TSTP Solution File: NUN025^3 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUN025^3 : 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 : n025.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 4.69s 4.93s
% Output : Proof 4.77s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_zero,type,
zero: $i ).
thf(ty_h,type,
h: $i > $i ).
thf(ty_s,type,
s: $i > $i ).
thf(ty_ite,type,
ite: $o > $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ~ ( ! [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 )
@ ( ite
@ ( X1
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i > $o] :
( ( X2 @ X1 )
=> ! [X3: $i] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( ( s @ zero )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ X1
@ X2 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( ( s @ zero )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ X1 )
= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ( ite @ ( zero = zero ) @ ( s @ zero )
@ ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
=> ( ~ ( ( ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( ( s @ ( s @ zero ) )
!= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
@ zero
@ X1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( zero = zero )
=> ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ ( s @ zero ) )
= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ( s @ zero )
= ( s @ ( s @ zero ) ) )
=> ( ( s @ ( s @ zero ) )
= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ ( s @ zero ) )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( ( s @ zero )
= X1 )
=> ( X1
= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( h @ ( s @ ( s @ zero ) ) )
= ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ( s @ zero )
!= zero )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP13
=> ! [X1: $i] :
( ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ ( s @ zero ) )
= X1 )
=> ( ( h @ ( s @ ( s @ zero ) ) )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP2
=> ( ( h @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i,X2: $i] :
( ( zero
!= ( s @ zero ) )
=> ( ( ite
@ ( zero
= ( s @ zero ) )
@ X1
@ X2 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $o] :
( ( X1 @ ( h @ zero ) )
=> ! [X2: $i] :
( ( ( h @ zero )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( ite
@ ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( sP4
=> ~ ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) )
=> ~ ! [X1: $i] :
( ( s @ X1 )
!= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( h @ ( s @ zero ) )
= ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( ~ ( ( ( h @ zero )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) )
=> ! [X1: $i] :
( ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= X1 )
=> ( ~ ( ( ( h @ zero )
= ( s @ zero ) )
=> ( X1 != zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] :
( ( ( s @ zero )
!= zero )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ X1
@ X2 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= X1 )
=> ( ~ ( ( ( h @ zero )
= ( s @ zero ) )
=> ( X1 != zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( ( s @ ( s @ zero ) )
!= zero )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( s @ zero )
= ( s @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( ( h @ ( s @ zero ) )
= X1 )
=> ( ~ ( ( ( h @ zero )
= ( s @ zero ) )
=> ( X1 != zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ ( ( ( h @ zero )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP19
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( h @ zero )
= ( ite @ ( zero = zero ) @ ( s @ zero )
@ ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ( ( h @ zero )
= ( s @ zero ) )
=> ( ( h @ ( s @ zero ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( zero
!= ( s @ zero ) )
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ( zero != zero )
=> ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ X1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( ite @ ( zero = zero ) @ ( s @ zero )
@ ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( zero = zero )
=> ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ X1 )
= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP4
=> ~ ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
=> ( ( ( s @ zero )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ ( s @ zero ) )
= X1 )
=> ( ~ ( ( X1
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP21
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i > $o] :
( ( X1
@ ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) )
=> ! [X2: $i] :
( ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP24
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( zero = zero ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
( ( ( ite
@ ( zero
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
= X1 )
=> ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ X1 )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ sP44
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( zero
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( s @ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ( ( s @ zero )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
= ( s @ zero ) )
=> ( ( ite @ sP48 @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( ( s @ ( s @ zero ) )
!= ( s @ zero ) )
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i > $o] :
( ( X1 @ ( h @ ( s @ zero ) ) )
=> ! [X2: $i] :
( ( ( h @ ( s @ zero ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP50
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( ( ite @ sP48 @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
= ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
=> ( ~ ( ( ( h @ zero )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP31
=> ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ( s @ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ( ( ite @ sP44 @ ( s @ zero ) @ ( s @ zero ) )
= ( s @ zero ) )
=> ( ~ ( ( ( s @ zero )
= ( s @ zero ) )
=> ( ( ite @ sP48 @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $i > $o] :
( ( X1 @ ( ite @ sP56 @ zero @ ( s @ zero ) ) )
=> ! [X2: $i] :
( ( ( ite @ sP56 @ zero @ ( s @ zero ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: $i] :
( ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ ( s @ zero ) )
= X1 )
=> ( ( h @ ( s @ ( s @ zero ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ ( sP24
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i > $i] :
( ~ ( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) )
=> ( ( X1 @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: $i > $o] :
( ( X1 @ ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) ) )
=> ! [X2: $i] :
( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ~ sP1
=> ~ sP61 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP24
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ( ( s @ zero )
= ( s @ zero ) )
=> ( ( ite @ sP48 @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) )
=> ! [X1: $i] :
( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
= X1 )
=> ( ~ ( ( X1
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP31
=> sP50 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [X1: $i,X2: $i] :
( ~ sP44
=> ( ( ite @ sP44 @ X1 @ X2 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [X1: $i] :
( ( ( h @ zero )
= X1 )
=> ( ~ ( ( X1
= ( s @ zero ) )
=> ( ( ite @ sP48 @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
!= zero ) )
=> ( ( h @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ( s @ zero )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( sP29
=> sP70 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( ( h @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
= ( s @ zero ) )
=> ( ( ite @ sP71 @ zero @ ( s @ zero ) )
!= zero ) )
=> ~ sP73 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( sP11
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ( h @ ( s @ ( s @ zero ) ) )
= ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ ( ite @ sP56 @ zero @ ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( ~ ( ( ( h @ zero )
= ( s @ zero ) )
=> ( ( ite @ sP71 @ zero @ ( s @ zero ) )
!= zero ) )
=> ~ sP73 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i > $o] :
( ( X1
@ ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ ( s @ zero ) ) )
=> ! [X2: $i] :
( ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ ( s @ zero ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ( ite @ sP44 @ ( s @ zero ) @ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ! [X1: $i] :
( ( s @ X1 )
!= zero ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ! [X1: $i,X2: $i] :
( ( ( s @ ( s @ zero ) )
!= zero )
=> ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ X1
@ X2 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ! [X1: $i] :
( ( h @ X1 )
= ( ite @ ( X1 = zero ) @ ( s @ zero )
@ ( ite
@ ( X1
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ! [X1: $i,X2: $i] :
( ~ sP56
=> ( ( ite @ sP56 @ X1 @ X2 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ! [X1: $i] :
( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
= X1 )
=> ( ~ ( ( X1
= ( s @ zero ) )
=> ( ( ite @ sP71 @ zero @ ( s @ zero ) )
!= zero ) )
=> ~ sP73 ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ! [X1: $i] :
( ( ( s @ ( s @ zero ) )
!= zero )
=> ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ X1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( ~ sP20
=> ~ ! [X1: $i] :
( ( s @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( sP32
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( ( ite @ sP71 @ zero @ ( s @ zero ) )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [X1: $i] :
( ( ( h @ zero )
= X1 )
=> ( ~ ( ( X1
= ( s @ zero ) )
=> ~ sP88 )
=> ~ sP73 ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ! [X1: $i] :
( ( ( ite @ sP48 @ ( s @ zero ) @ ( ite @ sP71 @ zero @ ( s @ zero ) ) )
= X1 )
=> ( sP71
=> ( X1 != zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( ( ite @ sP48 @ ( s @ zero ) @ ( ite @ sP71 @ zero @ ( s @ zero ) ) )
= ( ite @ sP71 @ zero @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ! [X1: $i] :
( ~ sP48
=> ( ( ite @ sP48 @ ( s @ zero ) @ X1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( sP77
=> sP89 ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ! [X1: $i,X2: $i] :
( sP44
=> ( ( ite @ sP44 @ X1 @ X2 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ! [X1: $i] :
( ( s @ X1 )
!= X1 ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( ( s @ ( s @ zero ) )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( sP71
=> ~ sP88 ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ! [X1: $i] :
( ~ sP47
=> ( ( ite @ sP47 @ zero @ X1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( sP66
=> sP90 ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ! [X1: $i > $o] :
( ( X1 @ ( ite @ sP44 @ ( s @ zero ) @ ( s @ zero ) ) )
=> ! [X2: $i] :
( ( ( ite @ sP44 @ ( s @ zero ) @ ( s @ zero ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ! [X1: $i] :
( ( ( ite @ sP56 @ zero @ ( s @ zero ) )
= X1 )
=> ( ( h @ ( s @ ( s @ zero ) ) )
= ( ite @ sP96 @ ( s @ zero ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( sP76
=> sP101 ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ! [X1: $i > $o] :
( ( X1 @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
=> ! [X2: $i] :
( ( ( ite @ sP47 @ zero @ ( s @ zero ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( ~ sP66
=> ~ sP73 ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(n10,conjecture,
sP64 ).
