TSTP Solution File: HWV001-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : HWV001-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n029.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 18:17:39 EDT 2022

% Result   : Unsatisfiable 1.45s 1.67s
% Output   : CNFRefutation 1.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   73
% Syntax   : Number of formulae    :  227 ( 202 unt;  25 typ;   0 def)
%            Number of atoms       :  508 ( 340 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  851 (   5   ~;   0   |;   0   &; 846   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  25 usr;  21 con; 0-2 aty)
%            Number of variables   :  266 (   0   ^ 266   !;   0   ?; 266   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a1,type,
    a1: $i ).

thf(tp_a2,type,
    a2: $i ).

thf(tp_and,type,
    and: $i > $i > $i ).

thf(tp_b1,type,
    b1: $i ).

thf(tp_b2,type,
    b2: $i ).

thf(tp_b3,type,
    b3: $i ).

thf(tp_c1,type,
    c1: $i ).

thf(tp_c2,type,
    c2: $i ).

thf(tp_circuit,type,
    circuit: $i > $i > $o ).

thf(tp_d1,type,
    d1: $i ).

thf(tp_d2,type,
    d2: $i ).

thf(tp_d3,type,
    d3: $i ).

thf(tp_e1,type,
    e1: $i ).

thf(tp_e2,type,
    e2: $i ).

thf(tp_f1,type,
    f1: $i ).

thf(tp_f2,type,
    f2: $i ).

thf(tp_f3,type,
    f3: $i ).

thf(tp_i1,type,
    i1: $i ).

thf(tp_i2,type,
    i2: $i ).

thf(tp_input,type,
    input: $i > $i > $i ).

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

thf(tp_n1,type,
    n1: $i ).

thf(tp_not,type,
    not: $i > $i ).

thf(tp_or,type,
    or: $i > $i > $i ).

thf(tp_output,type,
    output: $i > $i > $i ).

thf(1,axiom,
    ! [X: $i,Y: $i] :
      ( ( or @ ( and @ X @ Y ) @ ( and @ Y @ ( not @ X ) ) )
      = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_not_simplification2) ).

thf(2,axiom,
    ! [X: $i,Y: $i] :
      ( ( or @ ( and @ X @ Y ) @ ( and @ X @ ( not @ Y ) ) )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_not_simplification1) ).

thf(3,axiom,
    ! [X: $i] :
      ( ( not @ ( not @ X ) )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_simplification) ).

thf(4,axiom,
    ! [X: $i,Y: $i] :
      ( ( or @ ( or @ X @ Y ) @ ( not @ X ) )
      = n1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_not_simplification3) ).

thf(5,axiom,
    ! [X: $i,Y: $i] :
      ( ( or @ ( or @ X @ Y ) @ ( not @ Y ) )
      = n1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_not_simplification2) ).

thf(6,axiom,
    ! [X: $i] :
      ( ( or @ X @ ( not @ X ) )
      = n1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_not_simplification1) ).

thf(7,axiom,
    ! [X: $i,Y: $i] :
      ( ( and @ ( and @ X @ Y ) @ ( not @ X ) )
      = n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_not_simplification3) ).

thf(8,axiom,
    ! [X: $i,Y: $i] :
      ( ( and @ ( and @ X @ Y ) @ ( not @ Y ) )
      = n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_not_simplification2) ).

thf(9,axiom,
    ! [X: $i] :
      ( ( and @ X @ ( not @ X ) )
      = n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_not_simplification1) ).

thf(10,axiom,
    ! [X: $i,Y: $i] :
      ( ( or @ ( or @ X @ Y ) @ X )
      = ( or @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_simplification3) ).

thf(11,axiom,
    ! [X: $i,Y: $i] :
      ( ( or @ ( or @ X @ Y ) @ Y )
      = ( or @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_simplification2) ).

thf(12,axiom,
    ! [X: $i] :
      ( ( or @ X @ X )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_simplification1) ).

thf(13,axiom,
    ! [X: $i,Y: $i] :
      ( ( and @ ( and @ X @ Y ) @ X )
      = ( and @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_simplification3) ).

thf(14,axiom,
    ! [X: $i,Y: $i] :
      ( ( and @ ( and @ X @ Y ) @ Y )
      = ( and @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_simplification2) ).

thf(15,axiom,
    ! [X: $i] :
      ( ( and @ X @ X )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_simplification1) ).

