TSTP Solution File: NUN025^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUN025^2 : 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 : n017.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 16:37:46 EDT 2022
% Result : Theorem 47.56s 47.84s
% Output : Proof 47.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 64
% Syntax : Number of formulae : 245 ( 68 unt; 0 typ; 0 def)
% Number of atoms : 721 ( 77 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 650 ( 261 ~; 216 |; 2 &; 131 @)
% ( 0 <=>; 38 =>; 2 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 65 usr; 66 con; 0-2 aty)
% Number of variables : 35 ( 0 ^ 35 !; 0 ?; 35 :)
% 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 )
!= X1 ) )
=> ~ ! [X1: $i] :
( ( h @ X1 )
= ( ite
@ ( X1
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) )
=> ~ ! [X1: $i > $i] :
( ~ ( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) )
=> ( ( X1 @ ( s @ ( s @ zero ) ) )
!= ( s @ 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 )
!= X1 ) )
=> ~ ! [X1: $i] :
( ( h @ X1 )
= ( ite
@ ( X1
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) )
=> ~ ! [X1: $i > $i] :
( ~ ( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) )
=> ( ( X1 @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
inference(assume_negation,[status(cth)],[n10]) ).
thf(ax652,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax652) ).
thf(ax653,axiom,
~ p1,
file('<stdin>',ax653) ).
thf(ax650,axiom,
( p2
| ~ p4 ),
file('<stdin>',ax650) ).
thf(ax645,axiom,
( p4
| ~ p9 ),
file('<stdin>',ax645) ).
thf(ax599,axiom,
( ~ p12
| p53 ),
file('<stdin>',ax599) ).
thf(ax642,axiom,
( p9
| p12 ),
file('<stdin>',ax642) ).
thf(nax32,axiom,
( p32
<= ! [X1: $i] :
( ( fzero = X1 )
=> ( X1 = fzero ) ) ),
file('<stdin>',nax32) ).
thf(ax217,axiom,
( ~ p53
| p353 ),
file('<stdin>',ax217) ).
thf(ax605,axiom,
( ~ p32
| p48 ),
file('<stdin>',ax605) ).
thf(ax637,axiom,
( ~ p10
| ~ p17 ),
file('<stdin>',ax637) ).
thf(ax644,axiom,
( p4
| p10 ),
file('<stdin>',ax644) ).
thf(ax224,axiom,
( ~ p85
| p351 ),
file('<stdin>',ax224) ).
thf(ax218,axiom,
( ~ p353
| p352 ),
file('<stdin>',ax218) ).
thf(ax604,axiom,
( ~ p48
| ~ p45
| p17 ),
file('<stdin>',ax604) ).
thf(ax636,axiom,
( ~ p5
| p18 ),
file('<stdin>',ax636) ).
thf(ax649,axiom,
( p2
| p5 ),
file('<stdin>',ax649) ).
thf(ax223,axiom,
( ~ p351
| p350 ),
file('<stdin>',ax223) ).
thf(ax571,axiom,
p85,
file('<stdin>',ax571) ).
thf(ax359,axiom,
( ~ p85
| p244 ),
file('<stdin>',ax359) ).
thf(ax376,axiom,
( ~ p12
| p226 ),
file('<stdin>',ax376) ).
thf(ax219,axiom,
( ~ p352
| p45
| p347 ),
file('<stdin>',ax219) ).
thf(ax222,axiom,
( ~ p350
| ~ p18
| p349 ),
file('<stdin>',ax222) ).
thf(ax638,axiom,
( ~ p5
| p16 ),
file('<stdin>',ax638) ).
thf(ax358,axiom,
( ~ p244
| p243 ),
file('<stdin>',ax358) ).
thf(ax345,axiom,
( ~ p11
| p253 ),
file('<stdin>',ax345) ).
thf(ax643,axiom,
( p9
| p11 ),
file('<stdin>',ax643) ).
