A: $i] :
      ( ( element @ ( g @ A ) @ A )
      | ( element @ A @ n )
      | ( equalish @ A @ n ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_13) ).

thf(19,negated_conjecture,
    ! [A: $i] :
      ( ( element @ A @ ( g @ A ) )
      | ( element @ A @ n )
      | ( equalish @ A @ n ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).

thf(20,negated_conjecture,
    ! [A: $i] :
      ( ~ ( equalish @ ( g @ A ) @ A )
      | ( element @ A @ n )
      | ( equalish @ A @ n ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).

thf(21,negated_conjecture,
    ! [A: $i] :
      ( ~ ( equalish @ ( g @ A ) @ n )
      | ( element @ A @ n )
      | ( equalish @ A @ n ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).

thf(22,negated_conjecture,
    ! [A: $i,B: $i] :
      ( ~ ( element @ A @ B )
      | ~ ( element @ B @ A )
      | ( equalish @ A @ B )
      | ( equalish @ A @ m )
      | ( element @ B @ m )
      | ( equalish @ B @ m ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).

thf(23,negated_conjecture,
    ! [A: $i] :
      ( ( element @ ( f @ A ) @ A )
      | ~ ( element @ A @ m )
      | ( equalish @ A @ m ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).

thf(24,negated_conjecture,
    ! [A: $i] :
      ( ( element @ A @ ( f @ A ) )
      | ~ ( element @ A @ m )
      | ( equalish @ A @ m ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).

thf(25,negated_conjecture,
    ! [A: $i] :
      ( ~ ( equalish @ ( f @ A ) @ A )
      | ~ ( element @ A @ m )
      | ( equalish @ A @ m ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).

thf(26,negated_conjecture,
    ! [A: $i] :
      ( ~ ( equalish @ ( f @ A ) @ m )
      | ~ ( element @ A @ m )
      | ( equalish @ A @ m ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).

thf(27,negated_conjecture,
    ! [A: $i] :
      ( ~ ( equalish @ A @ k )
      | ( element @ A @ a )
      | ( equalish @ A @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_4) ).

thf(28,negated_conjecture,
    ! [A: $i] :
      ( ~ ( element @ A @ a )
      | ( equalish @ A @ k )
      | ( equalish @ A @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_3) ).

thf(29,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[7]) ).

thf(30,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( element @ A @ B )
          | ~ ( equalish @ A @ C )
          | ( element @ C @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(31,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( equalish @ A @ B )
          | ~ ( element @ C @ A )
          | ( element @ C @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( equalish @ X @ Y )
          | ~ ( equalish @ Y @ Z )
          | ( equalish @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(33,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ( equalish @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(34,plain,
    ( ( ! [X: $i] : ( equalish @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(35,plain,
    ( ( equalish @ m @ k )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(36,plain,
    ( ( ~ ( equalish @ k @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(37,plain,
    ( ( ~ ( equalish @ m @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(38,plain,
    ( ( equalish @ n @ k )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(39,plain,
    ( ( ~ ( equalish @ m @ n ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(40,plain,
    ( ( ~ ( equalish @ n @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(41,plain,
    ( ( ! [A: $i] :
          ( ~ ( element @ A @ k )
          | ( equalish @ A @ n )
          | ( equalish @ A @ m )
          | ( equalish @ A @ k ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(42,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ A @ n )
          | ( element @ A @ k )
          | ( equalish @ A @ k ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(43,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ A @ m )
          | ( element @ A @ k )
          | ( equalish @ A @ k ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(44,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( element @ A @ B )
          | ~ ( element @ B @ A )
          | ( equalish @ A @ B )
          | ( equalish @ A @ n )
          | ~ ( element @ B @ n )
          | ( equalish @ B @ n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(45,plain,
    ( ( ! [A: $i] :
          ( ( element @ ( g @ A ) @ A )
          | ( element @ A @ n )
          | ( equalish @ A @ n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(46,plain,
    ( ( ! [A: $i] :
          ( ( element @ A @ ( g @ A ) )
          | ( element @ A @ n )
          | ( equalish @ A @ n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(47,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ ( g @ A ) @ A )
          | ( element @ A @ n )
          | ( equalish @ A @ n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(48,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ ( g @ A ) @ n )
          | ( element @ A @ n )
          | ( equalish @ A @ n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(49,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( element @ A @ B )
          | ~ ( element @ B @ A )
          | ( equalish @ A @ B )
          | ( equalish @ A @ m )
          | ( element @ B @ m )
          | ( equalish @ B @ m ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(50,plain,
    ( ( ! [A: $i] :
          ( ( element @ ( f @ A ) @ A )
          | ~ ( element @ A @ m )
          | ( equalish @ A @ m ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(51,plain,
    ( ( ! [A: $i] :
          ( ( element @ A @ ( f @ A ) )
          | ~ ( element @ A @ m )
          | ( equalish @ A @ m ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(52,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ ( f @ A ) @ A )
          | ~ ( element @ A @ m )
          | ( equalish @ A @ m ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(53,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ ( f @ A ) @ m )
          | ~ ( element @ A @ m )
          | ( equalish @ A @ m ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(54,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ A @ k )
          | ( element @ A @ a )
          | ( equalish @ A @ a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(55,plain,
    ( ( ! [A: $i] :
          ( ~ ( element @ A @ a )
          | ( equalish @ A @ k )
          | ( equalish @ A @ a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(56,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[29]) ).