thf(16,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( and @ ( or @ X @ Y ) @ Z )
      = ( or @ ( and @ X @ Z ) @ ( and @ Y @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_canonicalization) ).

thf(17,axiom,
    ! [X: $i,Y: $i] :
      ( ( not @ ( or @ X @ Y ) )
      = ( and @ ( not @ X ) @ ( not @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_canonicalization2) ).

thf(18,axiom,
    ! [X: $i,Y: $i] :
      ( ( not @ ( and @ X @ Y ) )
      = ( or @ ( not @ X ) @ ( not @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_canonicalization1) ).

thf(19,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( and @ ( and @ X @ Y ) @ Z )
      = ( and @ ( and @ X @ Z ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_sorting) ).

thf(20,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( or @ ( or @ X @ Y ) @ Z )
      = ( or @ ( or @ X @ Z ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_sorting) ).

thf(21,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( or @ X @ ( or @ Y @ Z ) )
      = ( or @ ( or @ X @ Y ) @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_associativity) ).

thf(22,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( and @ X @ ( and @ Y @ Z ) )
      = ( and @ ( and @ X @ Y ) @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_associativity) ).

thf(23,axiom,
    ! [X: $i,Y: $i] :
      ( ( or @ X @ Y )
      = ( or @ Y @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutativity) ).

thf(24,axiom,
    ! [X: $i,Y: $i] :
      ( ( and @ X @ Y )
      = ( and @ Y @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutativity) ).

thf(25,axiom,
    ( ( not @ n1 )
    = n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition2) ).

thf(26,axiom,
    ( ( not @ n0 )
    = n1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition1) ).

thf(27,axiom,
    ! [X: $i] :
      ( ( or @ X @ n1 )
      = n1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition2) ).

thf(28,axiom,
    ! [X: $i] :
      ( ( or @ X @ n0 )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition1) ).

thf(29,axiom,
    ! [X: $i] :
      ( ( and @ X @ n1 )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition2) ).

thf(30,axiom,
    ! [X: $i] :
      ( ( and @ X @ n0 )
      = n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition1) ).

thf(31,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(32,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[31]) ).

thf(33,negated_conjecture,
    ~ ( circuit @ ( input @ i1 @ i2 ) @ ( output @ i2 @ i1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_interchange) ).

thf(34,negated_conjecture,
    circuit @ ( input @ i1 @ i2 ) @ ( output @ a1 @ a2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit_description) ).

thf(35,negated_conjecture,
    ( f3
    = ( and @ i1 @ i2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor15) ).

thf(36,negated_conjecture,
    ( f2
    = ( not @ i2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor14) ).

thf(37,negated_conjecture,
    ( f1
    = ( not @ i1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor13) ).

thf(38,negated_conjecture,
    ( e2
    = ( or @ f2 @ f3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor12) ).

thf(39,negated_conjecture,
    ( e1
    = ( or @ f1 @ f3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor11) ).

thf(40,negated_conjecture,
    ( d2
    = ( not @ e2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor10) ).

thf(41,negated_conjecture,
    ( d1
    = ( not @ e1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor9) ).

thf(42,negated_conjecture,
    d3 = f3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor8) ).

thf(43,negated_conjecture,
    ( c2
    = ( or @ d2 @ d3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor7) ).

thf(44,negated_conjecture,
    ( c1
    = ( or @ d1 @ d3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor6) ).

thf(45,negated_conjecture,
    ( b3
    = ( or @ c1 @ c2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor5) ).

thf(46,negated_conjecture,
    ( b2
    = ( not @ d2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor4) ).

thf(47,negated_conjecture,
    ( b1
    = ( not @ d1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor3) ).

thf(48,negated_conjecture,
    ( a2
    = ( and @ b2 @ b3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor2) ).

thf(49,negated_conjecture,
    ( a1
    = ( and @ b1 @ b3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor1) ).

thf(50,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[32]) ).