thf(ax27,axiom,
( ~ p226
| p514 ),
file('<stdin>',ax27) ).
thf(ax34,axiom,
( ~ p85
| p512 ),
file('<stdin>',ax34) ).
thf(ax220,axiom,
( ~ p348
| ~ p347
| p346 ),
file('<stdin>',ax220) ).
thf(ax221,axiom,
( ~ p349
| p348 ),
file('<stdin>',ax221) ).
thf(ax357,axiom,
( ~ p243
| ~ p16
| p242 ),
file('<stdin>',ax357) ).
thf(ax346,axiom,
( ~ p253
| p252 ),
file('<stdin>',ax346) ).
thf(ax28,axiom,
( ~ p514
| p513 ),
file('<stdin>',ax28) ).
thf(ax639,axiom,
( ~ p10
| ~ p15 ),
file('<stdin>',ax639) ).
thf(ax619,axiom,
( ~ p5
| p35 ),
file('<stdin>',ax619) ).
thf(ax33,axiom,
( ~ p512
| p511 ),
file('<stdin>',ax33) ).
thf(pax8,axiom,
( p8
=> ( ~ ( ( fzero
= ( fs @ fzero ) )
=> ( fzero != fzero ) )
=> ( fzero
!= ( fs @ fzero ) ) ) ),
file('<stdin>',pax8) ).
thf(ax646,axiom,
( ~ p3
| p8 ),
file('<stdin>',ax646) ).
thf(ax651,axiom,
( p1
| p3 ),
file('<stdin>',ax651) ).
thf(ax350,axiom,
( ~ p242
| p250 ),
file('<stdin>',ax350) ).
thf(ax347,axiom,
( ~ p252
| p251 ),
file('<stdin>',ax347) ).
thf(ax29,axiom,
( ~ p513
| p15
| p508 ),
file('<stdin>',ax29) ).
thf(ax32,axiom,
( ~ p511
| ~ p35
| p510 ),
file('<stdin>',ax32) ).
thf(pax346,axiom,
( p346
=> ( ( fh @ fzero )
= ( fs @ fzero ) ) ),
file('<stdin>',pax346) ).
thf(ax349,axiom,
( ~ p250
| ~ p249
| p248 ),
file('<stdin>',ax349) ).
thf(ax348,axiom,
( ~ p251
| ~ p25
| p249 ),
file('<stdin>',ax348) ).
thf(ax365,axiom,
( ~ p29
| p235 ),
file('<stdin>',ax365) ).
thf(ax30,axiom,
( ~ p509
| ~ p508
| p507 ),
file('<stdin>',ax30) ).
thf(ax31,axiom,
( ~ p510
| p509 ),
file('<stdin>',ax31) ).
thf(ax21,axiom,
( ~ p85
| p524 ),
file('<stdin>',ax21) ).
thf(pax401,axiom,
( p401
=> ! [X1: $i] :
( ( ( fh @ fzero )
= X1 )
=> ( X1 = fzero ) ) ),
file('<stdin>',pax401) ).
thf(ax629,axiom,
p25,
file('<stdin>',ax629) ).
thf(ax306,axiom,
( ~ p235
| p287 ),
file('<stdin>',ax306) ).
thf(ax627,axiom,
p29,
file('<stdin>',ax627) ).
thf(ax3,axiom,
( ~ p524
| p539 ),
file('<stdin>',ax3) ).
thf(nax401,axiom,
( p401
<= ! [X1: $i] :
( ( ( fh @ fzero )
= X1 )
=> ( X1 = fzero ) ) ),
file('<stdin>',nax401) ).
thf(ax305,axiom,
( ~ p287
| ~ p248
| p286 ),
file('<stdin>',ax305) ).
thf(ax2,axiom,
( ~ p539
| ~ p507
| p538 ),
file('<stdin>',ax2) ).