thf(57,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( element @ A @ B )
          | ! [C: $i] :
              ( ~ ( equalish @ A @ C )
              | ( element @ C @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[30]) ).

thf(58,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( equalish @ A @ B )
          | ! [C: $i] :
              ( ~ ( element @ C @ A )
              | ( element @ C @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[31]) ).

thf(59,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( equalish @ Y @ Z )
              | ( equalish @ X @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[32]) ).

thf(60,plain,
    ( ( ! [A: $i] :
          ( ~ ( element @ A @ a )
          | ( equalish @ A @ k )
          | ( equalish @ A @ a ) ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(61,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ A @ k )
          | ( element @ A @ a )
          | ( equalish @ A @ a ) ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(62,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ ( f @ A ) @ m )
          | ~ ( element @ A @ m )
          | ( equalish @ A @ m ) ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(63,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ ( f @ A ) @ A )
          | ~ ( element @ A @ m )
          | ( equalish @ A @ m ) ) )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(64,plain,
    ( ( ! [A: $i] :
          ( ( element @ A @ ( f @ A ) )
          | ~ ( element @ A @ m )
          | ( equalish @ A @ m ) ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(65,plain,
    ( ( ! [A: $i] :
          ( ( element @ ( f @ A ) @ A )
          | ~ ( element @ A @ m )
          | ( equalish @ A @ m ) ) )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(66,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( element @ A @ B )
          | ~ ( element @ B @ A )
          | ( equalish @ A @ B )
          | ( equalish @ A @ m )
          | ( element @ B @ m )
          | ( equalish @ B @ m ) ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(67,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ ( g @ A ) @ n )
          | ( element @ A @ n )
          | ( equalish @ A @ n ) ) )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(68,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ ( g @ A ) @ A )
          | ( element @ A @ n )
          | ( equalish @ A @ n ) ) )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(69,plain,
    ( ( ! [A: $i] :
          ( ( element @ A @ ( g @ A ) )
          | ( element @ A @ n )
          | ( equalish @ A @ n ) ) )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(70,plain,
    ( ( ! [A: $i] :
          ( ( element @ ( g @ A ) @ A )
          | ( element @ A @ n )
          | ( equalish @ A @ n ) ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(71,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( element @ A @ B )
          | ~ ( element @ B @ A )
          | ( equalish @ A @ B )
          | ( equalish @ A @ n )
          | ~ ( element @ B @ n )
          | ( equalish @ B @ n ) ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(72,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ A @ m )
          | ( element @ A @ k )
          | ( equalish @ A @ k ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(73,plain,
    ( ( ! [A: $i] :
          ( ~ ( equalish @ A @ n )
          | ( element @ A @ k )
          | ( equalish @ A @ k ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(74,plain,
    ( ( ! [A: $i] :
          ( ~ ( element @ A @ k )
          | ( equalish @ A @ n )
          | ( equalish @ A @ m )
          | ( equalish @ A @ k ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(75,plain,
    ( ( ~ ( equalish @ n @ a ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(76,plain,
    ( ( ~ ( equalish @ m @ n ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(77,plain,
    ( ( equalish @ n @ k )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(78,plain,
    ( ( ~ ( equalish @ m @ a ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(79,plain,
    ( ( ~ ( equalish @ k @ a ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(80,plain,
    ( ( equalish @ m @ k )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(81,plain,
    ( ( ! [X: $i] : ( equalish @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(82,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ( equalish @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(83,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( equalish @ Y @ Z )
              | ( equalish @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(84,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( equalish @ A @ B )
          | ! [C: $i] :
              ( ~ ( element @ C @ A )
              | ( element @ C @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[58]) ).

thf(85,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( element @ A @ B )
          | ! [C: $i] :
              ( ~ ( equalish @ A @ C )
              | ( element @ C @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[57]) ).

