TSTP Solution File: NUN024^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUN024^2 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 16:37:45 EDT 2022
% Result : Theorem 50.63s 47.83s
% Output : Proof 50.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 63
% Syntax : Number of formulae : 241 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 699 ( 77 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 636 ( 264 ~; 210 |; 1 &; 119 @)
% ( 0 <=>; 40 =>; 2 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 63 usr; 64 con; 0-2 aty)
% Number of variables : 37 ( 0 ^ 37 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(n10,conjecture,
( ~ ( ~ ( ~ ( ~ ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
=> ~ ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) )
=> ~ ! [X1: $i] :
( ( s @ X1 )
!= zero ) )
=> ~ ! [X1: $i] :
( ( s @ X1 )
!= X1 ) )
=> ~ ! [X1: $i] :
( ( h @ X1 )
= ( ite @ ( X1 = zero ) @ ( s @ zero ) @ zero ) ) )
=> ~ ! [X1: $i > $i] :
( ~ ( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) )
=> ( ( X1 @ ( s @ ( s @ zero ) ) )
!= zero ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
=> ~ ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) )
=> ~ ! [X1: $i] :
( ( s @ X1 )
!= zero ) )
=> ~ ! [X1: $i] :
( ( s @ X1 )
!= X1 ) )
=> ~ ! [X1: $i] :
( ( h @ X1 )
= ( ite @ ( X1 = zero ) @ ( s @ zero ) @ zero ) ) )
=> ~ ! [X1: $i > $i] :
( ~ ( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) )
=> ( ( X1 @ ( s @ ( s @ zero ) ) )
!= zero ) ) ),
inference(assume_negation,[status(cth)],[n10]) ).
thf(ax671,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax671) ).
thf(ax672,axiom,
~ p1,
file('<stdin>',ax672) ).
thf(ax669,axiom,
( p2
| ~ p4 ),
file('<stdin>',ax669) ).
thf(ax664,axiom,
( p4
| ~ p9 ),
file('<stdin>',ax664) ).
thf(ax662,axiom,
( p9
| ~ p11 ),
file('<stdin>',ax662) ).
thf(ax395,axiom,
( ~ p104
| p247 ),
file('<stdin>',ax395) ).
thf(ax653,axiom,
( ~ p5
| p19 ),
file('<stdin>',ax653) ).
thf(ax668,axiom,
( p2
| p5 ),
file('<stdin>',ax668) ).
thf(ax394,axiom,
( ~ p247
| p246 ),
file('<stdin>',ax394) ).
thf(ax569,axiom,
p104,
file('<stdin>',ax569) ).
thf(ax381,axiom,
( ~ p15
| p256 ),
file('<stdin>',ax381) ).
thf(ax658,axiom,
( p11
| p15 ),
file('<stdin>',ax658) ).
thf(ax393,axiom,
( ~ p246
| ~ p19
| p245 ),
file('<stdin>',ax393) ).
thf(ax382,axiom,
( ~ p256
| p255 ),
file('<stdin>',ax382) ).
thf(ax602,axiom,
( ~ p16
| p66 ),
file('<stdin>',ax602) ).
thf(ax657,axiom,
( p11
| p16 ),
file('<stdin>',ax657) ).
thf(ax633,axiom,
( ~ p16
| p38 ),
file('<stdin>',ax633) ).
thf(ax386,axiom,
( ~ p245
| p253 ),
file('<stdin>',ax386) ).
thf(nax75,axiom,
( p75
<= ( fzero = fzero ) ),
file('<stdin>',nax75) ).
thf(ax383,axiom,
( ~ p255
| p254 ),
file('<stdin>',ax383) ).
thf(ax238,axiom,
( ~ p66
| p366 ),
file('<stdin>',ax238) ).
thf(ax245,axiom,
( ~ p104
| p364 ),
file('<stdin>',ax245) ).
thf(ax50,axiom,
( ~ p38
| p525 ),
file('<stdin>',ax50) ).
thf(ax57,axiom,
( ~ p104
| p523 ),
file('<stdin>',ax57) ).
thf(ax385,axiom,
( ~ p253
| ~ p252
| p251 ),
file('<stdin>',ax385) ).
thf(ax384,axiom,
( ~ p254
| ~ p75
| p252 ),
file('<stdin>',ax384) ).
thf(ax239,axiom,
( ~ p366
| p365 ),
file('<stdin>',ax239) ).
thf(ax654,axiom,
( ~ p10
| ~ p18 ),
file('<stdin>',ax654) ).