thf(pax286,axiom,
( p286
=> ( fzero
= ( fh @ ( fs @ fzero ) ) ) ),
file('<stdin>',pax286) ).
thf(pax538,axiom,
( p538
=> ! [X1: $i] :
( ( ( fh @ ( fs @ ( fs @ fzero ) ) )
= X1 )
=> ( X1
= ( fs @ fzero ) ) ) ),
file('<stdin>',pax538) ).
thf(ax298,axiom,
( ~ p3
| p292 ),
file('<stdin>',ax298) ).
thf(pax292,axiom,
( p292
=> ( ~ ( ( ( fh @ fzero )
= ( fs @ fzero ) )
=> ( ( fh @ ( fs @ fzero ) )
!= fzero ) )
=> ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= ( fs @ fzero ) ) ) ),
file('<stdin>',pax292) ).
thf(c_0_62,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax652]) ).
thf(c_0_63,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax653]) ).
thf(c_0_64,plain,
( p2
| ~ p4 ),
inference(fof_simplification,[status(thm)],[ax650]) ).
thf(c_0_65,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_66,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_67,plain,
( p4
| ~ p9 ),
inference(fof_simplification,[status(thm)],[ax645]) ).
thf(c_0_68,plain,
( p2
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_69,plain,
~ p2,
inference(sr,[status(thm)],[c_0_65,c_0_66]) ).
thf(c_0_70,plain,
( p4
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_71,plain,
~ p4,
inference(sr,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_72,plain,
( ~ p12
| p53 ),
inference(fof_simplification,[status(thm)],[ax599]) ).
thf(c_0_73,plain,
( p9
| p12 ),
inference(split_conjunct,[status(thm)],[ax642]) ).
thf(c_0_74,plain,
~ p9,
inference(sr,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_75,plain,
( ( ( fzero = esk32_0 )
| p32 )
& ( ( esk32_0 != fzero )
| p32 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax32])])])])]) ).
thf(c_0_76,plain,
( ~ p53
| p353 ),
inference(fof_simplification,[status(thm)],[ax217]) ).
thf(c_0_77,plain,
( p53
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
thf(c_0_78,plain,
p12,
inference(sr,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_79,plain,
( ~ p32
| p48 ),
inference(fof_simplification,[status(thm)],[ax605]) ).
thf(c_0_80,plain,
( ( fzero = esk32_0 )
| p32 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_81,plain,
( p32
| ( esk32_0 != fzero ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_82,plain,
( ~ p10
| ~ p17 ),
inference(fof_simplification,[status(thm)],[ax637]) ).
thf(c_0_83,plain,
( p4
| p10 ),
inference(split_conjunct,[status(thm)],[ax644]) ).
thf(c_0_84,plain,
( ~ p85
| p351 ),
inference(fof_simplification,[status(thm)],[ax224]) ).
thf(c_0_85,plain,
( ~ p353
| p352 ),
inference(fof_simplification,[status(thm)],[ax218]) ).
thf(c_0_86,plain,
( p353
| ~ p53 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_87,plain,
p53,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
thf(c_0_88,plain,
( ~ p48
| ~ p45
| p17 ),
inference(fof_simplification,[status(thm)],[ax604]) ).
thf(c_0_89,plain,
( p48
| ~ p32 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_90,plain,
p32,
inference(csr,[status(thm)],[c_0_80,c_0_81]) ).
thf(c_0_91,plain,
( ~ p10
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_92,plain,
p10,
inference(sr,[status(thm)],[c_0_83,c_0_71]) ).
thf(c_0_93,plain,
( ~ p5
| p18 ),
inference(fof_simplification,[status(thm)],[ax636]) ).
thf(c_0_94,plain,
( p2
| p5 ),
inference(split_conjunct,[status(thm)],[ax649]) ).
thf(c_0_95,plain,
( ~ p351
| p350 ),
inference(fof_simplification,[status(thm)],[ax223]) ).