thf(86,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(87,plain,
    ! [SV1: $i] :
      ( ( ~ ( element @ SV1 @ a )
        | ( equalish @ SV1 @ k )
        | ( equalish @ SV1 @ a ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(88,plain,
    ! [SV2: $i] :
      ( ( ~ ( equalish @ SV2 @ k )
        | ( element @ SV2 @ a )
        | ( equalish @ SV2 @ a ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(89,plain,
    ! [SV3: $i] :
      ( ( ~ ( equalish @ ( f @ SV3 ) @ m )
        | ~ ( element @ SV3 @ m )
        | ( equalish @ SV3 @ m ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(90,plain,
    ! [SV4: $i] :
      ( ( ~ ( equalish @ ( f @ SV4 ) @ SV4 )
        | ~ ( element @ SV4 @ m )
        | ( equalish @ SV4 @ m ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(91,plain,
    ! [SV5: $i] :
      ( ( ( element @ SV5 @ ( f @ SV5 ) )
        | ~ ( element @ SV5 @ m )
        | ( equalish @ SV5 @ m ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(92,plain,
    ! [SV6: $i] :
      ( ( ( element @ ( f @ SV6 ) @ SV6 )
        | ~ ( element @ SV6 @ m )
        | ( equalish @ SV6 @ m ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(93,plain,
    ! [SV7: $i] :
      ( ( ! [SY29: $i] :
            ( ~ ( element @ SV7 @ SY29 )
            | ~ ( element @ SY29 @ SV7 )
            | ( equalish @ SV7 @ SY29 )
            | ( equalish @ SV7 @ m )
            | ( element @ SY29 @ m )
            | ( equalish @ SY29 @ m ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(94,plain,
    ! [SV8: $i] :
      ( ( ~ ( equalish @ ( g @ SV8 ) @ n )
        | ( element @ SV8 @ n )
        | ( equalish @ SV8 @ n ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(95,plain,
    ! [SV9: $i] :
      ( ( ~ ( equalish @ ( g @ SV9 ) @ SV9 )
        | ( element @ SV9 @ n )
        | ( equalish @ SV9 @ n ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(96,plain,
    ! [SV10: $i] :
      ( ( ( element @ SV10 @ ( g @ SV10 ) )
        | ( element @ SV10 @ n )
        | ( equalish @ SV10 @ n ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(97,plain,
    ! [SV11: $i] :
      ( ( ( element @ ( g @ SV11 ) @ SV11 )
        | ( element @ SV11 @ n )
        | ( equalish @ SV11 @ n ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(98,plain,
    ! [SV12: $i] :
      ( ( ! [SY30: $i] :
            ( ~ ( element @ SV12 @ SY30 )
            | ~ ( element @ SY30 @ SV12 )
            | ( equalish @ SV12 @ SY30 )
            | ( equalish @ SV12 @ n )
            | ~ ( element @ SY30 @ n )
            | ( equalish @ SY30 @ n ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(99,plain,
    ! [SV13: $i] :
      ( ( ~ ( equalish @ SV13 @ m )
        | ( element @ SV13 @ k )
        | ( equalish @ SV13 @ k ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(100,plain,
    ! [SV14: $i] :
      ( ( ~ ( equalish @ SV14 @ n )
        | ( element @ SV14 @ k )
        | ( equalish @ SV14 @ k ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(101,plain,
    ! [SV15: $i] :
      ( ( ~ ( element @ SV15 @ k )
        | ( equalish @ SV15 @ n )
        | ( equalish @ SV15 @ m )
        | ( equalish @ SV15 @ k ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(102,plain,
    ( ( equalish @ n @ a )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(103,plain,
    ( ( equalish @ m @ n )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(104,plain,
    ( ( equalish @ m @ a )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[78]) ).

thf(105,plain,
    ( ( equalish @ k @ a )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(106,plain,
    ! [SV16: $i] :
      ( ( equalish @ SV16 @ SV16 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(107,plain,
    ! [SV17: $i] :
      ( ( ! [SY31: $i] :
            ( ~ ( equalish @ SV17 @ SY31 )
            | ( equalish @ SY31 @ SV17 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(108,plain,
    ! [SV18: $i] :
      ( ( ! [SY32: $i] :
            ( ~ ( equalish @ SV18 @ SY32 )
            | ! [SY33: $i] :
                ( ~ ( equalish @ SY32 @ SY33 )
                | ( equalish @ SV18 @ SY33 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(109,plain,
    ! [SV19: $i] :
      ( ( ! [SY34: $i] :
            ( ~ ( equalish @ SV19 @ SY34 )
            | ! [SY35: $i] :
                ( ~ ( element @ SY35 @ SV19 )
                | ( element @ SY35 @ SY34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(110,plain,
    ! [SV20: $i] :
      ( ( ! [SY36: $i] :
            ( ~ ( element @ SV20 @ SY36 )
            | ! [SY37: $i] :
                ( ~ ( equalish @ SV20 @ SY37 )
                | ( element @ SY37 @ SY36 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(111,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[86]) ).

thf(112,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( element @ SV1 @ a ) )
        = $true )
      | ( ( ( equalish @ SV1 @ k )
          | ( equalish @ SV1 @ a ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[87]) ).