thf(ax663,axiom,
( p4
| p10 ),
file('<stdin>',ax663) ).
thf(ax650,axiom,
( ~ p5
| p22 ),
file('<stdin>',ax650) ).
thf(ax244,axiom,
( ~ p364
| p363 ),
file('<stdin>',ax244) ).
thf(ax51,axiom,
( ~ p525
| p524 ),
file('<stdin>',ax51) ).
thf(ax652,axiom,
( ~ p12
| ~ p20 ),
file('<stdin>',ax652) ).
thf(ax661,axiom,
( p9
| p12 ),
file('<stdin>',ax661) ).
thf(ax634,axiom,
( ~ p5
| p37 ),
file('<stdin>',ax634) ).
thf(ax56,axiom,
( ~ p523
| p522 ),
file('<stdin>',ax56) ).
thf(pax8,axiom,
( p8
=> ( ~ ( ( fzero
= ( fs @ fzero ) )
=> ( fzero != fzero ) )
=> ( fzero != fzero ) ) ),
file('<stdin>',pax8) ).
thf(ax665,axiom,
( ~ p3
| p8 ),
file('<stdin>',ax665) ).
thf(ax670,axiom,
( p1
| p3 ),
file('<stdin>',ax670) ).
thf(ax240,axiom,
( ~ p365
| p18
| p360 ),
file('<stdin>',ax240) ).
thf(ax243,axiom,
( ~ p363
| ~ p22
| p362 ),
file('<stdin>',ax243) ).
thf(ax52,axiom,
( ~ p524
| p20
| p519 ),
file('<stdin>',ax52) ).
thf(ax55,axiom,
( ~ p522
| ~ p37
| p521 ),
file('<stdin>',ax55) ).
thf(pax251,axiom,
( p251
=> ( ( fh @ fzero )
= ( fs @ fzero ) ) ),
file('<stdin>',pax251) ).
thf(ax241,axiom,
( ~ p361
| ~ p360
| p359 ),
file('<stdin>',ax241) ).
thf(ax242,axiom,
( ~ p362
| p361 ),
file('<stdin>',ax242) ).
thf(ax251,axiom,
( ~ p31
| p355 ),
file('<stdin>',ax251) ).
thf(ax53,axiom,
( ~ p520
| ~ p519
| p518 ),
file('<stdin>',ax53) ).
thf(ax54,axiom,
( ~ p521
| p520 ),
file('<stdin>',ax54) ).
thf(ax44,axiom,
( ~ p104
| p535 ),
file('<stdin>',ax44) ).
thf(pax271,axiom,
( p271
=> ! [X1: $i] :
( ( ( fh @ fzero )
= X1 )
=> ( X1 = fzero ) ) ),
file('<stdin>',pax271) ).
thf(ax218,axiom,
( ~ p355
| p387 ),
file('<stdin>',ax218) ).
thf(ax643,axiom,
p31,
file('<stdin>',ax643) ).
thf(ax26,axiom,
( ~ p535
| p550 ),
file('<stdin>',ax26) ).
thf(nax271,axiom,
( p271
<= ! [X1: $i] :
( ( ( fh @ fzero )
= X1 )
=> ( X1 = fzero ) ) ),
file('<stdin>',nax271) ).
thf(ax217,axiom,
( ~ p387
| ~ p359
| p386 ),
file('<stdin>',ax217) ).
thf(ax25,axiom,
( ~ p550
| ~ p518
| p549 ),
file('<stdin>',ax25) ).
thf(pax386,axiom,
( p386
=> ( fzero
= ( fh @ ( fs @ fzero ) ) ) ),
file('<stdin>',pax386) ).
thf(pax549,axiom,
( p549
=> ! [X1: $i] :
( ( ( fh @ ( fs @ ( fs @ fzero ) ) )
= X1 )
=> ( X1 = fzero ) ) ),
file('<stdin>',pax549) ).
thf(ax335,axiom,
( ~ p3
| p294 ),
file('<stdin>',ax335) ).
thf(pax294,axiom,
( p294
=> ( ~ ( ( ( fh @ fzero )
= ( fs @ fzero ) )
=> ( ( fh @ ( fs @ fzero ) )
!= fzero ) )
=> ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= fzero ) ) ),
file('<stdin>',pax294) ).
thf(c_0_61,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax671]) ).
thf(c_0_62,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax672]) ).
thf(c_0_63,plain,
( p2
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax669]) ).
