TSTP Solution File: PUZ030-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : PUZ030-1 : 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 : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 18:19:19 EDT 2022

% Result   : Unsatisfiable 0.17s 0.48s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   54
% Syntax   : Number of formulae    :  281 ( 110 unt;  10 typ;   0 def)
%            Number of atoms       : 1508 ( 397 equ;   0 cnn)
%            Maximal formula atoms :    7 (   5 avg)
%            Number of connectives : 1446 ( 297   ~; 443   |;   0   &; 706   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   84 (   0   ^  84   !;   0   ?;  84   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_barry,type,
    barry: $i ).

thf(tp_both,type,
    both: $i > $o ).

thf(tp_cole,type,
    cole: $i ).

thf(tp_dix,type,
    dix: $i ).

thf(tp_lang,type,
    lang: $i ).

thf(tp_mill,type,
    mill: $i ).

thf(tp_mustard,type,
    mustard: $i > $o ).

thf(tp_neither,type,
    neither: $i > $o ).

thf(tp_oneof,type,
    oneof: $i > $o ).

thf(tp_salt,type,
    salt: $i > $o ).

thf(1,axiom,
    ! [X: $i] :
      ( ( salt @ X )
      | ( mustard @ X )
      | ( neither @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neither4) ).

thf(2,axiom,
    ! [X: $i] :
      ( ~ ( neither @ X )
      | ~ ( mustard @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neither3) ).

thf(3,axiom,
    ! [X: $i] :
      ( ~ ( neither @ X )
      | ~ ( salt @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neither2) ).

thf(4,axiom,
    ! [X: $i] :
      ( ~ ( both @ X )
      | ~ ( neither @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neither1) ).

thf(5,axiom,
    ! [X: $i] :
      ( ~ ( oneof @ X )
      | ~ ( salt @ X )
      | ~ ( mustard @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneof4) ).

thf(6,axiom,
    ! [X: $i] :
      ( ( both @ X )
      | ( neither @ X )
      | ( oneof @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_condition_holds1) ).

thf(7,axiom,
    ! [X: $i] :
      ( ~ ( oneof @ X )
      | ~ ( neither @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneof3) ).

thf(8,axiom,
    ! [X: $i] :
      ( ~ ( oneof @ X )
      | ~ ( both @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneof2) ).

thf(9,axiom,
    ! [X: $i] :
      ( ~ ( oneof @ X )
      | ( salt @ X )
      | ( mustard @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneof1) ).

thf(10,axiom,
    ! [X: $i] :
      ( ~ ( salt @ X )
      | ~ ( mustard @ X )
      | ( both @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both3) ).

thf(11,axiom,
    ! [X: $i] :
      ( ~ ( both @ X )
      | ( mustard @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both2) ).

thf(12,axiom,
    ! [X: $i] :
      ( ~ ( both @ X )
      | ( salt @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both1) ).

thf(13,axiom,
    ( ~ ( oneof @ dix )
    | ( mustard @ mill ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10_3) ).

thf(14,axiom,
    ( ~ ( oneof @ cole )
    | ( mustard @ mill ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10_2) ).

thf(15,axiom,
    ( ~ ( mustard @ mill )
    | ( oneof @ cole )
    | ( oneof @ dix ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10_1) ).

thf(16,axiom,
    ( ~ ( both @ lang )
    | ( mustard @ mill ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9_3) ).

thf(17,axiom,
    ( ~ ( both @ barry )
    | ( salt @ mill ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9_2) ).

thf(18,axiom,
    ( ~ ( salt @ mill )
    | ( both @ barry )
    | ( both @ lang ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9_1) ).

thf(19,axiom,
    ( ~ ( neither @ mill )
    | ( mustard @ lang ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule8_3) ).

thf(20,axiom,
    ( ~ ( neither @ cole )
    | ( mustard @ lang ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule8_2) ).

thf(21,axiom,
    ( ~ ( mustard @ lang )
    | ( neither @ cole )
    | ( neither @ mill ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule8_1) ).

thf(22,axiom,
    ( ~ ( oneof @ dix )
    | ( salt @ lang ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7_3) ).

thf(23,axiom,
    ( ~ ( oneof @ barry )
    | ( salt @ lang ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7_2) ).

thf(24,axiom,
    ( ~ ( salt @ lang )
    | ( oneof @ barry )
    | ( oneof @ dix ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7_1) ).

thf(25,axiom,
    ( ~ ( neither @ mill )
    | ( mustard @ dix ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6_3) ).

thf(26,axiom,
    ( ~ ( neither @ lang )
    | ( mustard @ dix ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6_2) ).

thf(27,axiom,
    ( ~ ( mustard @ dix )
    | ( neither @ lang )
    | ( neither @ mill ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6_1) ).

thf(28,axiom,
    ( ~ ( both @ cole )
    | ( salt @ dix ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5_3) ).

thf(29,axiom,
    ( ~ ( neither @ barry )
    | ( salt @ dix ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5_2) ).

thf(30,axiom,
    ( ~ ( salt @ dix )
    | ( neither @ barry )
    | ( both @ cole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5_1) ).

thf(31,axiom,
    ( ~ ( both @ lang )
    | ( mustard @ cole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4_3) ).

thf(32,axiom,
    ( ~ ( both @ dix )
    | ( mustard @ cole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4_2) ).

thf(33,axiom,
    ( ~ ( mustard @ cole )
    | ( both @ dix )
    | ( both @ lang ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4_1) ).