thf(51,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( and @ X @ Y ) @ ( and @ Y @ ( not @ X ) ) )
          = Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(52,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( and @ X @ Y ) @ ( and @ X @ ( not @ Y ) ) )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(53,plain,
    ( ( ! [X: $i] :
          ( ( not @ ( not @ X ) )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(54,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( or @ X @ Y ) @ ( not @ X ) )
          = n1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(55,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( or @ X @ Y ) @ ( not @ Y ) )
          = n1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(56,plain,
    ( ( ! [X: $i] :
          ( ( or @ X @ ( not @ X ) )
          = n1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(57,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ ( and @ X @ Y ) @ ( not @ X ) )
          = n0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(58,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ ( and @ X @ Y ) @ ( not @ Y ) )
          = n0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(59,plain,
    ( ( ! [X: $i] :
          ( ( and @ X @ ( not @ X ) )
          = n0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(60,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( or @ X @ Y ) @ X )
          = ( or @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(61,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( or @ X @ Y ) @ Y )
          = ( or @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(62,plain,
    ( ( ! [X: $i] :
          ( ( or @ X @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(63,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ ( and @ X @ Y ) @ X )
          = ( and @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(64,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ ( and @ X @ Y ) @ Y )
          = ( and @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(65,plain,
    ( ( ! [X: $i] :
          ( ( and @ X @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(66,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( and @ ( or @ X @ Y ) @ Z )
          = ( or @ ( and @ X @ Z ) @ ( and @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(67,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( not @ ( or @ X @ Y ) )
          = ( and @ ( not @ X ) @ ( not @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(68,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( not @ ( and @ X @ Y ) )
          = ( or @ ( not @ X ) @ ( not @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(69,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( and @ ( and @ X @ Y ) @ Z )
          = ( and @ ( and @ X @ Z ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(70,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( or @ ( or @ X @ Y ) @ Z )
          = ( or @ ( or @ X @ Z ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(71,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( or @ X @ ( or @ Y @ Z ) )
          = ( or @ ( or @ X @ Y ) @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(72,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( and @ X @ ( and @ Y @ Z ) )
          = ( and @ ( and @ X @ Y ) @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(73,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ X @ Y )
          = ( or @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(74,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ X @ Y )
          = ( and @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(75,plain,
    ( ( ( not @ n1 )
      = n0 )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(76,plain,
    ( ( ( not @ n0 )
      = n1 )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(77,plain,
    ( ( ! [X: $i] :
          ( ( or @ X @ n1 )
          = n1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(78,plain,
    ( ( ! [X: $i] :
          ( ( or @ X @ n0 )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(79,plain,
    ( ( ! [X: $i] :
          ( ( and @ X @ n1 )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(80,plain,
    ( ( ! [X: $i] :
          ( ( and @ X @ n0 )
          = n0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(81,plain,
    ( ( ~ ( circuit @ ( input @ i1 @ i2 ) @ ( output @ i2 @ i1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(82,plain,
    ( ( circuit @ ( input @ i1 @ i2 ) @ ( output @ a1 @ a2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(83,plain,
    ( ( f3
      = ( and @ i1 @ i2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(84,plain,
    ( ( f2
      = ( not @ i2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(85,plain,
    ( ( f1
      = ( not @ i1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(86,plain,
    ( ( e2
      = ( or @ f2 @ f3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[38]) ).

thf(87,plain,
    ( ( e1
      = ( or @ f1 @ f3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(88,plain,
    ( ( d2
      = ( not @ e2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[40]) ).

thf(89,plain,
    ( ( d1
      = ( not @ e1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[41]) ).

thf(90,plain,
    ( ( d3 = f3 )
    = $true ),
    inference(unfold_def,[status(thm)],[42]) ).

thf(91,plain,
    ( ( c2
      = ( or @ d2 @ d3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[43]) ).

thf(92,plain,
    ( ( c1
      = ( or @ d1 @ d3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[44]) ).

thf(93,plain,
    ( ( b3
      = ( or @ c1 @ c2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[45]) ).

thf(94,plain,
    ( ( b2
      = ( not @ d2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[46]) ).

thf(95,plain,
    ( ( b1
      = ( not @ d1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[47]) ).

thf(96,plain,
    ( ( a2
      = ( and @ b2 @ b3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[48]) ).

thf(97,plain,
    ( ( a1
      = ( and @ b1 @ b3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[49]) ).

thf(98,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[50]) ).