thf(c_0_96,plain,
( p351
| ~ p85 ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_97,plain,
p85,
inference(split_conjunct,[status(thm)],[ax571]) ).
thf(c_0_98,plain,
( ~ p85
| p244 ),
inference(fof_simplification,[status(thm)],[ax359]) ).
thf(c_0_99,plain,
( ~ p12
| p226 ),
inference(fof_simplification,[status(thm)],[ax376]) ).
thf(c_0_100,plain,
( ~ p352
| p45
| p347 ),
inference(fof_simplification,[status(thm)],[ax219]) ).
thf(c_0_101,plain,
( p352
| ~ p353 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
thf(c_0_102,plain,
p353,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
thf(c_0_103,plain,
( p17
| ~ p48
| ~ p45 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
thf(c_0_104,plain,
p48,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90])]) ).
thf(c_0_105,plain,
~ p17,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
thf(c_0_106,plain,
( ~ p350
| ~ p18
| p349 ),
inference(fof_simplification,[status(thm)],[ax222]) ).
thf(c_0_107,plain,
( p18
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_108,plain,
p5,
inference(sr,[status(thm)],[c_0_94,c_0_69]) ).
thf(c_0_109,plain,
( p350
| ~ p351 ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
thf(c_0_110,plain,
p351,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97])]) ).
thf(c_0_111,plain,
( ~ p5
| p16 ),
inference(fof_simplification,[status(thm)],[ax638]) ).
thf(c_0_112,plain,
( ~ p244
| p243 ),
inference(fof_simplification,[status(thm)],[ax358]) ).
thf(c_0_113,plain,
( p244
| ~ p85 ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
thf(c_0_114,plain,
( ~ p11
| p253 ),
inference(fof_simplification,[status(thm)],[ax345]) ).
thf(c_0_115,plain,
( p9
| p11 ),
inference(split_conjunct,[status(thm)],[ax643]) ).
thf(c_0_116,plain,
( ~ p226
| p514 ),
inference(fof_simplification,[status(thm)],[ax27]) ).
thf(c_0_117,plain,
( p226
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
thf(c_0_118,plain,
( ~ p85
| p512 ),
inference(fof_simplification,[status(thm)],[ax34]) ).
thf(c_0_119,plain,
( ~ p348
| ~ p347
| p346 ),
inference(fof_simplification,[status(thm)],[ax220]) ).
thf(c_0_120,plain,
( p45
| p347
| ~ p352 ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
thf(c_0_121,plain,
p352,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
thf(c_0_122,plain,
~ p45,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]),c_0_105]) ).
thf(c_0_123,plain,
( ~ p349
| p348 ),
inference(fof_simplification,[status(thm)],[ax221]) ).
thf(c_0_124,plain,
( p349
| ~ p350
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
thf(c_0_125,plain,
p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108])]) ).
thf(c_0_126,plain,
p350,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
thf(c_0_127,plain,
( ~ p243
| ~ p16
| p242 ),
inference(fof_simplification,[status(thm)],[ax357]) ).
thf(c_0_128,plain,
( p16
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
thf(c_0_129,plain,
( p243
| ~ p244 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_130,plain,
p244,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_97])]) ).
thf(c_0_131,plain,
( ~ p253
| p252 ),
inference(fof_simplification,[status(thm)],[ax346]) ).
thf(c_0_132,plain,
( p253
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_133,plain,
p11,
inference(sr,[status(thm)],[c_0_115,c_0_74]) ).
thf(c_0_134,plain,
( ~ p514
| p513 ),
inference(fof_simplification,[status(thm)],[ax28]) ).
thf(c_0_135,plain,
( p514
| ~ p226 ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
thf(c_0_136,plain,
p226,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_78])]) ).
thf(c_0_137,plain,
( ~ p10
| ~ p15 ),
inference(fof_simplification,[status(thm)],[ax639]) ).