thf(34,axiom,
    ( ~ ( neither @ mill )
    | ( salt @ cole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3_3) ).

thf(35,axiom,
    ( ~ ( oneof @ barry )
    | ( salt @ cole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3_2) ).

thf(36,axiom,
    ( ~ ( salt @ cole )
    | ( oneof @ barry )
    | ( neither @ mill ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3_1) ).

thf(37,axiom,
    ( ~ ( both @ mill )
    | ( mustard @ barry ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2_3) ).

thf(38,axiom,
    ( ~ ( neither @ dix )
    | ( mustard @ barry ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2_2) ).

thf(39,axiom,
    ( ~ ( mustard @ barry )
    | ( neither @ dix )
    | ( both @ mill ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2_1) ).

thf(40,axiom,
    ( ~ ( oneof @ lang )
    | ( salt @ barry ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1_3) ).

thf(41,axiom,
    ( ~ ( oneof @ cole )
    | ( salt @ barry ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1_2) ).

thf(42,axiom,
    ( ~ ( salt @ barry )
    | ( oneof @ cole )
    | ( oneof @ lang ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1_1) ).

thf(43,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(44,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[43]) ).

thf(45,negated_conjecture,
    ( ~ ( neither @ cole )
    | ~ ( neither @ dix )
    | ~ ( both @ barry )
    | ~ ( oneof @ lang )
    | ~ ( salt @ mill )
    | ~ ( mustard @ lang )
    | ~ ( oneof @ mill ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_who_takes_what) ).

thf(46,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[44]) ).

thf(47,plain,
    ( ( ! [X: $i] :
          ( ( salt @ X )
          | ( mustard @ X )
          | ( neither @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(48,plain,
    ( ( ! [X: $i] :
          ( ~ ( neither @ X )
          | ~ ( mustard @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(49,plain,
    ( ( ! [X: $i] :
          ( ~ ( neither @ X )
          | ~ ( salt @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(50,plain,
    ( ( ! [X: $i] :
          ( ~ ( both @ X )
          | ~ ( neither @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(51,plain,
    ( ( ! [X: $i] :
          ( ~ ( oneof @ X )
          | ~ ( salt @ X )
          | ~ ( mustard @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(52,plain,
    ( ( ! [X: $i] :
          ( ( both @ X )
          | ( neither @ X )
          | ( oneof @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(53,plain,
    ( ( ! [X: $i] :
          ( ~ ( oneof @ X )
          | ~ ( neither @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(54,plain,
    ( ( ! [X: $i] :
          ( ~ ( oneof @ X )
          | ~ ( both @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(55,plain,
    ( ( ! [X: $i] :
          ( ~ ( oneof @ X )
          | ( salt @ X )
          | ( mustard @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(56,plain,
    ( ( ! [X: $i] :
          ( ~ ( salt @ X )
          | ~ ( mustard @ X )
          | ( both @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(57,plain,
    ( ( ! [X: $i] :
          ( ~ ( both @ X )
          | ( mustard @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(58,plain,
    ( ( ! [X: $i] :
          ( ~ ( both @ X )
          | ( salt @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(59,plain,
    ( ( ~ ( oneof @ dix )
      | ( mustard @ mill ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(60,plain,
    ( ( ~ ( oneof @ cole )
      | ( mustard @ mill ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(61,plain,
    ( ( ~ ( mustard @ mill )
      | ( oneof @ cole )
      | ( oneof @ dix ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(62,plain,
    ( ( ~ ( both @ lang )
      | ( mustard @ mill ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(63,plain,
    ( ( ~ ( both @ barry )
      | ( salt @ mill ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(64,plain,
    ( ( ~ ( salt @ mill )
      | ( both @ barry )
      | ( both @ lang ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(65,plain,
    ( ( ~ ( neither @ mill )
      | ( mustard @ lang ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(66,plain,
    ( ( ~ ( neither @ cole )
      | ( mustard @ lang ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(67,plain,
    ( ( ~ ( mustard @ lang )
      | ( neither @ cole )
      | ( neither @ mill ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(68,plain,
    ( ( ~ ( oneof @ dix )
      | ( salt @ lang ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(69,plain,
    ( ( ~ ( oneof @ barry )
      | ( salt @ lang ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(70,plain,
    ( ( ~ ( salt @ lang )
      | ( oneof @ barry )
      | ( oneof @ dix ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(71,plain,
    ( ( ~ ( neither @ mill )
      | ( mustard @ dix ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(72,plain,
    ( ( ~ ( neither @ lang )
      | ( mustard @ dix ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(73,plain,
    ( ( ~ ( mustard @ dix )
      | ( neither @ lang )
      | ( neither @ mill ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(74,plain,
    ( ( ~ ( both @ cole )
      | ( salt @ dix ) )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(75,plain,
    ( ( ~ ( neither @ barry )
      | ( salt @ dix ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(76,plain,
    ( ( ~ ( salt @ dix )
      | ( neither @ barry )
      | ( both @ cole ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(77,plain,
    ( ( ~ ( both @ lang )
      | ( mustard @ cole ) )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(78,plain,
    ( ( ~ ( both @ dix )
      | ( mustard @ cole ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(79,plain,
    ( ( ~ ( mustard @ cole )
      | ( both @ dix )
      | ( both @ lang ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(80,plain,
    ( ( ~ ( neither @ mill )
      | ( salt @ cole ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(81,plain,
    ( ( ~ ( oneof @ barry )
      | ( salt @ cole ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(82,plain,
    ( ( ~ ( salt @ cole )
      | ( oneof @ barry )
      | ( neither @ mill ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(83,plain,
    ( ( ~ ( both @ mill )
      | ( mustard @ barry ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(84,plain,
    ( ( ~ ( neither @ dix )
      | ( mustard @ barry ) )
    = $true ),
    inference(unfold_def,[status(thm)],[38]) ).

