%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PUZ030-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:36:40 AM UTC 2026
% Result : Unsatisfiable 0.22s 5.31s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 44
% Syntax : Number of formulae : 267 ( 106 unt; 0 typ; 0 def)
% Number of atoms : 1488 ( 393 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 1422 ( 293 ~; 435 |; 0 &; 694 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 83 ( 0 ^; 83 !; 0 ?; 83 :)
% 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,
( ( ~ ( neither @ cole )
| ~ ( neither @ dix )
| ~ ( both @ barry )
| ~ ( oneof @ lang )
| ~ ( salt @ mill )
| ~ ( mustard @ lang )
| ~ ( oneof @ mill ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(92,plain,
( ( ~ ( salt @ barry )
| ( oneof @ cole )
| ( oneof @ lang ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(93,plain,
( ( ~ ( oneof @ cole )
| ( salt @ barry ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(94,plain,
( ( ~ ( oneof @ lang )
| ( salt @ barry ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(95,plain,
( ( ~ ( mustard @ barry )
| ( neither @ dix )
| ( both @ mill ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(96,plain,
( ( ~ ( neither @ dix )
| ( mustard @ barry ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(97,plain,
( ( ~ ( both @ mill )
| ( mustard @ barry ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(98,plain,
( ( ~ ( salt @ cole )
| ( oneof @ barry )
| ( neither @ mill ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(99,plain,
( ( ~ ( oneof @ barry )
| ( salt @ cole ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(100,plain,
( ( ~ ( neither @ mill )
| ( salt @ cole ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(101,plain,
( ( ~ ( mustard @ cole )
| ( both @ dix )
| ( both @ lang ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(102,plain,
( ( ~ ( both @ dix )
| ( mustard @ cole ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(103,plain,
( ( ~ ( both @ lang )
| ( mustard @ cole ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(104,plain,
( ( ~ ( salt @ dix )
| ( neither @ barry )
| ( both @ cole ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(105,plain,
( ( ~ ( neither @ barry )
| ( salt @ dix ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(106,plain,
( ( ~ ( both @ cole )
| ( salt @ dix ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(107,plain,
( ( ~ ( mustard @ dix )
| ( neither @ lang )
| ( neither @ mill ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(108,plain,
( ( ~ ( neither @ lang )
| ( mustard @ dix ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(109,plain,
( ( ~ ( neither @ mill )
| ( mustard @ dix ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(110,plain,
( ( ~ ( salt @ lang )
| ( oneof @ barry )
| ( oneof @ dix ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(111,plain,
( ( ~ ( oneof @ barry )
| ( salt @ lang ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(112,plain,
( ( ~ ( oneof @ dix )
| ( salt @ lang ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(113,plain,
( ( ~ ( mustard @ lang )
| ( neither @ cole )
| ( neither @ mill ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(114,plain,
( ( ~ ( neither @ cole )
| ( mustard @ lang ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(115,plain,
( ( ~ ( neither @ mill )
| ( mustard @ lang ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(116,plain,
( ( ~ ( salt @ mill )
| ( both @ barry )
| ( both @ lang ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(117,plain,
( ( ~ ( both @ barry )
| ( salt @ mill ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(118,plain,
( ( ~ ( both @ lang )
| ( mustard @ mill ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(119,plain,
( ( ~ ( mustard @ mill )
| ( oneof @ cole )
| ( oneof @ dix ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(120,plain,
( ( ~ ( oneof @ cole )
| ( mustard @ mill ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(121,plain,
( ( ~ ( oneof @ dix )
| ( mustard @ mill ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(122,plain,
( ( ! [X: $i] :
( ~ ( both @ X )
| ( salt @ X ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(123,plain,
( ( ! [X: $i] :
( ~ ( both @ X )
| ( mustard @ X ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(124,plain,
( ( ! [X: $i] :
( ~ ( salt @ X )
| ~ ( mustard @ X )
| ( both @ X ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(125,plain,
( ( ! [X: $i] :
( ~ ( oneof @ X )
| ( salt @ X )
| ( mustard @ X ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(126,plain,
( ( ! [X: $i] :
( ~ ( oneof @ X )
| ~ ( both @ X ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(127,plain,
( ( ! [X: $i] :
( ~ ( oneof @ X )
| ~ ( neither @ X ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(128,plain,
( ( ! [X: $i] :
( ( both @ X )
| ( neither @ X )
| ( oneof @ X ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(129,plain,
( ( ! [X: $i] :
( ~ ( oneof @ X )
| ~ ( salt @ X )
| ~ ( mustard @ X ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(130,plain,
( ( ! [X: $i] :
( ~ ( both @ X )
| ~ ( neither @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(131,plain,
( ( ! [X: $i] :
( ~ ( neither @ X )
| ~ ( salt @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(132,plain,
( ( ! [X: $i] :
( ~ ( neither @ X )
| ~ ( mustard @ X ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(133,plain,
( ( ! [X: $i] :
( ( salt @ X )
| ( mustard @ X )
| ( neither @ X ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(134,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[90]) ).