thf(99,plain,
    ( ( a1
      = ( and @ b1 @ b3 ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(100,plain,
    ( ( a2
      = ( and @ b2 @ b3 ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(101,plain,
    ( ( b1
      = ( not @ d1 ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(102,plain,
    ( ( b2
      = ( not @ d2 ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(103,plain,
    ( ( b3
      = ( or @ c1 @ c2 ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(104,plain,
    ( ( c1
      = ( or @ d1 @ d3 ) )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(105,plain,
    ( ( c2
      = ( or @ d2 @ d3 ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(106,plain,
    ( ( d3 = f3 )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(107,plain,
    ( ( d1
      = ( not @ e1 ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(108,plain,
    ( ( d2
      = ( not @ e2 ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(109,plain,
    ( ( e1
      = ( or @ f1 @ f3 ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(110,plain,
    ( ( e2
      = ( or @ f2 @ f3 ) )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(111,plain,
    ( ( f1
      = ( not @ i1 ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(112,plain,
    ( ( f2
      = ( not @ i2 ) )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(113,plain,
    ( ( f3
      = ( and @ i1 @ i2 ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(114,plain,
    ( ( circuit @ ( input @ i1 @ i2 ) @ ( output @ a1 @ a2 ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(115,plain,
    ( ( ~ ( circuit @ ( input @ i1 @ i2 ) @ ( output @ i2 @ i1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[81]) ).

thf(116,plain,
    ( ( ! [X: $i] :
          ( ( and @ X @ n0 )
          = n0 ) )
    = $true ),
    inference(copy,[status(thm)],[80]) ).

thf(117,plain,
    ( ( ! [X: $i] :
          ( ( and @ X @ n1 )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[79]) ).

thf(118,plain,
    ( ( ! [X: $i] :
          ( ( or @ X @ n0 )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[78]) ).

thf(119,plain,
    ( ( ! [X: $i] :
          ( ( or @ X @ n1 )
          = n1 ) )
    = $true ),
    inference(copy,[status(thm)],[77]) ).

thf(120,plain,
    ( ( ( not @ n0 )
      = n1 )
    = $true ),
    inference(copy,[status(thm)],[76]) ).

thf(121,plain,
    ( ( ( not @ n1 )
      = n0 )
    = $true ),
    inference(copy,[status(thm)],[75]) ).

thf(122,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ X @ Y )
          = ( and @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[74]) ).

thf(123,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ X @ Y )
          = ( or @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[73]) ).

thf(124,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( and @ X @ ( and @ Y @ Z ) )
          = ( and @ ( and @ X @ Y ) @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[72]) ).

thf(125,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( or @ X @ ( or @ Y @ Z ) )
          = ( or @ ( or @ X @ Y ) @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[71]) ).

thf(126,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( or @ ( or @ X @ Y ) @ Z )
          = ( or @ ( or @ X @ Z ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(127,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( and @ ( and @ X @ Y ) @ Z )
          = ( and @ ( and @ X @ Z ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(128,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( not @ ( and @ X @ Y ) )
          = ( or @ ( not @ X ) @ ( not @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[68]) ).

thf(129,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( not @ ( or @ X @ Y ) )
          = ( and @ ( not @ X ) @ ( not @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[67]) ).

thf(130,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( and @ ( or @ X @ Y ) @ Z )
          = ( or @ ( and @ X @ Z ) @ ( and @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[66]) ).

thf(131,plain,
    ( ( ! [X: $i] :
          ( ( and @ X @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[65]) ).

thf(132,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ ( and @ X @ Y ) @ Y )
          = ( and @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(133,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ ( and @ X @ Y ) @ X )
          = ( and @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(134,plain,
    ( ( ! [X: $i] :
          ( ( or @ X @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[62]) ).

thf(135,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( or @ X @ Y ) @ Y )
          = ( or @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[61]) ).

thf(136,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( or @ X @ Y ) @ X )
          = ( or @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[60]) ).

thf(137,plain,
    ( ( ! [X: $i] :
          ( ( and @ X @ ( not @ X ) )
          = n0 ) )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(138,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ ( and @ X @ Y ) @ ( not @ Y ) )
          = n0 ) )
    = $true ),
    inference(copy,[status(thm)],[58]) ).

thf(139,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( and @ ( and @ X @ Y ) @ ( not @ X ) )
          = n0 ) )
    = $true ),
    inference(copy,[status(thm)],[57]) ).

thf(140,plain,
    ( ( ! [X: $i] :
          ( ( or @ X @ ( not @ X ) )
          = n1 ) )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(141,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( or @ X @ Y ) @ ( not @ Y ) )
          = n1 ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(142,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( or @ X @ Y ) @ ( not @ X ) )
          = n1 ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(143,plain,
    ( ( ! [X: $i] :
          ( ( not @ ( not @ X ) )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(144,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( and @ X @ Y ) @ ( and @ X @ ( not @ Y ) ) )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(145,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( or @ ( and @ X @ Y ) @ ( and @ Y @ ( not @ X ) ) )
          = Y ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(146,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(147,plain,
    ( ( circuit @ ( input @ i1 @ i2 ) @ ( output @ i2 @ i1 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[115]) ).