thf(85,plain,
    ( ( ~ ( mustard @ barry )
      | ( neither @ dix )
      | ( both @ mill ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(86,plain,
    ( ( ~ ( oneof @ lang )
      | ( salt @ barry ) )
    = $true ),
    inference(unfold_def,[status(thm)],[40]) ).

thf(87,plain,
    ( ( ~ ( oneof @ cole )
      | ( salt @ barry ) )
    = $true ),
    inference(unfold_def,[status(thm)],[41]) ).

thf(88,plain,
    ( ( ~ ( salt @ barry )
      | ( oneof @ cole )
      | ( oneof @ lang ) )
    = $true ),
    inference(unfold_def,[status(thm)],[42]) ).

thf(89,plain,
    ( ( ~ ( neither @ cole )
      | ~ ( neither @ dix )
      | ~ ( both @ barry )
      | ~ ( oneof @ lang )
      | ~ ( salt @ mill )
      | ~ ( mustard @ lang )
      | ~ ( oneof @ mill ) )
    = $true ),
    inference(unfold_def,[status(thm)],[45]) ).

thf(90,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[46]) ).

thf(91,plain,
    ( ( ! [X: $i] :
          ( ~ ( oneof @ X )
          | ( mustard @ X )
          | ( salt @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[55]) ).

thf(92,plain,
    ( ( ~ ( salt @ dix )
      | ( both @ cole )
      | ( neither @ barry ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[76]) ).

thf(93,plain,
    ( ( ~ ( salt @ cole )
      | ( neither @ mill )
      | ( oneof @ barry ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[82]) ).

thf(94,plain,
    ( ( ~ ( mustard @ barry )
      | ( both @ mill )
      | ( neither @ dix ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[85]) ).

thf(95,plain,
    ( ( ~ ( neither @ cole )
      | ~ ( neither @ dix )
      | ~ ( both @ barry )
      | ~ ( oneof @ lang )
      | ~ ( salt @ mill )
      | ~ ( mustard @ lang )
      | ~ ( oneof @ mill ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(96,plain,
    ( ( ~ ( salt @ barry )
      | ( oneof @ cole )
      | ( oneof @ lang ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(97,plain,
    ( ( ~ ( oneof @ cole )
      | ( salt @ barry ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(98,plain,
    ( ( ~ ( oneof @ lang )
      | ( salt @ barry ) )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(99,plain,
    ( ( ~ ( mustard @ barry )
      | ( both @ mill )
      | ( neither @ dix ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(100,plain,
    ( ( ~ ( neither @ dix )
      | ( mustard @ barry ) )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(101,plain,
    ( ( ~ ( both @ mill )
      | ( mustard @ barry ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(102,plain,
    ( ( ~ ( salt @ cole )
      | ( neither @ mill )
      | ( oneof @ barry ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(103,plain,
    ( ( ~ ( oneof @ barry )
      | ( salt @ cole ) )
    = $true ),
    inference(copy,[status(thm)],[81]) ).

thf(104,plain,
    ( ( ~ ( neither @ mill )
      | ( salt @ cole ) )
    = $true ),
    inference(copy,[status(thm)],[80]) ).

thf(105,plain,
    ( ( ~ ( mustard @ cole )
      | ( both @ dix )
      | ( both @ lang ) )
    = $true ),
    inference(copy,[status(thm)],[79]) ).

thf(106,plain,
    ( ( ~ ( both @ dix )
      | ( mustard @ cole ) )
    = $true ),
    inference(copy,[status(thm)],[78]) ).

thf(107,plain,
    ( ( ~ ( both @ lang )
      | ( mustard @ cole ) )
    = $true ),
    inference(copy,[status(thm)],[77]) ).

thf(108,plain,
    ( ( ~ ( salt @ dix )
      | ( both @ cole )
      | ( neither @ barry ) )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(109,plain,
    ( ( ~ ( neither @ barry )
      | ( salt @ dix ) )
    = $true ),
    inference(copy,[status(thm)],[75]) ).

thf(110,plain,
    ( ( ~ ( both @ cole )
      | ( salt @ dix ) )
    = $true ),
    inference(copy,[status(thm)],[74]) ).

thf(111,plain,
    ( ( ~ ( mustard @ dix )
      | ( neither @ lang )
      | ( neither @ mill ) )
    = $true ),
    inference(copy,[status(thm)],[73]) ).

thf(112,plain,
    ( ( ~ ( neither @ lang )
      | ( mustard @ dix ) )
    = $true ),
    inference(copy,[status(thm)],[72]) ).

thf(113,plain,
    ( ( ~ ( neither @ mill )
      | ( mustard @ dix ) )
    = $true ),
    inference(copy,[status(thm)],[71]) ).

thf(114,plain,
    ( ( ~ ( salt @ lang )
      | ( oneof @ barry )
      | ( oneof @ dix ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(115,plain,
    ( ( ~ ( oneof @ barry )
      | ( salt @ lang ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(116,plain,
    ( ( ~ ( oneof @ dix )
      | ( salt @ lang ) )
    = $true ),
    inference(copy,[status(thm)],[68]) ).