thf(135,plain,
( ( ( ~ ( neither @ cole ) )
= $true )
| ( ( ~ ( neither @ dix )
| ~ ( both @ barry )
| ~ ( oneof @ lang )
| ~ ( salt @ mill )
| ~ ( mustard @ lang )
| ~ ( oneof @ mill ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(136,plain,
( ( ( ~ ( salt @ barry ) )
= $true )
| ( ( ( oneof @ cole )
| ( oneof @ lang ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(137,plain,
( ( ( ~ ( oneof @ cole ) )
= $true )
| ( ( salt @ barry )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(138,plain,
( ( ( ~ ( oneof @ lang ) )
= $true )
| ( ( salt @ barry )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(139,plain,
( ( ( ~ ( mustard @ barry ) )
= $true )
| ( ( ( neither @ dix )
| ( both @ mill ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(140,plain,
( ( ( ~ ( neither @ dix ) )
= $true )
| ( ( mustard @ barry )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(141,plain,
( ( ( ~ ( both @ mill ) )
= $true )
| ( ( mustard @ barry )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(142,plain,
( ( ( ~ ( salt @ cole ) )
= $true )
| ( ( ( oneof @ barry )
| ( neither @ mill ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(143,plain,
( ( ( ~ ( oneof @ barry ) )
= $true )
| ( ( salt @ cole )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(144,plain,
( ( ( ~ ( neither @ mill ) )
= $true )
| ( ( salt @ cole )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(145,plain,
( ( ( ~ ( mustard @ cole ) )
= $true )
| ( ( ( both @ dix )
| ( both @ lang ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(146,plain,
( ( ( ~ ( both @ dix ) )
= $true )
| ( ( mustard @ cole )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(147,plain,
( ( ( ~ ( both @ lang ) )
= $true )
| ( ( mustard @ cole )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(148,plain,
( ( ( ~ ( salt @ dix ) )
= $true )
| ( ( ( neither @ barry )
| ( both @ cole ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(149,plain,
( ( ( ~ ( neither @ barry ) )
= $true )
| ( ( salt @ dix )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(150,plain,
( ( ( ~ ( both @ cole ) )
= $true )
| ( ( salt @ dix )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(151,plain,
( ( ( ~ ( mustard @ dix ) )
= $true )
| ( ( ( neither @ lang )
| ( neither @ mill ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(152,plain,
( ( ( ~ ( neither @ lang ) )
= $true )
| ( ( mustard @ dix )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(153,plain,
( ( ( ~ ( neither @ mill ) )
= $true )
| ( ( mustard @ dix )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(154,plain,
( ( ( ~ ( salt @ lang ) )
= $true )
| ( ( ( oneof @ barry )
| ( oneof @ dix ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(155,plain,
( ( ( ~ ( oneof @ barry ) )
= $true )
| ( ( salt @ lang )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(156,plain,
( ( ( ~ ( oneof @ dix ) )
= $true )
| ( ( salt @ lang )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(157,plain,
( ( ( ~ ( mustard @ lang ) )
= $true )
| ( ( ( neither @ cole )
| ( neither @ mill ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(158,plain,
( ( ( ~ ( neither @ cole ) )
= $true )
| ( ( mustard @ lang )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(159,plain,
( ( ( ~ ( neither @ mill ) )
= $true )
| ( ( mustard @ lang )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(160,plain,
( ( ( ~ ( salt @ mill ) )
= $true )
| ( ( ( both @ barry )
| ( both @ lang ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(161,plain,
( ( ( ~ ( both @ barry ) )
= $true )
| ( ( salt @ mill )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(162,plain,
( ( ( ~ ( both @ lang ) )
= $true )
| ( ( mustard @ mill )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(163,plain,
( ( ( ~ ( mustard @ mill ) )