thf(148,plain,
    ! [SV1: $i] :
      ( ( ( and @ SV1 @ n0 )
        = n0 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(149,plain,
    ! [SV2: $i] :
      ( ( ( and @ SV2 @ n1 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[117]) ).

thf(150,plain,
    ! [SV3: $i] :
      ( ( ( or @ SV3 @ n0 )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(151,plain,
    ! [SV4: $i] :
      ( ( ( or @ SV4 @ n1 )
        = n1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[119]) ).

thf(152,plain,
    ! [SV5: $i] :
      ( ( ! [SY52: $i] :
            ( ( and @ SV5 @ SY52 )
            = ( and @ SY52 @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(153,plain,
    ! [SV6: $i] :
      ( ( ! [SY53: $i] :
            ( ( or @ SV6 @ SY53 )
            = ( or @ SY53 @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(154,plain,
    ! [SV7: $i] :
      ( ( ! [SY54: $i,SY55: $i] :
            ( ( and @ SV7 @ ( and @ SY54 @ SY55 ) )
            = ( and @ ( and @ SV7 @ SY54 ) @ SY55 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(155,plain,
    ! [SV8: $i] :
      ( ( ! [SY56: $i,SY57: $i] :
            ( ( or @ SV8 @ ( or @ SY56 @ SY57 ) )
            = ( or @ ( or @ SV8 @ SY56 ) @ SY57 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[125]) ).

thf(156,plain,
    ! [SV9: $i] :
      ( ( ! [SY58: $i,SY59: $i] :
            ( ( or @ ( or @ SV9 @ SY58 ) @ SY59 )
            = ( or @ ( or @ SV9 @ SY59 ) @ SY58 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(157,plain,
    ! [SV10: $i] :
      ( ( ! [SY60: $i,SY61: $i] :
            ( ( and @ ( and @ SV10 @ SY60 ) @ SY61 )
            = ( and @ ( and @ SV10 @ SY61 ) @ SY60 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[127]) ).

thf(158,plain,
    ! [SV11: $i] :
      ( ( ! [SY62: $i] :
            ( ( not @ ( and @ SV11 @ SY62 ) )
            = ( or @ ( not @ SV11 ) @ ( not @ SY62 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(159,plain,
    ! [SV12: $i] :
      ( ( ! [SY63: $i] :
            ( ( not @ ( or @ SV12 @ SY63 ) )
            = ( and @ ( not @ SV12 ) @ ( not @ SY63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(160,plain,
    ! [SV13: $i] :
      ( ( ! [SY64: $i,SY65: $i] :
            ( ( and @ ( or @ SV13 @ SY64 ) @ SY65 )
            = ( or @ ( and @ SV13 @ SY65 ) @ ( and @ SY64 @ SY65 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[130]) ).

thf(161,plain,
    ! [SV14: $i] :
      ( ( ( and @ SV14 @ SV14 )
        = SV14 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[131]) ).

thf(162,plain,
    ! [SV15: $i] :
      ( ( ! [SY66: $i] :
            ( ( and @ ( and @ SV15 @ SY66 ) @ SY66 )
            = ( and @ SV15 @ SY66 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[132]) ).

thf(163,plain,
    ! [SV16: $i] :
      ( ( ! [SY67: $i] :
            ( ( and @ ( and @ SV16 @ SY67 ) @ SV16 )
            = ( and @ SV16 @ SY67 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(164,plain,
    ! [SV17: $i] :
      ( ( ( or @ SV17 @ SV17 )
        = SV17 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(165,plain,
    ! [SV18: $i] :
      ( ( ! [SY68: $i] :
            ( ( or @ ( or @ SV18 @ SY68 ) @ SY68 )
            = ( or @ SV18 @ SY68 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(166,plain,
    ! [SV19: $i] :
      ( ( ! [SY69: $i] :
            ( ( or @ ( or @ SV19 @ SY69 ) @ SV19 )
            = ( or @ SV19 @ SY69 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(167,plain,
    ! [SV20: $i] :
      ( ( ( and @ SV20 @ ( not @ SV20 ) )
        = n0 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[137]) ).