thf(117,plain,
    ( ( ~ ( mustard @ lang )
      | ( neither @ cole )
      | ( neither @ mill ) )
    = $true ),
    inference(copy,[status(thm)],[67]) ).

thf(118,plain,
    ( ( ~ ( neither @ cole )
      | ( mustard @ lang ) )
    = $true ),
    inference(copy,[status(thm)],[66]) ).

thf(119,plain,
    ( ( ~ ( neither @ mill )
      | ( mustard @ lang ) )
    = $true ),
    inference(copy,[status(thm)],[65]) ).

thf(120,plain,
    ( ( ~ ( salt @ mill )
      | ( both @ barry )
      | ( both @ lang ) )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(121,plain,
    ( ( ~ ( both @ barry )
      | ( salt @ mill ) )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(122,plain,
    ( ( ~ ( both @ lang )
      | ( mustard @ mill ) )
    = $true ),
    inference(copy,[status(thm)],[62]) ).

thf(123,plain,
    ( ( ~ ( mustard @ mill )
      | ( oneof @ cole )
      | ( oneof @ dix ) )
    = $true ),
    inference(copy,[status(thm)],[61]) ).

thf(124,plain,
    ( ( ~ ( oneof @ cole )
      | ( mustard @ mill ) )
    = $true ),
    inference(copy,[status(thm)],[60]) ).

thf(125,plain,
    ( ( ~ ( oneof @ dix )
      | ( mustard @ mill ) )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(126,plain,
    ( ( ! [X: $i] :
          ( ~ ( both @ X )
          | ( salt @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[58]) ).

thf(127,plain,
    ( ( ! [X: $i] :
          ( ~ ( both @ X )
          | ( mustard @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[57]) ).

thf(128,plain,
    ( ( ! [X: $i] :
          ( ~ ( salt @ X )
          | ~ ( mustard @ X )
          | ( both @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(129,plain,
    ( ( ! [X: $i] :
          ( ~ ( oneof @ X )
          | ( mustard @ X )
          | ( salt @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(130,plain,
    ( ( ! [X: $i] :
          ( ~ ( oneof @ X )
          | ~ ( both @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(131,plain,
    ( ( ! [X: $i] :
          ( ~ ( oneof @ X )
          | ~ ( neither @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(132,plain,
    ( ( ! [X: $i] :
          ( ( both @ X )
          | ( neither @ X )
          | ( oneof @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(133,plain,
    ( ( ! [X: $i] :
          ( ~ ( oneof @ X )
          | ~ ( salt @ X )
          | ~ ( mustard @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(134,plain,
    ( ( ! [X: $i] :
          ( ~ ( both @ X )
          | ~ ( neither @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(135,plain,
    ( ( ! [X: $i] :
          ( ~ ( neither @ X )
          | ~ ( salt @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(136,plain,
    ( ( ! [X: $i] :
          ( ~ ( neither @ X )
          | ~ ( mustard @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(137,plain,
    ( ( ! [X: $i] :
          ( ( salt @ X )
          | ( mustard @ X )
          | ( neither @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(138,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(139,plain,
    ( ( ( ~ ( neither @ cole ) )
      = $true )
    | ( ( ~ ( neither @ dix )
        | ~ ( both @ barry )
        | ~ ( oneof @ lang )
        | ~ ( salt @ mill )
        | ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(140,plain,
    ( ( ( ~ ( salt @ barry ) )
      = $true )
    | ( ( ( oneof @ cole )
        | ( oneof @ lang ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[96]) ).

thf(141,plain,
    ( ( ( ~ ( oneof @ cole ) )
      = $true )
    | ( ( salt @ barry )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[97]) ).

thf(142,plain,
    ( ( ( ~ ( oneof @ lang ) )
      = $true )
    | ( ( salt @ barry )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[98]) ).

thf(143,plain,
    ( ( ( ~ ( mustard @ barry ) )
      = $true )
    | ( ( ( both @ mill )
        | ( neither @ dix ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(144,plain,
    ( ( ( ~ ( neither @ dix ) )
      = $true )
    | ( ( mustard @ barry )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[100]) ).

thf(145,plain,
    ( ( ( ~ ( both @ mill ) )
      = $true )
    | ( ( mustard @ barry )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[101]) ).

thf(146,plain,
    ( ( ( ~ ( salt @ cole ) )
      = $true )
    | ( ( ( neither @ mill )
        | ( oneof @ barry ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[102]) ).

thf(147,plain,
    ( ( ( ~ ( oneof @ barry ) )
      = $true )
    | ( ( salt @ cole )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[103]) ).

thf(148,plain,
    ( ( ( ~ ( neither @ mill ) )
      = $true )
    | ( ( salt @ cole )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[104]) ).

thf(149,plain,
    ( ( ( ~ ( mustard @ cole ) )
      = $true )
    | ( ( ( both @ dix )
        | ( both @ lang ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[105]) ).

thf(150,plain,
    ( ( ( ~ ( both @ dix ) )
      = $true )
    | ( ( mustard @ cole )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[106]) ).

thf(151,plain,
    ( ( ( ~ ( both @ lang ) )
      = $true )
    | ( ( mustard @ cole )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[107]) ).