thf(113,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( equalish @ SV2 @ k ) )
        = $true )
      | ( ( ( element @ SV2 @ a )
          | ( equalish @ SV2 @ a ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(114,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( equalish @ ( f @ SV3 ) @ m ) )
        = $true )
      | ( ( ~ ( element @ SV3 @ m )
          | ( equalish @ SV3 @ m ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(115,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( equalish @ ( f @ SV4 ) @ SV4 ) )
        = $true )
      | ( ( ~ ( element @ SV4 @ m )
          | ( equalish @ SV4 @ m ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[90]) ).

thf(116,plain,
    ! [SV5: $i] :
      ( ( ( element @ SV5 @ ( f @ SV5 ) )
        = $true )
      | ( ( ~ ( element @ SV5 @ m )
          | ( equalish @ SV5 @ m ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(117,plain,
    ! [SV6: $i] :
      ( ( ( element @ ( f @ SV6 ) @ SV6 )
        = $true )
      | ( ( ~ ( element @ SV6 @ m )
          | ( equalish @ SV6 @ m ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[92]) ).

thf(118,plain,
    ! [SV21: $i,SV7: $i] :
      ( ( ~ ( element @ SV7 @ SV21 )
        | ~ ( element @ SV21 @ SV7 )
        | ( equalish @ SV7 @ SV21 )
        | ( equalish @ SV7 @ m )
        | ( element @ SV21 @ m )
        | ( equalish @ SV21 @ m ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(119,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( equalish @ ( g @ SV8 ) @ n ) )
        = $true )
      | ( ( ( element @ SV8 @ n )
          | ( equalish @ SV8 @ n ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[94]) ).

thf(120,plain,
    ! [SV9: $i] :
      ( ( ( ~ ( equalish @ ( g @ SV9 ) @ SV9 ) )
        = $true )
      | ( ( ( element @ SV9 @ n )
          | ( equalish @ SV9 @ n ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(121,plain,
    ! [SV10: $i] :
      ( ( ( element @ SV10 @ ( g @ SV10 ) )
        = $true )
      | ( ( ( element @ SV10 @ n )
          | ( equalish @ SV10 @ n ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[96]) ).

thf(122,plain,
    ! [SV11: $i] :
      ( ( ( element @ ( g @ SV11 ) @ SV11 )
        = $true )
      | ( ( ( element @ SV11 @ n )
          | ( equalish @ SV11 @ n ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[97]) ).

thf(123,plain,
    ! [SV22: $i,SV12: $i] :
      ( ( ~ ( element @ SV12 @ SV22 )
        | ~ ( element @ SV22 @ SV12 )
        | ( equalish @ SV12 @ SV22 )
        | ( equalish @ SV12 @ n )
        | ~ ( element @ SV22 @ n )
        | ( equalish @ SV22 @ n ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(124,plain,
    ! [SV13: $i] :
      ( ( ( ~ ( equalish @ SV13 @ m ) )
        = $true )
      | ( ( ( element @ SV13 @ k )
          | ( equalish @ SV13 @ k ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(125,plain,
    ! [SV14: $i] :
      ( ( ( ~ ( equalish @ SV14 @ n ) )
        = $true )
      | ( ( ( element @ SV14 @ k )
          | ( equalish @ SV14 @ k ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[100]) ).

thf(126,plain,
    ! [SV15: $i] :
      ( ( ( ~ ( element @ SV15 @ k ) )
        = $true )
      | ( ( ( equalish @ SV15 @ n )
          | ( equalish @ SV15 @ m )
          | ( equalish @ SV15 @ k ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[101]) ).

thf(127,plain,
    ! [SV23: $i,SV17: $i] :
      ( ( ~ ( equalish @ SV17 @ SV23 )
        | ( equalish @ SV23 @ SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(128,plain,
    ! [SV24: $i,SV18: $i] :
      ( ( ~ ( equalish @ SV18 @ SV24 )
        | ! [SY38: $i] :
            ( ~ ( equalish @ SV24 @ SY38 )
            | ( equalish @ SV18 @ SY38 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(129,plain,
    ! [SV25: $i,SV19: $i] :
      ( ( ~ ( equalish @ SV19 @ SV25 )
        | ! [SY39: $i] :
            ( ~ ( element @ SY39 @ SV19 )
            | ( element @ SY39 @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(130,plain,
    ! [SV26: $i,SV20: $i] :
      ( ( ~ ( element @ SV20 @ SV26 )
        | ! [SY40: $i] :
            ( ~ ( equalish @ SV20 @ SY40 )
            | ( element @ SY40 @ SV26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(131,plain,
    ! [SV1: $i] :
      ( ( ( element @ SV1 @ a )
        = $false )
      | ( ( ( equalish @ SV1 @ k )
          | ( equalish @ SV1 @ a ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[112]) ).