thf(168,plain,
    ! [SV21: $i] :
      ( ( ! [SY70: $i] :
            ( ( and @ ( and @ SV21 @ SY70 ) @ ( not @ SY70 ) )
            = n0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[138]) ).

thf(169,plain,
    ! [SV22: $i] :
      ( ( ! [SY71: $i] :
            ( ( and @ ( and @ SV22 @ SY71 ) @ ( not @ SV22 ) )
            = n0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(170,plain,
    ! [SV23: $i] :
      ( ( ( or @ SV23 @ ( not @ SV23 ) )
        = n1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(171,plain,
    ! [SV24: $i] :
      ( ( ! [SY72: $i] :
            ( ( or @ ( or @ SV24 @ SY72 ) @ ( not @ SY72 ) )
            = n1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(172,plain,
    ! [SV25: $i] :
      ( ( ! [SY73: $i] :
            ( ( or @ ( or @ SV25 @ SY73 ) @ ( not @ SV25 ) )
            = n1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[142]) ).

thf(173,plain,
    ! [SV26: $i] :
      ( ( ( not @ ( not @ SV26 ) )
        = SV26 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(174,plain,
    ! [SV27: $i] :
      ( ( ! [SY74: $i] :
            ( ( or @ ( and @ SV27 @ SY74 ) @ ( and @ SV27 @ ( not @ SY74 ) ) )
            = SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[144]) ).

thf(175,plain,
    ! [SV28: $i] :
      ( ( ! [SY75: $i] :
            ( ( or @ ( and @ SV28 @ SY75 ) @ ( and @ SY75 @ ( not @ SV28 ) ) )
            = SY75 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[145]) ).

thf(176,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[146]) ).

thf(177,plain,
    ! [SV29: $i,SV5: $i] :
      ( ( ( and @ SV5 @ SV29 )
        = ( and @ SV29 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[152]) ).

thf(178,plain,
    ! [SV30: $i,SV6: $i] :
      ( ( ( or @ SV6 @ SV30 )
        = ( or @ SV30 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[153]) ).

thf(179,plain,
    ! [SV31: $i,SV7: $i] :
      ( ( ! [SY76: $i] :
            ( ( and @ SV7 @ ( and @ SV31 @ SY76 ) )
            = ( and @ ( and @ SV7 @ SV31 ) @ SY76 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[154]) ).

thf(180,plain,
    ! [SV32: $i,SV8: $i] :
      ( ( ! [SY77: $i] :
            ( ( or @ SV8 @ ( or @ SV32 @ SY77 ) )
            = ( or @ ( or @ SV8 @ SV32 ) @ SY77 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[155]) ).

thf(181,plain,
    ! [SV33: $i,SV9: $i] :
      ( ( ! [SY78: $i] :
            ( ( or @ ( or @ SV9 @ SV33 ) @ SY78 )
            = ( or @ ( or @ SV9 @ SY78 ) @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[156]) ).

thf(182,plain,
    ! [SV34: $i,SV10: $i] :
      ( ( ! [SY79: $i] :
            ( ( and @ ( and @ SV10 @ SV34 ) @ SY79 )
            = ( and @ ( and @ SV10 @ SY79 ) @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[157]) ).

thf(183,plain,
    ! [SV35: $i,SV11: $i] :
      ( ( ( not @ ( and @ SV11 @ SV35 ) )
        = ( or @ ( not @ SV11 ) @ ( not @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[158]) ).

thf(184,plain,
    ! [SV36: $i,SV12: $i] :
      ( ( ( not @ ( or @ SV12 @ SV36 ) )
        = ( and @ ( not @ SV12 ) @ ( not @ SV36 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[159]) ).

thf(185,plain,
    ! [SV37: $i,SV13: $i] :
      ( ( ! [SY80: $i] :
            ( ( and @ ( or @ SV13 @ SV37 ) @ SY80 )
            = ( or @ ( and @ SV13 @ SY80 ) @ ( and @ SV37 @ SY80 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[160]) ).

thf(186,plain,
    ! [SV38: $i,SV15: $i] :
      ( ( ( and @ ( and @ SV15 @ SV38 ) @ SV38 )
        = ( and @ SV15 @ SV38 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[162]) ).

thf(187,plain,
    ! [SV39: $i,SV16: $i] :
      ( ( ( and @ ( and @ SV16 @ SV39 ) @ SV16 )
        = ( and @ SV16 @ SV39 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[163]) ).