thf(152,plain,
    ( ( ( ~ ( salt @ dix ) )
      = $true )
    | ( ( ( both @ cole )
        | ( neither @ barry ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[108]) ).

thf(153,plain,
    ( ( ( ~ ( neither @ barry ) )
      = $true )
    | ( ( salt @ dix )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[109]) ).

thf(154,plain,
    ( ( ( ~ ( both @ cole ) )
      = $true )
    | ( ( salt @ dix )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[110]) ).

thf(155,plain,
    ( ( ( ~ ( mustard @ dix ) )
      = $true )
    | ( ( ( neither @ lang )
        | ( neither @ mill ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[111]) ).

thf(156,plain,
    ( ( ( ~ ( neither @ lang ) )
      = $true )
    | ( ( mustard @ dix )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[112]) ).

thf(157,plain,
    ( ( ( ~ ( neither @ mill ) )
      = $true )
    | ( ( mustard @ dix )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[113]) ).

thf(158,plain,
    ( ( ( ~ ( salt @ lang ) )
      = $true )
    | ( ( ( oneof @ barry )
        | ( oneof @ dix ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[114]) ).

thf(159,plain,
    ( ( ( ~ ( oneof @ barry ) )
      = $true )
    | ( ( salt @ lang )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[115]) ).

thf(160,plain,
    ( ( ( ~ ( oneof @ dix ) )
      = $true )
    | ( ( salt @ lang )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[116]) ).

thf(161,plain,
    ( ( ( ~ ( mustard @ lang ) )
      = $true )
    | ( ( ( neither @ cole )
        | ( neither @ mill ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[117]) ).

thf(162,plain,
    ( ( ( ~ ( neither @ cole ) )
      = $true )
    | ( ( mustard @ lang )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[118]) ).

thf(163,plain,
    ( ( ( ~ ( neither @ mill ) )
      = $true )
    | ( ( mustard @ lang )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[119]) ).

thf(164,plain,
    ( ( ( ~ ( salt @ mill ) )
      = $true )
    | ( ( ( both @ barry )
        | ( both @ lang ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[120]) ).

thf(165,plain,
    ( ( ( ~ ( both @ barry ) )
      = $true )
    | ( ( salt @ mill )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[121]) ).

thf(166,plain,
    ( ( ( ~ ( both @ lang ) )
      = $true )
    | ( ( mustard @ mill )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[122]) ).

thf(167,plain,
    ( ( ( ~ ( mustard @ mill ) )
      = $true )
    | ( ( ( oneof @ cole )
        | ( oneof @ dix ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[123]) ).

thf(168,plain,
    ( ( ( ~ ( oneof @ cole ) )
      = $true )
    | ( ( mustard @ mill )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[124]) ).

thf(169,plain,
    ( ( ( ~ ( oneof @ dix ) )
      = $true )
    | ( ( mustard @ mill )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[125]) ).

thf(170,plain,
    ! [SV1: $i] :
      ( ( ~ ( both @ SV1 )
        | ( salt @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(171,plain,
    ! [SV2: $i] :
      ( ( ~ ( both @ SV2 )
        | ( mustard @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[127]) ).

thf(172,plain,
    ! [SV3: $i] :
      ( ( ~ ( salt @ SV3 )
        | ~ ( mustard @ SV3 )
        | ( both @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(173,plain,
    ! [SV4: $i] :
      ( ( ~ ( oneof @ SV4 )
        | ( mustard @ SV4 )
        | ( salt @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(174,plain,
    ! [SV5: $i] :
      ( ( ~ ( oneof @ SV5 )
        | ~ ( both @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[130]) ).

thf(175,plain,
    ! [SV6: $i] :
      ( ( ~ ( oneof @ SV6 )
        | ~ ( neither @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[131]) ).

thf(176,plain,
    ! [SV7: $i] :
      ( ( ( both @ SV7 )
        | ( neither @ SV7 )
        | ( oneof @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[132]) ).

thf(177,plain,
    ! [SV8: $i] :
      ( ( ~ ( oneof @ SV8 )
        | ~ ( salt @ SV8 )
        | ~ ( mustard @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(178,plain,
    ! [SV9: $i] :
      ( ( ~ ( both @ SV9 )
        | ~ ( neither @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(179,plain,
    ! [SV10: $i] :
      ( ( ~ ( neither @ SV10 )
        | ~ ( salt @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(180,plain,
    ! [SV11: $i] :
      ( ( ~ ( neither @ SV11 )
        | ~ ( mustard @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(181,plain,
    ! [SV12: $i] :
      ( ( ( salt @ SV12 )
        | ( mustard @ SV12 )
        | ( neither @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[137]) ).

thf(182,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[138]) ).

thf(183,plain,
    ( ( ( neither @ cole )
      = $false )
    | ( ( ~ ( neither @ dix )
        | ~ ( both @ barry )
        | ~ ( oneof @ lang )
        | ~ ( salt @ mill )
        | ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[139]) ).

thf(184,plain,
    ( ( ( salt @ barry )
      = $false )
    | ( ( ( oneof @ cole )
        | ( oneof @ lang ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[140]) ).

thf(185,plain,
    ( ( ( oneof @ cole )
      = $false )
    | ( ( salt @ barry )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[141]) ).

thf(186,plain,
    ( ( ( oneof @ lang )
      = $false )
    | ( ( salt @ barry )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[142]) ).