thf(c_0_138,plain,
( ~ p5
| p35 ),
inference(fof_simplification,[status(thm)],[ax619]) ).
thf(c_0_139,plain,
( ~ p512
| p511 ),
inference(fof_simplification,[status(thm)],[ax33]) ).
thf(c_0_140,plain,
( p512
| ~ p85 ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
thf(c_0_141,plain,
( p346
| ~ p348
| ~ p347 ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
thf(c_0_142,plain,
p347,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]),c_0_122]) ).
thf(c_0_143,plain,
( p348
| ~ p349 ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
thf(c_0_144,plain,
p349,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125]),c_0_126])]) ).
thf(c_0_145,plain,
( ~ p8
| ( fzero
!= ( fs @ fzero ) )
| ( fzero != fzero )
| ( fzero
!= ( fs @ fzero ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax8])]) ).
thf(c_0_146,plain,
( ~ p3
| p8 ),
inference(fof_simplification,[status(thm)],[ax646]) ).
thf(c_0_147,plain,
( p1
| p3 ),
inference(split_conjunct,[status(thm)],[ax651]) ).
thf(c_0_148,plain,
( ~ p242
| p250 ),
inference(fof_simplification,[status(thm)],[ax350]) ).
thf(c_0_149,plain,
( p242
| ~ p243
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
thf(c_0_150,plain,
p16,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_108])]) ).
thf(c_0_151,plain,
p243,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130])]) ).
thf(c_0_152,plain,
( ~ p252
| p251 ),
inference(fof_simplification,[status(thm)],[ax347]) ).
thf(c_0_153,plain,
( p252
| ~ p253 ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
thf(c_0_154,plain,
p253,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133])]) ).
thf(c_0_155,plain,
( ~ p513
| p15
| p508 ),
inference(fof_simplification,[status(thm)],[ax29]) ).
thf(c_0_156,plain,
( p513
| ~ p514 ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
thf(c_0_157,plain,
p514,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136])]) ).
thf(c_0_158,plain,
( ~ p10
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
thf(c_0_159,plain,
( ~ p511
| ~ p35
| p510 ),
inference(fof_simplification,[status(thm)],[ax32]) ).
thf(c_0_160,plain,
( p35
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_161,plain,
( p511
| ~ p512 ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
thf(c_0_162,plain,
p512,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_97])]) ).
thf(c_0_163,plain,
( ~ p346
| ( ( fh @ fzero )
= ( fs @ fzero ) ) ),
inference(fof_nnf,[status(thm)],[pax346]) ).
thf(c_0_164,plain,
( p346
| ~ p348 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142])]) ).
thf(c_0_165,plain,
p348,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144])]) ).
thf(c_0_166,plain,
( ~ p8
| ( fzero
!= ( fs @ fzero ) )
| ( fzero != fzero )
| ( fzero
!= ( fs @ fzero ) ) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
thf(c_0_167,plain,
( p8
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
thf(c_0_168,plain,
p3,
inference(sr,[status(thm)],[c_0_147,c_0_66]) ).
thf(c_0_169,plain,
( ~ p250
| ~ p249
| p248 ),
inference(fof_simplification,[status(thm)],[ax349]) ).
thf(c_0_170,plain,
( p250
| ~ p242 ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
thf(c_0_171,plain,
p242,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150]),c_0_151])]) ).
thf(c_0_172,plain,
( ~ p251
| ~ p25
| p249 ),
inference(fof_simplification,[status(thm)],[ax348]) ).
thf(c_0_173,plain,
( p251
| ~ p252 ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
thf(c_0_174,plain,
p252,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_154])]) ).
thf(c_0_175,plain,
( ~ p29
| p235 ),
inference(fof_simplification,[status(thm)],[ax365]) ).
thf(c_0_176,plain,
( ~ p509
| ~ p508
| p507 ),
inference(fof_simplification,[status(thm)],[ax30]) ).