thf(132,plain,
    ! [SV2: $i] :
      ( ( ( equalish @ SV2 @ k )
        = $false )
      | ( ( ( element @ SV2 @ a )
          | ( equalish @ SV2 @ a ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[113]) ).

thf(133,plain,
    ! [SV3: $i] :
      ( ( ( equalish @ ( f @ SV3 ) @ m )
        = $false )
      | ( ( ~ ( element @ SV3 @ m )
          | ( equalish @ SV3 @ m ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(134,plain,
    ! [SV4: $i] :
      ( ( ( equalish @ ( f @ SV4 ) @ SV4 )
        = $false )
      | ( ( ~ ( element @ SV4 @ m )
          | ( equalish @ SV4 @ m ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[115]) ).

thf(135,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( element @ SV5 @ m ) )
        = $true )
      | ( ( equalish @ SV5 @ m )
        = $true )
      | ( ( element @ SV5 @ ( f @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[116]) ).

thf(136,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( element @ SV6 @ m ) )
        = $true )
      | ( ( equalish @ SV6 @ m )
        = $true )
      | ( ( element @ ( f @ SV6 ) @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[117]) ).

thf(137,plain,
    ! [SV21: $i,SV7: $i] :
      ( ( ( ~ ( element @ SV7 @ SV21 ) )
        = $true )
      | ( ( ~ ( element @ SV21 @ SV7 )
          | ( equalish @ SV7 @ SV21 )
          | ( equalish @ SV7 @ m )
          | ( element @ SV21 @ m )
          | ( equalish @ SV21 @ m ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[118]) ).

thf(138,plain,
    ! [SV8: $i] :
      ( ( ( equalish @ ( g @ SV8 ) @ n )
        = $false )
      | ( ( ( element @ SV8 @ n )
          | ( equalish @ SV8 @ n ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[119]) ).

thf(139,plain,
    ! [SV9: $i] :
      ( ( ( equalish @ ( g @ SV9 ) @ SV9 )
        = $false )
      | ( ( ( element @ SV9 @ n )
          | ( equalish @ SV9 @ n ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[120]) ).

thf(140,plain,
    ! [SV10: $i] :
      ( ( ( element @ SV10 @ n )
        = $true )
      | ( ( equalish @ SV10 @ n )
        = $true )
      | ( ( element @ SV10 @ ( g @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[121]) ).

thf(141,plain,
    ! [SV11: $i] :
      ( ( ( element @ SV11 @ n )
        = $true )
      | ( ( equalish @ SV11 @ n )
        = $true )
      | ( ( element @ ( g @ SV11 ) @ SV11 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[122]) ).

thf(142,plain,
    ! [SV22: $i,SV12: $i] :
      ( ( ( ~ ( element @ SV12 @ SV22 ) )
        = $true )
      | ( ( ~ ( element @ SV22 @ SV12 )
          | ( equalish @ SV12 @ SV22 )
          | ( equalish @ SV12 @ n )
          | ~ ( element @ SV22 @ n )
          | ( equalish @ SV22 @ n ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[123]) ).

thf(143,plain,
    ! [SV13: $i] :
      ( ( ( equalish @ SV13 @ m )
        = $false )
      | ( ( ( element @ SV13 @ k )
          | ( equalish @ SV13 @ k ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[124]) ).

thf(144,plain,
    ! [SV14: $i] :
      ( ( ( equalish @ SV14 @ n )
        = $false )
      | ( ( ( element @ SV14 @ k )
          | ( equalish @ SV14 @ k ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[125]) ).

thf(145,plain,
    ! [SV15: $i] :
      ( ( ( element @ SV15 @ k )
        = $false )
      | ( ( ( equalish @ SV15 @ n )
          | ( equalish @ SV15 @ m )
          | ( equalish @ SV15 @ k ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[126]) ).

thf(146,plain,
    ! [SV23: $i,SV17: $i] :
      ( ( ( ~ ( equalish @ SV17 @ SV23 ) )
        = $true )
      | ( ( equalish @ SV23 @ SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[127]) ).

thf(147,plain,
    ! [SV24: $i,SV18: $i] :
      ( ( ( ~ ( equalish @ SV18 @ SV24 ) )
        = $true )
      | ( ( ! [SY38: $i] :
              ( ~ ( equalish @ SV24 @ SY38 )
              | ( equalish @ SV18 @ SY38 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[128]) ).

thf(148,plain,
    ! [SV25: $i,SV19: $i] :
      ( ( ( ~ ( equalish @ SV19 @ SV25 ) )
        = $true )
      | ( ( ! [SY39: $i] :
              ( ~ ( element @ SY39 @ SV19 )
              | ( element @ SY39 @ SV25 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[129]) ).