thf(187,plain,
    ( ( ( mustard @ barry )
      = $false )
    | ( ( ( both @ mill )
        | ( neither @ dix ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[143]) ).

thf(188,plain,
    ( ( ( neither @ dix )
      = $false )
    | ( ( mustard @ barry )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[144]) ).

thf(189,plain,
    ( ( ( both @ mill )
      = $false )
    | ( ( mustard @ barry )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[145]) ).

thf(190,plain,
    ( ( ( salt @ cole )
      = $false )
    | ( ( ( neither @ mill )
        | ( oneof @ barry ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[146]) ).

thf(191,plain,
    ( ( ( oneof @ barry )
      = $false )
    | ( ( salt @ cole )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(192,plain,
    ( ( ( neither @ mill )
      = $false )
    | ( ( salt @ cole )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[148]) ).

thf(193,plain,
    ( ( ( mustard @ cole )
      = $false )
    | ( ( ( both @ dix )
        | ( both @ lang ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(194,plain,
    ( ( ( both @ dix )
      = $false )
    | ( ( mustard @ cole )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[150]) ).

thf(195,plain,
    ( ( ( both @ lang )
      = $false )
    | ( ( mustard @ cole )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[151]) ).

thf(196,plain,
    ( ( ( salt @ dix )
      = $false )
    | ( ( ( both @ cole )
        | ( neither @ barry ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(197,plain,
    ( ( ( neither @ barry )
      = $false )
    | ( ( salt @ dix )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[153]) ).

thf(198,plain,
    ( ( ( both @ cole )
      = $false )
    | ( ( salt @ dix )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[154]) ).

thf(199,plain,
    ( ( ( mustard @ dix )
      = $false )
    | ( ( ( neither @ lang )
        | ( neither @ mill ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[155]) ).

thf(200,plain,
    ( ( ( neither @ lang )
      = $false )
    | ( ( mustard @ dix )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[156]) ).

thf(201,plain,
    ( ( ( neither @ mill )
      = $false )
    | ( ( mustard @ dix )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[157]) ).

thf(202,plain,
    ( ( ( salt @ lang )
      = $false )
    | ( ( ( oneof @ barry )
        | ( oneof @ dix ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[158]) ).

thf(203,plain,
    ( ( ( oneof @ barry )
      = $false )
    | ( ( salt @ lang )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[159]) ).

thf(204,plain,
    ( ( ( oneof @ dix )
      = $false )
    | ( ( salt @ lang )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[160]) ).

thf(205,plain,
    ( ( ( mustard @ lang )
      = $false )
    | ( ( ( neither @ cole )
        | ( neither @ mill ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[161]) ).

thf(206,plain,
    ( ( ( neither @ cole )
      = $false )
    | ( ( mustard @ lang )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[162]) ).

thf(207,plain,
    ( ( ( neither @ mill )
      = $false )
    | ( ( mustard @ lang )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[163]) ).

thf(208,plain,
    ( ( ( salt @ mill )
      = $false )
    | ( ( ( both @ barry )
        | ( both @ lang ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[164]) ).

thf(209,plain,
    ( ( ( both @ barry )
      = $false )
    | ( ( salt @ mill )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[165]) ).

thf(210,plain,
    ( ( ( both @ lang )
      = $false )
    | ( ( mustard @ mill )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[166]) ).

thf(211,plain,
    ( ( ( mustard @ mill )
      = $false )
    | ( ( ( oneof @ cole )
        | ( oneof @ dix ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[167]) ).

thf(212,plain,
    ( ( ( oneof @ cole )
      = $false )
    | ( ( mustard @ mill )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[168]) ).

thf(213,plain,
    ( ( ( oneof @ dix )
      = $false )
    | ( ( mustard @ mill )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[169]) ).

thf(214,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( both @ SV1 ) )
        = $true )
      | ( ( salt @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[170]) ).

thf(215,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( both @ SV2 ) )
        = $true )
      | ( ( mustard @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[171]) ).

thf(216,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( salt @ SV3 ) )
        = $true )
      | ( ( ~ ( mustard @ SV3 )
          | ( both @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[172]) ).

thf(217,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( oneof @ SV4 ) )
        = $true )
      | ( ( ( mustard @ SV4 )
          | ( salt @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[173]) ).

thf(218,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( oneof @ SV5 ) )
        = $true )
      | ( ( ~ ( both @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[174]) ).

thf(219,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( oneof @ SV6 ) )
        = $true )
      | ( ( ~ ( neither @ SV6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[175]) ).

thf(220,plain,
    ! [SV7: $i] :
      ( ( ( both @ SV7 )
        = $true )
      | ( ( ( neither @ SV7 )
          | ( oneof @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[176]) ).

thf(221,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( oneof @ SV8 ) )
        = $true )
      | ( ( ~ ( salt @ SV8 )
          | ~ ( mustard @ SV8 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[177]) ).

thf(222,plain,
    ! [SV9: $i] :
      ( ( ( ~ ( both @ SV9 ) )
        = $true )
      | ( ( ~ ( neither @ SV9 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[178]) ).

thf(223,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( neither @ SV10 ) )
        = $true )
      | ( ( ~ ( salt @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[179]) ).

thf(224,plain,
    ! [SV11: $i] :
      ( ( ( ~ ( neither @ SV11 ) )
        = $true )
      | ( ( ~ ( mustard @ SV11 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[180]) ).