thf(c_0_64,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_65,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_66,plain,
( p4
| ~ p9 ),
inference(fof_simplification,[status(thm)],[ax664]) ).
thf(c_0_67,plain,
( p2
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_68,plain,
~ p2,
inference(sr,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_69,plain,
( p9
| ~ p11 ),
inference(fof_simplification,[status(thm)],[ax662]) ).
thf(c_0_70,plain,
( p4
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_71,plain,
~ p4,
inference(sr,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_72,plain,
( ~ p104
| p247 ),
inference(fof_simplification,[status(thm)],[ax395]) ).
thf(c_0_73,plain,
( p9
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_74,plain,
~ p9,
inference(sr,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_75,plain,
( ~ p5
| p19 ),
inference(fof_simplification,[status(thm)],[ax653]) ).
thf(c_0_76,plain,
( p2
| p5 ),
inference(split_conjunct,[status(thm)],[ax668]) ).
thf(c_0_77,plain,
( ~ p247
| p246 ),
inference(fof_simplification,[status(thm)],[ax394]) ).
thf(c_0_78,plain,
( p247
| ~ p104 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
thf(c_0_79,plain,
p104,
inference(split_conjunct,[status(thm)],[ax569]) ).
thf(c_0_80,plain,
( ~ p15
| p256 ),
inference(fof_simplification,[status(thm)],[ax381]) ).
thf(c_0_81,plain,
( p11
| p15 ),
inference(split_conjunct,[status(thm)],[ax658]) ).
thf(c_0_82,plain,
~ p11,
inference(sr,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_83,plain,
( ~ p246
| ~ p19
| p245 ),
inference(fof_simplification,[status(thm)],[ax393]) ).
thf(c_0_84,plain,
( p19
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_85,plain,
p5,
inference(sr,[status(thm)],[c_0_76,c_0_68]) ).
thf(c_0_86,plain,
( p246
| ~ p247 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_87,plain,
p247,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79])]) ).
thf(c_0_88,plain,
( ~ p256
| p255 ),
inference(fof_simplification,[status(thm)],[ax382]) ).
thf(c_0_89,plain,
( p256
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_90,plain,
p15,
inference(sr,[status(thm)],[c_0_81,c_0_82]) ).
thf(c_0_91,plain,
( ~ p16
| p66 ),
inference(fof_simplification,[status(thm)],[ax602]) ).
thf(c_0_92,plain,
( p11
| p16 ),
inference(split_conjunct,[status(thm)],[ax657]) ).
thf(c_0_93,plain,
( ~ p16
| p38 ),
inference(fof_simplification,[status(thm)],[ax633]) ).
thf(c_0_94,plain,
( ~ p245
| p253 ),
inference(fof_simplification,[status(thm)],[ax386]) ).
thf(c_0_95,plain,
( p245
| ~ p246
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
thf(c_0_96,plain,
p19,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
thf(c_0_97,plain,
p246,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
thf(c_0_98,plain,
( ( fzero != fzero )
| p75 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax75])]) ).
thf(c_0_99,plain,
( ~ p255
| p254 ),
inference(fof_simplification,[status(thm)],[ax383]) ).
thf(c_0_100,plain,
( p255
| ~ p256 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
thf(c_0_101,plain,
p256,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90])]) ).
thf(c_0_102,plain,
( ~ p66
| p366 ),
inference(fof_simplification,[status(thm)],[ax238]) ).
thf(c_0_103,plain,
( p66
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
thf(c_0_104,plain,
p16,
inference(sr,[status(thm)],[c_0_92,c_0_82]) ).
thf(c_0_105,plain,
( ~ p104
| p364 ),
inference(fof_simplification,[status(thm)],[ax245]) ).
thf(c_0_106,plain,
( ~ p38
| p525 ),
inference(fof_simplification,[status(thm)],[ax50]) ).
thf(c_0_107,plain,
( p38
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_108,plain,
( ~ p104
| p523 ),
inference(fof_simplification,[status(thm)],[ax57]) ).
thf(c_0_109,plain,
( ~ p253
| ~ p252
| p251 ),
inference(fof_simplification,[status(thm)],[ax385]) ).
thf(c_0_110,plain,
( p253
| ~ p245 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
thf(c_0_111,plain,
p245,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
thf(c_0_112,plain,
( ~ p254
| ~ p75
| p252 ),
inference(fof_simplification,[status(thm)],[ax384]) ).