thf(149,plain,
    ! [SV26: $i,SV20: $i] :
      ( ( ( ~ ( element @ SV20 @ SV26 ) )
        = $true )
      | ( ( ! [SY40: $i] :
              ( ~ ( equalish @ SV20 @ SY40 )
              | ( element @ SY40 @ SV26 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[130]) ).

thf(150,plain,
    ! [SV1: $i] :
      ( ( ( equalish @ SV1 @ k )
        = $true )
      | ( ( equalish @ SV1 @ a )
        = $true )
      | ( ( element @ SV1 @ a )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[131]) ).

thf(151,plain,
    ! [SV2: $i] :
      ( ( ( element @ SV2 @ a )
        = $true )
      | ( ( equalish @ SV2 @ a )
        = $true )
      | ( ( equalish @ SV2 @ k )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[132]) ).

thf(152,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( element @ SV3 @ m ) )
        = $true )
      | ( ( equalish @ SV3 @ m )
        = $true )
      | ( ( equalish @ ( f @ SV3 ) @ m )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[133]) ).

thf(153,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( element @ SV4 @ m ) )
        = $true )
      | ( ( equalish @ SV4 @ m )
        = $true )
      | ( ( equalish @ ( f @ SV4 ) @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[134]) ).

thf(154,plain,
    ! [SV5: $i] :
      ( ( ( element @ SV5 @ m )
        = $false )
      | ( ( equalish @ SV5 @ m )
        = $true )
      | ( ( element @ SV5 @ ( f @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[135]) ).

thf(155,plain,
    ! [SV6: $i] :
      ( ( ( element @ SV6 @ m )
        = $false )
      | ( ( equalish @ SV6 @ m )
        = $true )
      | ( ( element @ ( f @ SV6 ) @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[136]) ).

thf(156,plain,
    ! [SV21: $i,SV7: $i] :
      ( ( ( element @ SV7 @ SV21 )
        = $false )
      | ( ( ~ ( element @ SV21 @ SV7 )
          | ( equalish @ SV7 @ SV21 )
          | ( equalish @ SV7 @ m )
          | ( element @ SV21 @ m )
          | ( equalish @ SV21 @ m ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[137]) ).

thf(157,plain,
    ! [SV8: $i] :
      ( ( ( element @ SV8 @ n )
        = $true )
      | ( ( equalish @ SV8 @ n )
        = $true )
      | ( ( equalish @ ( g @ SV8 ) @ n )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[138]) ).

thf(158,plain,
    ! [SV9: $i] :
      ( ( ( element @ SV9 @ n )
        = $true )
      | ( ( equalish @ SV9 @ n )
        = $true )
      | ( ( equalish @ ( g @ SV9 ) @ SV9 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[139]) ).

thf(159,plain,
    ! [SV22: $i,SV12: $i] :
      ( ( ( element @ SV12 @ SV22 )
        = $false )
      | ( ( ~ ( element @ SV22 @ SV12 )
          | ( equalish @ SV12 @ SV22 )
          | ( equalish @ SV12 @ n )
          | ~ ( element @ SV22 @ n )
          | ( equalish @ SV22 @ n ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[142]) ).

thf(160,plain,
    ! [SV13: $i] :
      ( ( ( element @ SV13 @ k )
        = $true )
      | ( ( equalish @ SV13 @ k )
        = $true )
      | ( ( equalish @ SV13 @ m )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[143]) ).

thf(161,plain,
    ! [SV14: $i] :
      ( ( ( element @ SV14 @ k )
        = $true )
      | ( ( equalish @ SV14 @ k )
        = $true )
      | ( ( equalish @ SV14 @ n )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[144]) ).

thf(162,plain,
    ! [SV15: $i] :
      ( ( ( equalish @ SV15 @ n )
        = $true )
      | ( ( ( equalish @ SV15 @ m )
          | ( equalish @ SV15 @ k ) )
        = $true )
      | ( ( element @ SV15 @ k )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[145]) ).

thf(163,plain,
    ! [SV23: $i,SV17: $i] :
      ( ( ( equalish @ SV17 @ SV23 )
        = $false )
      | ( ( equalish @ SV23 @ SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[146]) ).

thf(164,plain,
    ! [SV24: $i,SV18: $i] :
      ( ( ( equalish @ SV18 @ SV24 )
        = $false )
      | ( ( ! [SY38: $i] :
              ( ~ ( equalish @ SV24 @ SY38 )
              | ( equalish @ SV18 @ SY38 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(165,plain,
    ! [SV25: $i,SV19: $i] :
      ( ( ( equalish @ SV19 @ SV25 )
        = $false )
      | ( ( ! [SY39: $i] :
              ( ~ ( element @ SY39 @ SV19 )
              | ( element @ SY39 @ SV25 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[148]) ).