thf(188,plain,
    ! [SV40: $i,SV18: $i] :
      ( ( ( or @ ( or @ SV18 @ SV40 ) @ SV40 )
        = ( or @ SV18 @ SV40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[165]) ).

thf(189,plain,
    ! [SV41: $i,SV19: $i] :
      ( ( ( or @ ( or @ SV19 @ SV41 ) @ SV19 )
        = ( or @ SV19 @ SV41 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[166]) ).

thf(190,plain,
    ! [SV42: $i,SV21: $i] :
      ( ( ( and @ ( and @ SV21 @ SV42 ) @ ( not @ SV42 ) )
        = n0 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[168]) ).

thf(191,plain,
    ! [SV43: $i,SV22: $i] :
      ( ( ( and @ ( and @ SV22 @ SV43 ) @ ( not @ SV22 ) )
        = n0 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[169]) ).

thf(192,plain,
    ! [SV44: $i,SV24: $i] :
      ( ( ( or @ ( or @ SV24 @ SV44 ) @ ( not @ SV44 ) )
        = n1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[171]) ).

thf(193,plain,
    ! [SV45: $i,SV25: $i] :
      ( ( ( or @ ( or @ SV25 @ SV45 ) @ ( not @ SV25 ) )
        = n1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[172]) ).

thf(194,plain,
    ! [SV46: $i,SV27: $i] :
      ( ( ( or @ ( and @ SV27 @ SV46 ) @ ( and @ SV27 @ ( not @ SV46 ) ) )
        = SV27 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[174]) ).

thf(195,plain,
    ! [SV47: $i,SV28: $i] :
      ( ( ( or @ ( and @ SV28 @ SV47 ) @ ( and @ SV47 @ ( not @ SV28 ) ) )
        = SV47 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[175]) ).

thf(196,plain,
    ! [SV48: $i,SV31: $i,SV7: $i] :
      ( ( ( and @ SV7 @ ( and @ SV31 @ SV48 ) )
        = ( and @ ( and @ SV7 @ SV31 ) @ SV48 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[179]) ).

thf(197,plain,
    ! [SV49: $i,SV32: $i,SV8: $i] :
      ( ( ( or @ SV8 @ ( or @ SV32 @ SV49 ) )
        = ( or @ ( or @ SV8 @ SV32 ) @ SV49 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[180]) ).

thf(198,plain,
    ! [SV50: $i,SV33: $i,SV9: $i] :
      ( ( ( or @ ( or @ SV9 @ SV33 ) @ SV50 )
        = ( or @ ( or @ SV9 @ SV50 ) @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[181]) ).

thf(199,plain,
    ! [SV51: $i,SV34: $i,SV10: $i] :
      ( ( ( and @ ( and @ SV10 @ SV34 ) @ SV51 )
        = ( and @ ( and @ SV10 @ SV51 ) @ SV34 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[182]) ).

thf(200,plain,
    ! [SV52: $i,SV37: $i,SV13: $i] :
      ( ( ( and @ ( or @ SV13 @ SV37 ) @ SV52 )
        = ( or @ ( and @ SV13 @ SV52 ) @ ( and @ SV37 @ SV52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[185]) ).

thf(201,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[99,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,184,183,178,177,176,173,170,167,164,161,151,150,149,148,147,121,120,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100]) ).

thf(202,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[201]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : HWV001-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Thu Jun 16 23:21:57 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.37  
% 0.13/0.37   No.of.Axioms: 47
% 0.13/0.37  
% 0.13/0.37   Length.of.Defs: 0
% 0.13/0.37  
% 0.13/0.37   Contains.Choice.Funs: false
% 0.13/0.37  .
% 0.13/0.38  (rf:0,axioms:47,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:49,loop_count:0,foatp_calls:0,translation:fof_full)........
% 1.45/1.67  
% 1.45/1.67  ********************************
% 1.45/1.67  *   All subproblems solved!    *
% 1.45/1.67  ********************************
% 1.45/1.67  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:47,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:201,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.45/1.68  
% 1.45/1.68  %**** Beginning of derivation protocol ****
% 1.45/1.68  % SZS output start CNFRefutation
% See solution above
% 1.45/1.68  
% 1.45/1.68  %**** End of derivation protocol ****
% 1.45/1.68  %**** no. of clauses in derivation: 202 ****
% 1.45/1.68  %**** clause counter: 201 ****
% 1.45/1.68  
% 1.45/1.68  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:47,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:201,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------