= $true )
| ( ( ( oneof @ cole )
| ( oneof @ dix ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(164,plain,
( ( ( ~ ( oneof @ cole ) )
= $true )
| ( ( mustard @ mill )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(165,plain,
( ( ( ~ ( oneof @ dix ) )
= $true )
| ( ( mustard @ mill )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(166,plain,
! [SV1: $i] :
( ( ~ ( both @ SV1 )
| ( salt @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(167,plain,
! [SV2: $i] :
( ( ~ ( both @ SV2 )
| ( mustard @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(168,plain,
! [SV3: $i] :
( ( ~ ( salt @ SV3 )
| ~ ( mustard @ SV3 )
| ( both @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(169,plain,
! [SV4: $i] :
( ( ~ ( oneof @ SV4 )
| ( salt @ SV4 )
| ( mustard @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(170,plain,
! [SV5: $i] :
( ( ~ ( oneof @ SV5 )
| ~ ( both @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(171,plain,
! [SV6: $i] :
( ( ~ ( oneof @ SV6 )
| ~ ( neither @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(172,plain,
! [SV7: $i] :
( ( ( both @ SV7 )
| ( neither @ SV7 )
| ( oneof @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(173,plain,
! [SV8: $i] :
( ( ~ ( oneof @ SV8 )
| ~ ( salt @ SV8 )
| ~ ( mustard @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(174,plain,
! [SV9: $i] :
( ( ~ ( both @ SV9 )
| ~ ( neither @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(175,plain,
! [SV10: $i] :
( ( ~ ( neither @ SV10 )
| ~ ( salt @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(176,plain,
! [SV11: $i] :
( ( ~ ( neither @ SV11 )
| ~ ( mustard @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(177,plain,
! [SV12: $i] :
( ( ( salt @ SV12 )
| ( mustard @ SV12 )
| ( neither @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(178,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(179,plain,
( ( ( neither @ cole )
= $false )
| ( ( ~ ( neither @ dix )
| ~ ( both @ barry )
| ~ ( oneof @ lang )
| ~ ( salt @ mill )
| ~ ( mustard @ lang )
| ~ ( oneof @ mill ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(180,plain,
( ( ( salt @ barry )
= $false )
| ( ( ( oneof @ cole )
| ( oneof @ lang ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(181,plain,
( ( ( oneof @ cole )
= $false )
| ( ( salt @ barry )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(182,plain,
( ( ( oneof @ lang )
= $false )
| ( ( salt @ barry )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(183,plain,
( ( ( mustard @ barry )
= $false )
| ( ( ( neither @ dix )
| ( both @ mill ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(184,plain,
( ( ( neither @ dix )
= $false )
| ( ( mustard @ barry )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(185,plain,
( ( ( both @ mill )
= $false )
| ( ( mustard @ barry )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(186,plain,
( ( ( salt @ cole )
= $false )
| ( ( ( oneof @ barry )
| ( neither @ mill ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(187,plain,
( ( ( oneof @ barry )
= $false )
| ( ( salt @ cole )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(188,plain,
( ( ( neither @ mill )
= $false )
| ( ( salt @ cole )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(189,plain,
( ( ( mustard @ cole )
= $false )
| ( ( ( both @ dix )
| ( both @ lang ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(190,plain,
( ( ( both @ dix )
= $false )
| ( ( mustard @ cole )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(191,plain,
( ( ( both @ lang )
= $false )
| ( ( mustard @ cole )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(192,plain,
( ( ( salt @ dix )
= $false )
| ( ( ( neither @ barry )
| ( both @ cole ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(193,plain,
( ( ( neither @ barry )