thf(c_0_113,plain,
( p75
| ( fzero != fzero ) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
thf(c_0_114,plain,
( p254
| ~ p255 ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
thf(c_0_115,plain,
p255,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
thf(c_0_116,plain,
( ~ p366
| p365 ),
inference(fof_simplification,[status(thm)],[ax239]) ).
thf(c_0_117,plain,
( p366
| ~ p66 ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
thf(c_0_118,plain,
p66,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]) ).
thf(c_0_119,plain,
( ~ p10
| ~ p18 ),
inference(fof_simplification,[status(thm)],[ax654]) ).
thf(c_0_120,plain,
( p4
| p10 ),
inference(split_conjunct,[status(thm)],[ax663]) ).
thf(c_0_121,plain,
( ~ p5
| p22 ),
inference(fof_simplification,[status(thm)],[ax650]) ).
thf(c_0_122,plain,
( ~ p364
| p363 ),
inference(fof_simplification,[status(thm)],[ax244]) ).
thf(c_0_123,plain,
( p364
| ~ p104 ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
thf(c_0_124,plain,
( ~ p525
| p524 ),
inference(fof_simplification,[status(thm)],[ax51]) ).
thf(c_0_125,plain,
( p525
| ~ p38 ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
thf(c_0_126,plain,
p38,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_104])]) ).
thf(c_0_127,plain,
( ~ p12
| ~ p20 ),
inference(fof_simplification,[status(thm)],[ax652]) ).
thf(c_0_128,plain,
( p9
| p12 ),
inference(split_conjunct,[status(thm)],[ax661]) ).
thf(c_0_129,plain,
( ~ p5
| p37 ),
inference(fof_simplification,[status(thm)],[ax634]) ).
thf(c_0_130,plain,
( ~ p523
| p522 ),
inference(fof_simplification,[status(thm)],[ax56]) ).
thf(c_0_131,plain,
( p523
| ~ p104 ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
thf(c_0_132,plain,
( p251
| ~ p253
| ~ p252 ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
thf(c_0_133,plain,
p253,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).
thf(c_0_134,plain,
( p252
| ~ p254
| ~ p75 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_135,plain,
p75,
inference(cn,[status(thm)],[c_0_113]) ).
thf(c_0_136,plain,
p254,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
thf(c_0_137,plain,
( ~ p8
| ( fzero
!= ( fs @ fzero ) )
| ( fzero != fzero )
| ( fzero != fzero ) ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax8])]) ).
thf(c_0_138,plain,
( ~ p3
| p8 ),
inference(fof_simplification,[status(thm)],[ax665]) ).
thf(c_0_139,plain,
( p1
| p3 ),
inference(split_conjunct,[status(thm)],[ax670]) ).
thf(c_0_140,plain,
( ~ p365
| p18
| p360 ),
inference(fof_simplification,[status(thm)],[ax240]) ).
thf(c_0_141,plain,
( p365
| ~ p366 ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
thf(c_0_142,plain,
p366,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118])]) ).
thf(c_0_143,plain,
( ~ p10
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
thf(c_0_144,plain,
p10,
inference(sr,[status(thm)],[c_0_120,c_0_71]) ).
thf(c_0_145,plain,
( ~ p363
| ~ p22
| p362 ),
inference(fof_simplification,[status(thm)],[ax243]) ).
thf(c_0_146,plain,
( p22
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
thf(c_0_147,plain,
( p363
| ~ p364 ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
thf(c_0_148,plain,
p364,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_79])]) ).
thf(c_0_149,plain,
( ~ p524
| p20
| p519 ),
inference(fof_simplification,[status(thm)],[ax52]) ).
thf(c_0_150,plain,
( p524
| ~ p525 ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
thf(c_0_151,plain,
p525,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126])]) ).
thf(c_0_152,plain,
( ~ p12
| ~ p20 ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
thf(c_0_153,plain,
p12,
inference(sr,[status(thm)],[c_0_128,c_0_74]) ).
thf(c_0_154,plain,
( ~ p522
| ~ p37
| p521 ),
inference(fof_simplification,[status(thm)],[ax55]) ).
thf(c_0_155,plain,
( p37
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_156,plain,
( p522
| ~ p523 ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
thf(c_0_157,plain,
p523,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_79])]) ).
thf(c_0_158,plain,
( ~ p251
| ( ( fh @ fzero )
= ( fs @ fzero ) ) ),
inference(fof_nnf,[status(thm)],[pax251]) ).
thf(c_0_159,plain,
( p251
| ~ p252 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133])]) ).
thf(c_0_160,plain,
p252,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135]),c_0_136])]) ).