thf(c_0_177,plain,
( p15
| p508
| ~ p513 ),
inference(split_conjunct,[status(thm)],[c_0_155]) ).
thf(c_0_178,plain,
p513,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_157])]) ).
thf(c_0_179,plain,
~ p15,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_92])]) ).
thf(c_0_180,plain,
( ~ p510
| p509 ),
inference(fof_simplification,[status(thm)],[ax31]) ).
thf(c_0_181,plain,
( p510
| ~ p511
| ~ p35 ),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
thf(c_0_182,plain,
p35,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_108])]) ).
thf(c_0_183,plain,
p511,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_162])]) ).
thf(c_0_184,plain,
( ~ p85
| p524 ),
inference(fof_simplification,[status(thm)],[ax21]) ).
thf(c_0_185,plain,
! [X20: $i] :
( ~ p401
| ( ( fh @ fzero )
!= X20 )
| ( X20 = fzero ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax401])])]) ).
thf(c_0_186,plain,
( ( ( fh @ fzero )
= ( fs @ fzero ) )
| ~ p346 ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
thf(c_0_187,plain,
p346,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_165])]) ).
thf(c_0_188,plain,
( ( fzero
!= ( fs @ fzero ) )
| ~ p8 ),
inference(cn,[status(thm)],[c_0_166]) ).
thf(c_0_189,plain,
p8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_168])]) ).
thf(c_0_190,plain,
( p248
| ~ p250
| ~ p249 ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
thf(c_0_191,plain,
p250,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171])]) ).
thf(c_0_192,plain,
( p249
| ~ p251
| ~ p25 ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
thf(c_0_193,plain,
p25,
inference(split_conjunct,[status(thm)],[ax629]) ).
thf(c_0_194,plain,
p251,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174])]) ).
thf(c_0_195,plain,
( ~ p235
| p287 ),
inference(fof_simplification,[status(thm)],[ax306]) ).
thf(c_0_196,plain,
( p235
| ~ p29 ),
inference(split_conjunct,[status(thm)],[c_0_175]) ).
thf(c_0_197,plain,
p29,
inference(split_conjunct,[status(thm)],[ax627]) ).
thf(c_0_198,plain,
( p507
| ~ p509
| ~ p508 ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
thf(c_0_199,plain,
p508,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_178])]),c_0_179]) ).
thf(c_0_200,plain,
( p509
| ~ p510 ),
inference(split_conjunct,[status(thm)],[c_0_180]) ).
thf(c_0_201,plain,
p510,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_182]),c_0_183])]) ).
thf(c_0_202,plain,
( ~ p524
| p539 ),
inference(fof_simplification,[status(thm)],[ax3]) ).
thf(c_0_203,plain,
( p524
| ~ p85 ),
inference(split_conjunct,[status(thm)],[c_0_184]) ).
thf(c_0_204,plain,
( ( ( ( fh @ fzero )
= esk9_0 )
| p401 )
& ( ( esk9_0 != fzero )
| p401 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax401])])])])]) ).
thf(c_0_205,plain,
! [X1: $i] :
( ( X1 = fzero )
| ~ p401
| ( ( fh @ fzero )
!= X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_185]) ).
thf(c_0_206,plain,
( ( fh @ fzero )
= ( fs @ fzero ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_187])]) ).
thf(c_0_207,plain,
( fs @ fzero )
!= fzero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_189])]) ).
thf(c_0_208,plain,
( ~ p287
| ~ p248
| p286 ),
inference(fof_simplification,[status(thm)],[ax305]) ).
thf(c_0_209,plain,
( p248
| ~ p249 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_191])]) ).
thf(c_0_210,plain,
p249,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_193]),c_0_194])]) ).
thf(c_0_211,plain,
( p287
| ~ p235 ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
thf(c_0_212,plain,
p235,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197])]) ).
thf(c_0_213,plain,
( ~ p539
| ~ p507
| p538 ),
inference(fof_simplification,[status(thm)],[ax2]) ).