thf(166,plain,
    ! [SV26: $i,SV20: $i] :
      ( ( ( element @ SV20 @ SV26 )
        = $false )
      | ( ( ! [SY40: $i] :
              ( ~ ( equalish @ SV20 @ SY40 )
              | ( element @ SY40 @ SV26 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(167,plain,
    ! [SV3: $i] :
      ( ( ( element @ SV3 @ m )
        = $false )
      | ( ( equalish @ SV3 @ m )
        = $true )
      | ( ( equalish @ ( f @ SV3 ) @ m )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(168,plain,
    ! [SV4: $i] :
      ( ( ( element @ SV4 @ m )
        = $false )
      | ( ( equalish @ SV4 @ m )
        = $true )
      | ( ( equalish @ ( f @ SV4 ) @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[153]) ).

thf(169,plain,
    ! [SV7: $i,SV21: $i] :
      ( ( ( ~ ( element @ SV21 @ SV7 ) )
        = $true )
      | ( ( ( equalish @ SV7 @ SV21 )
          | ( equalish @ SV7 @ m )
          | ( element @ SV21 @ m )
          | ( equalish @ SV21 @ m ) )
        = $true )
      | ( ( element @ SV7 @ SV21 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[156]) ).

thf(170,plain,
    ! [SV12: $i,SV22: $i] :
      ( ( ( ~ ( element @ SV22 @ SV12 ) )
        = $true )
      | ( ( ( equalish @ SV12 @ SV22 )
          | ( equalish @ SV12 @ n )
          | ~ ( element @ SV22 @ n )
          | ( equalish @ SV22 @ n ) )
        = $true )
      | ( ( element @ SV12 @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[159]) ).

thf(171,plain,
    ! [SV15: $i] :
      ( ( ( equalish @ SV15 @ m )
        = $true )
      | ( ( equalish @ SV15 @ k )
        = $true )
      | ( ( equalish @ SV15 @ n )
        = $true )
      | ( ( element @ SV15 @ k )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[162]) ).

thf(172,plain,
    ! [SV18: $i,SV27: $i,SV24: $i] :
      ( ( ( ~ ( equalish @ SV24 @ SV27 )
          | ( equalish @ SV18 @ SV27 ) )
        = $true )
      | ( ( equalish @ SV18 @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(173,plain,
    ! [SV25: $i,SV19: $i,SV28: $i] :
      ( ( ( ~ ( element @ SV28 @ SV19 )
          | ( element @ SV28 @ SV25 ) )
        = $true )
      | ( ( equalish @ SV19 @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[165]) ).

thf(174,plain,
    ! [SV26: $i,SV29: $i,SV20: $i] :
      ( ( ( ~ ( equalish @ SV20 @ SV29 )
          | ( element @ SV29 @ SV26 ) )
        = $true )
      | ( ( element @ SV20 @ SV26 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[166]) ).

thf(175,plain,
    ! [SV7: $i,SV21: $i] :
      ( ( ( element @ SV21 @ SV7 )
        = $false )
      | ( ( ( equalish @ SV7 @ SV21 )
          | ( equalish @ SV7 @ m )
          | ( element @ SV21 @ m )
          | ( equalish @ SV21 @ m ) )
        = $true )
      | ( ( element @ SV7 @ SV21 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[169]) ).

thf(176,plain,
    ! [SV12: $i,SV22: $i] :
      ( ( ( element @ SV22 @ SV12 )
        = $false )
      | ( ( ( equalish @ SV12 @ SV22 )
          | ( equalish @ SV12 @ n )
          | ~ ( element @ SV22 @ n )
          | ( equalish @ SV22 @ n ) )
        = $true )
      | ( ( element @ SV12 @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[170]) ).

thf(177,plain,
    ! [SV18: $i,SV27: $i,SV24: $i] :
      ( ( ( ~ ( equalish @ SV24 @ SV27 ) )
        = $true )
      | ( ( equalish @ SV18 @ SV27 )
        = $true )
      | ( ( equalish @ SV18 @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[172]) ).

thf(178,plain,
    ! [SV25: $i,SV19: $i,SV28: $i] :
      ( ( ( ~ ( element @ SV28 @ SV19 ) )
        = $true )
      | ( ( element @ SV28 @ SV25 )
        = $true )
      | ( ( equalish @ SV19 @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[173]) ).

thf(179,plain,
    ! [SV26: $i,SV29: $i,SV20: $i] :
      ( ( ( ~ ( equalish @ SV20 @ SV29 ) )
        = $true )
      | ( ( element @ SV29 @ SV26 )
        = $true )
      | ( ( element @ SV20 @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[174]) ).

thf(180,plain,
    ! [SV21: $i,SV7: $i] :
      ( ( ( equalish @ SV7 @ SV21 )
        = $true )
      | ( ( ( equalish @ SV7 @ m )
          | ( element @ SV21 @ m )
          | ( equalish @ SV21 @ m ) )
        = $true )
      | ( ( element @ SV21 @ SV7 )
        = $false )
      | ( ( element @ SV7 @ SV21 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[175]) ).