= $false )
| ( ( salt @ dix )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(194,plain,
( ( ( both @ cole )
= $false )
| ( ( salt @ dix )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(195,plain,
( ( ( mustard @ dix )
= $false )
| ( ( ( neither @ lang )
| ( neither @ mill ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(196,plain,
( ( ( neither @ lang )
= $false )
| ( ( mustard @ dix )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(197,plain,
( ( ( neither @ mill )
= $false )
| ( ( mustard @ dix )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(198,plain,
( ( ( salt @ lang )
= $false )
| ( ( ( oneof @ barry )
| ( oneof @ dix ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(199,plain,
( ( ( oneof @ barry )
= $false )
| ( ( salt @ lang )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(200,plain,
( ( ( oneof @ dix )
= $false )
| ( ( salt @ lang )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(201,plain,
( ( ( mustard @ lang )
= $false )
| ( ( ( neither @ cole )
| ( neither @ mill ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(202,plain,
( ( ( neither @ cole )
= $false )
| ( ( mustard @ lang )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(203,plain,
( ( ( neither @ mill )
= $false )
| ( ( mustard @ lang )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(204,plain,
( ( ( salt @ mill )
= $false )
| ( ( ( both @ barry )
| ( both @ lang ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(205,plain,
( ( ( both @ barry )
= $false )
| ( ( salt @ mill )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(206,plain,
( ( ( both @ lang )
= $false )
| ( ( mustard @ mill )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(207,plain,
( ( ( mustard @ mill )
= $false )
| ( ( ( oneof @ cole )
| ( oneof @ dix ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(208,plain,
( ( ( oneof @ cole )
= $false )
| ( ( mustard @ mill )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(209,plain,
( ( ( oneof @ dix )
= $false )
| ( ( mustard @ mill )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(210,plain,
! [SV1: $i] :
( ( ( ~ ( both @ SV1 ) )
= $true )
| ( ( salt @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(211,plain,
! [SV2: $i] :
( ( ( ~ ( both @ SV2 ) )
= $true )
| ( ( mustard @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(212,plain,
! [SV3: $i] :
( ( ( ~ ( salt @ SV3 ) )
= $true )
| ( ( ~ ( mustard @ SV3 )
| ( both @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(213,plain,
! [SV4: $i] :
( ( ( ~ ( oneof @ SV4 ) )
= $true )
| ( ( ( salt @ SV4 )
| ( mustard @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(214,plain,
! [SV5: $i] :
( ( ( ~ ( oneof @ SV5 ) )
= $true )
| ( ( ~ ( both @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(215,plain,
! [SV6: $i] :
( ( ( ~ ( oneof @ SV6 ) )
= $true )
| ( ( ~ ( neither @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(216,plain,
! [SV7: $i] :
( ( ( both @ SV7 )
= $true )
| ( ( ( neither @ SV7 )
| ( oneof @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(217,plain,
! [SV8: $i] :
( ( ( ~ ( oneof @ SV8 ) )
= $true )
| ( ( ~ ( salt @ SV8 )
| ~ ( mustard @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(218,plain,
! [SV9: $i] :
( ( ( ~ ( both @ SV9 ) )
= $true )
| ( ( ~ ( neither @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(219,plain,
! [SV10: $i] :
( ( ( ~ ( neither @ SV10 ) )
= $true )
| ( ( ~ ( salt @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(220,plain,
! [SV11: $i] :
( ( ( ~ ( neither @ SV11 ) )
= $true )
| ( ( ~ ( mustard @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(221,plain,
! [SV12: $i] :
( ( ( salt @ SV12 )
= $true )
| ( ( ( mustard @ SV12 )
| ( neither @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(222,plain,