thf(c_0_214,plain,
( p507
| ~ p509 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_199])]) ).
thf(c_0_215,plain,
p509,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_201])]) ).
thf(c_0_216,plain,
( p539
| ~ p524 ),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
thf(c_0_217,plain,
p524,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_203,c_0_97])]) ).
thf(c_0_218,plain,
( ~ p286
| ( fzero
= ( fh @ ( fs @ fzero ) ) ) ),
inference(fof_nnf,[status(thm)],[pax286]) ).
thf(c_0_219,plain,
( ( ( fh @ fzero )
= esk9_0 )
| p401 ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
thf(c_0_220,plain,
~ p401,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_206])]),c_0_207]) ).
thf(c_0_221,plain,
( p286
| ~ p287
| ~ p248 ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
thf(c_0_222,plain,
p248,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_210])]) ).
thf(c_0_223,plain,
p287,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_212])]) ).
thf(c_0_224,plain,
! [X6: $i] :
( ~ p538
| ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= X6 )
| ( X6
= ( fs @ fzero ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax538])])]) ).
thf(c_0_225,plain,
( p538
| ~ p539
| ~ p507 ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
thf(c_0_226,plain,
p507,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_214,c_0_215])]) ).
thf(c_0_227,plain,
p539,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_216,c_0_217])]) ).
thf(c_0_228,plain,
( ~ p3
| p292 ),
inference(fof_simplification,[status(thm)],[ax298]) ).
thf(c_0_229,plain,
( ~ p292
| ( ( fh @ fzero )
!= ( fs @ fzero ) )
| ( ( fh @ ( fs @ fzero ) )
!= fzero )
| ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= ( fs @ fzero ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax292])]) ).
thf(c_0_230,plain,
( ( fzero
= ( fh @ ( fs @ fzero ) ) )
| ~ p286 ),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
thf(c_0_231,plain,
( ( fs @ fzero )
= esk9_0 ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_219,c_0_220]),c_0_206]) ).
thf(c_0_232,plain,
p286,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_221,c_0_222]),c_0_223])]) ).
thf(c_0_233,plain,
! [X1: $i] :
( ( X1
= ( fs @ fzero ) )
| ~ p538
| ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
thf(c_0_234,plain,
p538,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_225,c_0_226]),c_0_227])]) ).
thf(c_0_235,plain,
( p292
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
thf(c_0_236,plain,
( ~ p292
| ( ( fh @ fzero )
!= ( fs @ fzero ) )
| ( ( fh @ ( fs @ fzero ) )
!= fzero )
| ( ( fh @ ( fs @ ( fs @ fzero ) ) )
!= ( fs @ fzero ) ) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
thf(c_0_237,plain,
( ( fh @ esk9_0 )
= fzero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_230,c_0_231]),c_0_232])]) ).
thf(c_0_238,plain,
( ( fh @ ( fs @ esk9_0 ) )
= esk9_0 ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_233,c_0_231]),c_0_231]),c_0_234])])]) ).
thf(c_0_239,plain,
p292,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_235,c_0_168])]) ).
thf(c_0_240,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)],[inference(rw,[status(thm)],[c_0_236,c_0_206]),c_0_231]),c_0_231]),c_0_231]),c_0_237]),c_0_231]),c_0_238]),c_0_231]),c_0_239])]),
[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 )
!= X1 ) )
=> ~ ! [X1: $i] :
( ( h @ X1 )
= ( ite
@ ( X1
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) )
=> ~ ! [X1: $i > $i] :
( ~ ( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) )
=> ( ( X1 @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUN025^2 : TPTP v8.1.0. Released v6.4.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 2 07:35:42 EDT 2022
% 0.14/0.34 % CPUTime :
% 47.56/47.84 % SZS status Theorem
% 47.56/47.84 % Mode: mode371
% 47.56/47.84 % Inferences: 18679
% 47.56/47.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------