thf(c_0_161,plain,
( ~ p8
| ( fzero
!= ( fs @ fzero ) )
| ( fzero != fzero )
| ( fzero != fzero ) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
thf(c_0_162,plain,
( p8
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_163,plain,
p3,
inference(sr,[status(thm)],[c_0_139,c_0_65]) ).
thf(c_0_164,plain,
( ~ p361
| ~ p360
| p359 ),
inference(fof_simplification,[status(thm)],[ax241]) ).
thf(c_0_165,plain,
( p18
| p360
| ~ p365 ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
thf(c_0_166,plain,
p365,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142])]) ).
thf(c_0_167,plain,
~ p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144])]) ).
thf(c_0_168,plain,
( ~ p362
| p361 ),
inference(fof_simplification,[status(thm)],[ax242]) ).
thf(c_0_169,plain,
( p362
| ~ p363
| ~ p22 ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
thf(c_0_170,plain,
p22,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_85])]) ).
thf(c_0_171,plain,
p363,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148])]) ).
thf(c_0_172,plain,
( ~ p31
| p355 ),
inference(fof_simplification,[status(thm)],[ax251]) ).
thf(c_0_173,plain,
( ~ p520
| ~ p519
| p518 ),
inference(fof_simplification,[status(thm)],[ax53]) ).
thf(c_0_174,plain,
( p20
| p519
| ~ p524 ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
thf(c_0_175,plain,
p524,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151])]) ).
thf(c_0_176,plain,
~ p20,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153])]) ).
thf(c_0_177,plain,
( ~ p521
| p520 ),
inference(fof_simplification,[status(thm)],[ax54]) ).
thf(c_0_178,plain,
( p521
| ~ p522
| ~ p37 ),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
thf(c_0_179,plain,
p37,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_85])]) ).
thf(c_0_180,plain,
p522,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_157])]) ).
thf(c_0_181,plain,
( ~ p104
| p535 ),
inference(fof_simplification,[status(thm)],[ax44]) ).
thf(c_0_182,plain,
! [X38: $i] :
( ~ p271
| ( ( fh @ fzero )
!= X38 )
| ( X38 = fzero ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax271])])]) ).
thf(c_0_183,plain,
( ( ( fh @ fzero )
= ( fs @ fzero ) )
| ~ p251 ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
thf(c_0_184,plain,
p251,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]) ).
thf(c_0_185,plain,
( ( fzero
!= ( fs @ fzero ) )
| ~ p8 ),
inference(cn,[status(thm)],[c_0_161]) ).
thf(c_0_186,plain,
p8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_163])]) ).
thf(c_0_187,plain,
( p359
| ~ p361
| ~ p360 ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
thf(c_0_188,plain,
p360,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_166])]),c_0_167]) ).
thf(c_0_189,plain,
( p361
| ~ p362 ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
thf(c_0_190,plain,
p362,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_170]),c_0_171])]) ).
thf(c_0_191,plain,
( ~ p355
| p387 ),
inference(fof_simplification,[status(thm)],[ax218]) ).
thf(c_0_192,plain,
( p355
| ~ p31 ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
thf(c_0_193,plain,
p31,
inference(split_conjunct,[status(thm)],[ax643]) ).
thf(c_0_194,plain,
( p518
| ~ p520
| ~ p519 ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
thf(c_0_195,plain,
p519,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_175])]),c_0_176]) ).
thf(c_0_196,plain,
( p520
| ~ p521 ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
thf(c_0_197,plain,
p521,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_179]),c_0_180])]) ).
thf(c_0_198,plain,
( ~ p535
| p550 ),
inference(fof_simplification,[status(thm)],[ax26]) ).
thf(c_0_199,plain,
( p535
| ~ p104 ),
inference(split_conjunct,[status(thm)],[c_0_181]) ).
thf(c_0_200,plain,
( ( ( ( fh @ fzero )
= esk18_0 )
| p271 )
& ( ( esk18_0 != fzero )
| p271 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax271])])])])]) ).
thf(c_0_201,plain,
! [X1: $i] :
( ( X1 = fzero )
| ~ p271
| ( ( fh @ fzero )
!= X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_182]) ).
thf(c_0_202,plain,
( ( fh @ fzero )
= ( fs @ fzero ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_184])]) ).
thf(c_0_203,plain,
( fs @ fzero )
!= fzero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_186])]) ).
thf(c_0_204,plain,
( ~ p387
| ~ p359
| p386 ),
inference(fof_simplification,[status(thm)],[ax217]) ).