( ( ( ~ ( neither @ dix ) )
= $true )
| ( ( ~ ( both @ barry )
| ~ ( oneof @ lang )
| ~ ( salt @ mill )
| ~ ( mustard @ lang )
| ~ ( oneof @ mill ) )
= $true )
| ( ( neither @ cole )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(223,plain,
( ( ( oneof @ cole )
= $true )
| ( ( oneof @ lang )
= $true )
| ( ( salt @ barry )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(224,plain,
( ( ( neither @ dix )
= $true )
| ( ( both @ mill )
= $true )
| ( ( mustard @ barry )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(225,plain,
( ( ( oneof @ barry )
= $true )
| ( ( neither @ mill )
= $true )
| ( ( salt @ cole )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(226,plain,
( ( ( both @ dix )
= $true )
| ( ( both @ lang )
= $true )
| ( ( mustard @ cole )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(227,plain,
( ( ( neither @ barry )
= $true )
| ( ( both @ cole )
= $true )
| ( ( salt @ dix )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(228,plain,
( ( ( neither @ lang )
= $true )
| ( ( neither @ mill )
= $true )
| ( ( mustard @ dix )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(229,plain,
( ( ( oneof @ barry )
= $true )
| ( ( oneof @ dix )
= $true )
| ( ( salt @ lang )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(230,plain,
( ( ( neither @ cole )
= $true )
| ( ( neither @ mill )
= $true )
| ( ( mustard @ lang )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(231,plain,
( ( ( both @ barry )
= $true )
| ( ( both @ lang )
= $true )
| ( ( salt @ mill )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(232,plain,
( ( ( oneof @ cole )
= $true )
| ( ( oneof @ dix )
= $true )
| ( ( mustard @ mill )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(233,plain,
! [SV1: $i] :
( ( ( both @ SV1 )
= $false )
| ( ( salt @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(234,plain,
! [SV2: $i] :
( ( ( both @ SV2 )
= $false )
| ( ( mustard @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(235,plain,
! [SV3: $i] :
( ( ( salt @ SV3 )
= $false )
| ( ( ~ ( mustard @ SV3 )
| ( both @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(236,plain,
! [SV4: $i] :
( ( ( oneof @ SV4 )
= $false )
| ( ( ( salt @ SV4 )
| ( mustard @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(237,plain,
! [SV5: $i] :
( ( ( oneof @ SV5 )
= $false )
| ( ( ~ ( both @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(238,plain,
! [SV6: $i] :
( ( ( oneof @ SV6 )
= $false )
| ( ( ~ ( neither @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(239,plain,
! [SV7: $i] :
( ( ( neither @ SV7 )
= $true )
| ( ( oneof @ SV7 )
= $true )
| ( ( both @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(240,plain,
! [SV8: $i] :
( ( ( oneof @ SV8 )
= $false )
| ( ( ~ ( salt @ SV8 )
| ~ ( mustard @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(241,plain,
! [SV9: $i] :
( ( ( both @ SV9 )
= $false )
| ( ( ~ ( neither @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(242,plain,
! [SV10: $i] :
( ( ( neither @ SV10 )
= $false )
| ( ( ~ ( salt @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(243,plain,
! [SV11: $i] :
( ( ( neither @ SV11 )
= $false )
| ( ( ~ ( mustard @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(244,plain,
! [SV12: $i] :
( ( ( mustard @ SV12 )
= $true )
| ( ( neither @ SV12 )
= $true )
| ( ( salt @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(245,plain,
( ( ( neither @ dix )
= $false )
| ( ( ~ ( both @ barry )
| ~ ( oneof @ lang )
| ~ ( salt @ mill )
| ~ ( mustard @ lang )
| ~ ( oneof @ mill ) )
= $true )
| ( ( neither @ cole )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(246,plain,
! [SV3: $i] :
( ( ( ~ ( mustard @ SV3 ) )
= $true )
| ( ( both @ SV3 )
= $true )
| ( ( salt @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(247,plain,