thf(225,plain,
    ! [SV12: $i] :
      ( ( ( salt @ SV12 )
        = $true )
      | ( ( ( mustard @ SV12 )
          | ( neither @ SV12 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[181]) ).

thf(226,plain,
    ( ( ( ~ ( neither @ dix ) )
      = $true )
    | ( ( ~ ( both @ barry )
        | ~ ( oneof @ lang )
        | ~ ( salt @ mill )
        | ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[183]) ).

thf(227,plain,
    ( ( ( oneof @ cole )
      = $true )
    | ( ( oneof @ lang )
      = $true )
    | ( ( salt @ barry )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[184]) ).

thf(228,plain,
    ( ( ( both @ mill )
      = $true )
    | ( ( neither @ dix )
      = $true )
    | ( ( mustard @ barry )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[187]) ).

thf(229,plain,
    ( ( ( neither @ mill )
      = $true )
    | ( ( oneof @ barry )
      = $true )
    | ( ( salt @ cole )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[190]) ).

thf(230,plain,
    ( ( ( both @ dix )
      = $true )
    | ( ( both @ lang )
      = $true )
    | ( ( mustard @ cole )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[193]) ).

thf(231,plain,
    ( ( ( both @ cole )
      = $true )
    | ( ( neither @ barry )
      = $true )
    | ( ( salt @ dix )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[196]) ).

thf(232,plain,
    ( ( ( neither @ lang )
      = $true )
    | ( ( neither @ mill )
      = $true )
    | ( ( mustard @ dix )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[199]) ).

thf(233,plain,
    ( ( ( oneof @ barry )
      = $true )
    | ( ( oneof @ dix )
      = $true )
    | ( ( salt @ lang )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[202]) ).

thf(234,plain,
    ( ( ( neither @ cole )
      = $true )
    | ( ( neither @ mill )
      = $true )
    | ( ( mustard @ lang )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[205]) ).

thf(235,plain,
    ( ( ( both @ barry )
      = $true )
    | ( ( both @ lang )
      = $true )
    | ( ( salt @ mill )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[208]) ).

thf(236,plain,
    ( ( ( oneof @ cole )
      = $true )
    | ( ( oneof @ dix )
      = $true )
    | ( ( mustard @ mill )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[211]) ).

thf(237,plain,
    ! [SV1: $i] :
      ( ( ( both @ SV1 )
        = $false )
      | ( ( salt @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[214]) ).

thf(238,plain,
    ! [SV2: $i] :
      ( ( ( both @ SV2 )
        = $false )
      | ( ( mustard @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[215]) ).

thf(239,plain,
    ! [SV3: $i] :
      ( ( ( salt @ SV3 )
        = $false )
      | ( ( ~ ( mustard @ SV3 )
          | ( both @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[216]) ).

thf(240,plain,
    ! [SV4: $i] :
      ( ( ( oneof @ SV4 )
        = $false )
      | ( ( ( mustard @ SV4 )
          | ( salt @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[217]) ).

thf(241,plain,
    ! [SV5: $i] :
      ( ( ( oneof @ SV5 )
        = $false )
      | ( ( ~ ( both @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[218]) ).

thf(242,plain,
    ! [SV6: $i] :
      ( ( ( oneof @ SV6 )
        = $false )
      | ( ( ~ ( neither @ SV6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[219]) ).

thf(243,plain,
    ! [SV7: $i] :
      ( ( ( neither @ SV7 )
        = $true )
      | ( ( oneof @ SV7 )
        = $true )
      | ( ( both @ SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[220]) ).

thf(244,plain,
    ! [SV8: $i] :
      ( ( ( oneof @ SV8 )
        = $false )
      | ( ( ~ ( salt @ SV8 )
          | ~ ( mustard @ SV8 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[221]) ).

thf(245,plain,
    ! [SV9: $i] :
      ( ( ( both @ SV9 )
        = $false )
      | ( ( ~ ( neither @ SV9 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[222]) ).

thf(246,plain,
    ! [SV10: $i] :
      ( ( ( neither @ SV10 )
        = $false )
      | ( ( ~ ( salt @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[223]) ).

thf(247,plain,
    ! [SV11: $i] :
      ( ( ( neither @ SV11 )
        = $false )
      | ( ( ~ ( mustard @ SV11 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[224]) ).

thf(248,plain,
    ! [SV12: $i] :
      ( ( ( mustard @ SV12 )
        = $true )
      | ( ( neither @ SV12 )
        = $true )
      | ( ( salt @ SV12 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[225]) ).

thf(249,plain,
    ( ( ( neither @ dix )
      = $false )
    | ( ( ~ ( both @ barry )
        | ~ ( oneof @ lang )
        | ~ ( salt @ mill )
        | ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[226]) ).

thf(250,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( mustard @ SV3 ) )
        = $true )
      | ( ( both @ SV3 )
        = $true )
      | ( ( salt @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[239]) ).

thf(251,plain,
    ! [SV4: $i] :
      ( ( ( mustard @ SV4 )
        = $true )
      | ( ( salt @ SV4 )
        = $true )
      | ( ( oneof @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[240]) ).

thf(252,plain,
    ! [SV5: $i] :
      ( ( ( both @ SV5 )
        = $false )
      | ( ( oneof @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[241]) ).

thf(253,plain,
    ! [SV6: $i] :
      ( ( ( neither @ SV6 )
        = $false )
      | ( ( oneof @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[242]) ).