thf(c_0_205,plain,
( p359
| ~ p361 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_187,c_0_188])]) ).
thf(c_0_206,plain,
p361,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_190])]) ).
thf(c_0_207,plain,
( p387
| ~ p355 ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
thf(c_0_208,plain,
p355,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_193])]) ).
thf(c_0_209,plain,
( ~ p550
| ~ p518
| p549 ),
inference(fof_simplification,[status(thm)],[ax25]) ).
thf(c_0_210,plain,
( p518
| ~ p520 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_194,c_0_195])]) ).
thf(c_0_211,plain,
p520,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197])]) ).
thf(c_0_212,plain,
( p550
| ~ p535 ),
inference(split_conjunct,[status(thm)],[c_0_198]) ).
thf(c_0_213,plain,
p535,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_79])]) ).
thf(c_0_214,plain,
( ~ p386
| ( fzero
= ( fh @ ( fs @ fzero ) ) ) ),
inference(fof_nnf,[status(thm)],[pax386]) ).
thf(c_0_215,plain,
( ( ( fh @ fzero )
= esk18_0 )
| p271 ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
thf(c_0_216,plain,
~ p271,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_202])]),c_0_203]) ).
thf(c_0_217,plain,
( p386
| ~ p387
| ~ p359 ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
thf(c_0_218,plain,
p359,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_206])]) ).
thf(c_0_219,plain,
p387,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_207,c_0_208])]) ).
thf(c_0_220,plain,
! [X6: $i] :
( ~ p549
| ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= X6 )
| ( X6 = fzero ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax549])])]) ).
thf(c_0_221,plain,
( p549
| ~ p550
| ~ p518 ),
inference(split_conjunct,[status(thm)],[c_0_209]) ).
thf(c_0_222,plain,
p518,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_210,c_0_211])]) ).
thf(c_0_223,plain,
p550,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_212,c_0_213])]) ).
thf(c_0_224,plain,
( ~ p3
| p294 ),
inference(fof_simplification,[status(thm)],[ax335]) ).
thf(c_0_225,plain,
( ~ p294
| ( ( fh @ fzero )
!= ( fs @ fzero ) )
| ( ( fh @ ( fs @ fzero ) )
!= fzero )
| ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= fzero ) ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax294])]) ).
thf(c_0_226,plain,
( ( fzero
= ( fh @ ( fs @ fzero ) ) )
| ~ p386 ),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
thf(c_0_227,plain,
( ( fs @ fzero )
= esk18_0 ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_215,c_0_216]),c_0_202]) ).
thf(c_0_228,plain,
p386,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_217,c_0_218]),c_0_219])]) ).
thf(c_0_229,plain,
! [X1: $i] :
( ( X1 = fzero )
| ~ p549
| ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_220]) ).
thf(c_0_230,plain,
p549,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_221,c_0_222]),c_0_223])]) ).
thf(c_0_231,plain,
( p294
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
thf(c_0_232,plain,
( ~ p294
| ( ( fh @ fzero )
!= ( fs @ fzero ) )
| ( ( fh @ ( fs @ fzero ) )
!= fzero )
| ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= fzero ) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
thf(c_0_233,plain,
( ( fh @ esk18_0 )
= fzero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_226,c_0_227]),c_0_228])]) ).
thf(c_0_234,plain,
( ( fh @ ( fs @ esk18_0 ) )
= fzero ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_229,c_0_227]),c_0_230])])]) ).
thf(c_0_235,plain,
p294,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_231,c_0_163])]) ).
thf(c_0_236,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_232,c_0_202]),c_0_227]),c_0_227]),c_0_227]),c_0_233]),c_0_227]),c_0_234]),c_0_235])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
=> ~ ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) )
=> ~ ! [X1: $i] :
( ( s @ X1 )
!= zero ) )
=> ~ ! [X1: $i] :
( ( s @ X1 )
!= X1 ) )
=> ~ ! [X1: $i] :
( ( h @ X1 )
= ( ite @ ( X1 = zero ) @ ( s @ zero ) @ zero ) ) )
=> ~ ! [X1: $i > $i] :
( ~ ( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) )
=> ( ( X1 @ ( s @ ( s @ zero ) ) )
!= zero ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN024^2 : TPTP v8.1.0. Released v6.4.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 2 08:53:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 50.63/47.83 % SZS status Theorem
% 50.63/47.83 % Mode: mode371
% 50.63/47.83 % Inferences: 18640
% 50.63/47.83 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------