! [SV4: $i] :
( ( ( salt @ SV4 )
= $true )
| ( ( mustard @ SV4 )
= $true )
| ( ( oneof @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(248,plain,
! [SV5: $i] :
( ( ( both @ SV5 )
= $false )
| ( ( oneof @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(249,plain,
! [SV6: $i] :
( ( ( neither @ SV6 )
= $false )
| ( ( oneof @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(250,plain,
! [SV8: $i] :
( ( ( ~ ( salt @ SV8 ) )
= $true )
| ( ( ~ ( mustard @ SV8 ) )
= $true )
| ( ( oneof @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(251,plain,
! [SV9: $i] :
( ( ( neither @ SV9 )
= $false )
| ( ( both @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(252,plain,
! [SV10: $i] :
( ( ( salt @ SV10 )
= $false )
| ( ( neither @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(253,plain,
! [SV11: $i] :
( ( ( mustard @ SV11 )
= $false )
| ( ( neither @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(254,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)],[245]) ).
thf(255,plain,
! [SV3: $i] :
( ( ( mustard @ SV3 )
= $false )
| ( ( both @ SV3 )
= $true )
| ( ( salt @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(256,plain,
! [SV8: $i] :
( ( ( salt @ SV8 )
= $false )
| ( ( ~ ( mustard @ SV8 ) )
= $true )
| ( ( oneof @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(257,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)],[254]) ).
thf(258,plain,
! [SV8: $i] :
( ( ( mustard @ SV8 )
= $false )
| ( ( salt @ SV8 )
= $false )
| ( ( oneof @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(259,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)],[257]) ).
thf(260,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)],[259]) ).
thf(261,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)],[260]) ).
thf(262,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)],[261]) ).
thf(263,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)],[262]) ).
thf(264,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)],[263]) ).
thf(265,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)],[264]) ).
thf(266,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[178,265,258,255,253,252,251,249,248,247,244,239,234,233,232,231,230,229,228,227,226,225,224,223,209,208,206,205,203,202,200,199,197,196,194,193,191,190,188,187,185,184,182,181]) ).
thf(267,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ030-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.21 % Computer : n009.cluster.edu
% 0.16/5.21 % Model : x86_64 x86_64
% 0.16/5.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.21 % Memory : 8046.5625MB
% 0.16/5.21 % OS : Linux 6.8.0-71-generic
% 0.16/5.21 % CPULimit : 300
% 0.16/5.21 % WCLimit : 300
% 0.16/5.21 % DateTime : Tue Oct 6 13:57:23 UTC 2026
% 0.16/5.21 % CPUTime :
% 0.16/5.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/5.31
% 0.22/5.31 No.of.Axioms: 43
% 0.22/5.31
% 0.22/5.31 Length.of.Defs: 0
% 0.22/5.31
% 0.22/5.31 Contains.Choice.Funs: false
% 0.22/5.31 ...
% 0.22/5.31
% 0.22/5.31 ********************************
% 0.22/5.31 * All subproblems solved! *
% 0.22/5.31 ********************************
% 0.22/5.31 % 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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:266,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.22/5.31
% 0.22/5.31 %**** Beginning of derivation protocol ****
% 0.22/5.31 % SZS output start CNFRefutation
% See solution above
% 0.22/5.32
% 0.22/5.32 %**** End of derivation protocol ****
% 0.22/5.32 %**** no. of clauses in derivation: 267 ****
% 0.22/5.32 %**** clause counter: 266 ****
% 0.22/5.32
% 0.22/5.32 % 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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:266,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------