thf(181,plain,
    ! [SV22: $i,SV12: $i] :
      ( ( ( equalish @ SV12 @ SV22 )
        = $true )
      | ( ( ( equalish @ SV12 @ n )
          | ~ ( element @ SV22 @ n )
          | ( equalish @ SV22 @ n ) )
        = $true )
      | ( ( element @ SV22 @ SV12 )
        = $false )
      | ( ( element @ SV12 @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[176]) ).

thf(182,plain,
    ! [SV18: $i,SV27: $i,SV24: $i] :
      ( ( ( equalish @ SV24 @ SV27 )
        = $false )
      | ( ( equalish @ SV18 @ SV27 )
        = $true )
      | ( ( equalish @ SV18 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[177]) ).

thf(183,plain,
    ! [SV25: $i,SV19: $i,SV28: $i] :
      ( ( ( element @ SV28 @ SV19 )
        = $false )
      | ( ( element @ SV28 @ SV25 )
        = $true )
      | ( ( equalish @ SV19 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[178]) ).

thf(184,plain,
    ! [SV26: $i,SV29: $i,SV20: $i] :
      ( ( ( equalish @ SV20 @ SV29 )
        = $false )
      | ( ( element @ SV29 @ SV26 )
        = $true )
      | ( ( element @ SV20 @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[179]) ).

thf(185,plain,
    ! [SV21: $i,SV7: $i] :
      ( ( ( equalish @ SV7 @ m )
        = $true )
      | ( ( ( element @ SV21 @ m )
          | ( equalish @ SV21 @ m ) )
        = $true )
      | ( ( equalish @ SV7 @ SV21 )
        = $true )
      | ( ( element @ SV21 @ SV7 )
        = $false )
      | ( ( element @ SV7 @ SV21 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[180]) ).

thf(186,plain,
    ! [SV22: $i,SV12: $i] :
      ( ( ( equalish @ SV12 @ n )
        = $true )
      | ( ( ~ ( element @ SV22 @ n )
          | ( equalish @ SV22 @ n ) )
        = $true )
      | ( ( equalish @ SV12 @ SV22 )
        = $true )
      | ( ( element @ SV22 @ SV12 )
        = $false )
      | ( ( element @ SV12 @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[181]) ).

thf(187,plain,
    ! [SV7: $i,SV21: $i] :
      ( ( ( element @ SV21 @ m )
        = $true )
      | ( ( equalish @ SV21 @ m )
        = $true )
      | ( ( equalish @ SV7 @ m )
        = $true )
      | ( ( equalish @ SV7 @ SV21 )
        = $true )
      | ( ( element @ SV21 @ SV7 )
        = $false )
      | ( ( element @ SV7 @ SV21 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[185]) ).

thf(188,plain,
    ! [SV12: $i,SV22: $i] :
      ( ( ( ~ ( element @ SV22 @ n ) )
        = $true )
      | ( ( equalish @ SV22 @ n )
        = $true )
      | ( ( equalish @ SV12 @ n )
        = $true )
      | ( ( equalish @ SV12 @ SV22 )
        = $true )
      | ( ( element @ SV22 @ SV12 )
        = $false )
      | ( ( element @ SV12 @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[186]) ).

thf(189,plain,
    ! [SV12: $i,SV22: $i] :
      ( ( ( element @ SV22 @ n )
        = $false )
      | ( ( equalish @ SV22 @ n )
        = $true )
      | ( ( equalish @ SV12 @ n )
        = $true )
      | ( ( equalish @ SV12 @ SV22 )
        = $true )
      | ( ( element @ SV22 @ SV12 )
        = $false )
      | ( ( element @ SV12 @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[188]) ).

thf(190,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[77,189,187,184,183,182,171,168,167,163,161,160,158,157,155,154,151,150,141,140,111,106,105,104,103,102,80]) ).

thf(191,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[190]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYN014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n009.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul 11 23:22:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 26
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.36  .
% 0.13/0.36  (rf:0,axioms:26,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:28,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.20/0.43  
% 0.20/0.43  ********************************
% 0.20/0.43  *   All subproblems solved!    *
% 0.20/0.43  ********************************
% 0.20/0.43  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:26,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:190,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.44  
% 0.20/0.44  %**** Beginning of derivation protocol ****
% 0.20/0.44  % SZS output start CNFRefutation
% See solution above
% 0.20/0.44  
% 0.20/0.44  %**** End of derivation protocol ****
% 0.20/0.44  %**** no. of clauses in derivation: 191 ****
% 0.20/0.44  %**** clause counter: 190 ****
% 0.20/0.44  
% 0.20/0.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:26,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:190,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------