thf(254,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( salt @ SV8 ) )
        = $true )
      | ( ( ~ ( mustard @ SV8 ) )
        = $true )
      | ( ( oneof @ SV8 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[244]) ).

thf(255,plain,
    ! [SV9: $i] :
      ( ( ( neither @ SV9 )
        = $false )
      | ( ( both @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[245]) ).

thf(256,plain,
    ! [SV10: $i] :
      ( ( ( salt @ SV10 )
        = $false )
      | ( ( neither @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[246]) ).

thf(257,plain,
    ! [SV11: $i] :
      ( ( ( mustard @ SV11 )
        = $false )
      | ( ( neither @ SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[247]) ).

thf(258,plain,
    ( ( ( ~ ( both @ barry ) )
      = $true )
    | ( ( ~ ( oneof @ lang )
        | ~ ( salt @ mill )
        | ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true )
    | ( ( neither @ dix )
      = $false )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[249]) ).

thf(259,plain,
    ! [SV3: $i] :
      ( ( ( mustard @ SV3 )
        = $false )
      | ( ( both @ SV3 )
        = $true )
      | ( ( salt @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[250]) ).

thf(260,plain,
    ! [SV8: $i] :
      ( ( ( salt @ SV8 )
        = $false )
      | ( ( ~ ( mustard @ SV8 ) )
        = $true )
      | ( ( oneof @ SV8 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[254]) ).

thf(261,plain,
    ( ( ( both @ barry )
      = $false )
    | ( ( ~ ( oneof @ lang )
        | ~ ( salt @ mill )
        | ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true )
    | ( ( neither @ dix )
      = $false )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[258]) ).

thf(262,plain,
    ! [SV8: $i] :
      ( ( ( mustard @ SV8 )
        = $false )
      | ( ( salt @ SV8 )
        = $false )
      | ( ( oneof @ SV8 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[260]) ).

thf(263,plain,
    ( ( ( ~ ( oneof @ lang ) )
      = $true )
    | ( ( ~ ( salt @ mill )
        | ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true )
    | ( ( both @ barry )
      = $false )
    | ( ( neither @ dix )
      = $false )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[261]) ).

thf(264,plain,
    ( ( ( oneof @ lang )
      = $false )
    | ( ( ~ ( salt @ mill )
        | ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true )
    | ( ( both @ barry )
      = $false )
    | ( ( neither @ dix )
      = $false )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[263]) ).

thf(265,plain,
    ( ( ( ~ ( salt @ mill ) )
      = $true )
    | ( ( ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true )
    | ( ( oneof @ lang )
      = $false )
    | ( ( both @ barry )
      = $false )
    | ( ( neither @ dix )
      = $false )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[264]) ).

thf(266,plain,
    ( ( ( salt @ mill )
      = $false )
    | ( ( ~ ( mustard @ lang )
        | ~ ( oneof @ mill ) )
      = $true )
    | ( ( oneof @ lang )
      = $false )
    | ( ( both @ barry )
      = $false )
    | ( ( neither @ dix )
      = $false )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[265]) ).

thf(267,plain,
    ( ( ( ~ ( mustard @ lang ) )
      = $true )
    | ( ( ~ ( oneof @ mill ) )
      = $true )
    | ( ( salt @ mill )
      = $false )
    | ( ( oneof @ lang )
      = $false )
    | ( ( both @ barry )
      = $false )
    | ( ( neither @ dix )
      = $false )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[266]) ).

thf(268,plain,
    ( ( ( mustard @ lang )
      = $false )
    | ( ( ~ ( oneof @ mill ) )
      = $true )
    | ( ( salt @ mill )
      = $false )
    | ( ( oneof @ lang )
      = $false )
    | ( ( both @ barry )
      = $false )
    | ( ( neither @ dix )
      = $false )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[267]) ).

thf(269,plain,
    ( ( ( oneof @ mill )
      = $false )
    | ( ( mustard @ lang )
      = $false )
    | ( ( salt @ mill )
      = $false )
    | ( ( oneof @ lang )
      = $false )
    | ( ( both @ barry )
      = $false )
    | ( ( neither @ dix )
      = $false )
    | ( ( neither @ cole )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[268]) ).

thf(270,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[182,269,262,259,257,256,255,253,252,251,248,243,238,237,236,235,234,233,232,231,230,229,228,227,213,212,210,209,207,206,204,203,201,200,198,197,195,194,192,191,189,188,186,185]) ).

thf(271,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[270]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : PUZ030-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.32  % Computer : n021.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sat May 28 19:37:42 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.11/0.34  
% 0.11/0.34   No.of.Axioms: 43
% 0.11/0.34  
% 0.11/0.34   Length.of.Defs: 0
% 0.11/0.34  
% 0.11/0.34   Contains.Choice.Funs: false
% 0.11/0.35  (rf:0,axioms:43,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:45,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.17/0.48  
% 0.17/0.48  ********************************
% 0.17/0.48  *   All subproblems solved!    *
% 0.17/0.48  ********************************
% 0.17/0.48  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:43,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:270,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.17/0.49  
% 0.17/0.49  %**** Beginning of derivation protocol ****
% 0.17/0.49  % SZS output start CNFRefutation
% See solution above
% 0.17/0.49  
% 0.17/0.49  %**** End of derivation protocol ****
% 0.17/0.49  %**** no. of clauses in derivation: 271 ****
% 0.17/0.49  %**** clause counter: 270 ****
% 0.17/0.49  
% 0.17/0.49  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:43,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:270,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------