thf(h0,negated_conjecture,
~ sP64,
inference(assume_negation,[status(cth)],[n10]) ).
thf(1,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP49
| ~ sP71
| sP88 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP94 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP94
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP36
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| ~ sP44
| sP79 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP38
| ~ sP91
| sP97 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP90
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP99
| ~ sP66
| sP90 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP42
| sP99 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP65
| ~ sP24
| ~ sP88 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP97
| ~ sP71
| ~ sP88 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP27
| ~ sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP104
| sP66
| ~ sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP60
| sP65
| ~ sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP57
| ~ sP79
| sP104 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP39
| sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP75
| ~ sP11
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP100
| sP75 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP7
| ~ sP35
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP84
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP67
| ~ sP74
| sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP63
| sP67 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP55
| ~ sP31
| sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP89
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP93
| ~ sP77
| sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP18
| sP93 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP85
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP26
| sP96
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP16
| ~ sP2
| sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP59
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP15
| ~ sP13
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP78
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP3
| sP78 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP3
| sP100 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP30
| ~ sP19
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP101
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP102
| ~ sP76
| sP101 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP58
| sP102 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP54
| ~ sP91
| sP77 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP25
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP22
| ~ sP29
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP42
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP43
| ~ sP24
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP45
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP53
| ~ sP50
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP103
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP62
| sP83 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP83
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP8
| sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP51
| sP56
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP3
| sP58 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP62
| sP81 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP81
| sP85 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP62
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP23
| sP92 ),
inference(all_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP92
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP14
| sP48
| sP91 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP3
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP62
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP17
| sP98 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP98
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP33
| sP47
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP3
| sP103 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP62
| sP69 ),
inference(all_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP69
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP34
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP46
| sP44
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP3
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(72,plain,
( sP37
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( sP37
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP68
| ~ sP31
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP70
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP72
| ~ sP29
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP18
| sP72 ),
inference(all_rule,[status(thm)],]) ).
thf(78,plain,
( ~ sP41
| ~ sP21
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( ~ sP28
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(80,plain,
( ~ sP87
| ~ sP32
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP52
| sP87 ),
inference(all_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP80
| ~ sP96 ),
inference(all_rule,[status(thm)],]) ).
thf(83,plain,
( sP20
| sP80 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( sP20
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(85,plain,
( ~ sP82
| sP76 ),
inference(all_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP10
| ~ sP27
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(87,plain,
( ~ sP12
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(88,plain,
( ~ sP3
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(89,plain,
( ~ sP3
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(90,plain,
( ~ sP61
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(91,plain,
sP71,
inference(prop_rule,[status(thm)],]) ).
thf(92,plain,
( ~ sP82
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(93,plain,
( ~ sP95
| ~ sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(94,plain,
( ~ sP82
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(95,plain,
( ~ sP95
| ~ sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(96,plain,
( ~ sP40
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(97,plain,
( sP86
| sP95 ),
inference(prop_rule,[status(thm)],]) ).
thf(98,plain,
( sP86
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(99,plain,
sP3,
inference(eq_ind,[status(thm)],]) ).
thf(100,plain,
sP40,
inference(eq_sym,[status(thm)],]) ).
thf(101,plain,
( sP1
| sP82 ),
inference(prop_rule,[status(thm)],]) ).
thf(102,plain,
( sP1
| ~ sP86 ),
inference(prop_rule,[status(thm)],]) ).
thf(103,plain,
( sP64
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(104,plain,
( sP64
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(105,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,h0]) ).
thf(0,theorem,
sP64,
inference(contra,[status(thm),contra(discharge,[h0])],[105,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN025^3 : TPTP v8.1.0. Released v6.4.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n025.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 08:15:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.69/4.93 % SZS status Theorem
% 4.69/4.93 % Mode: mode506
% 4.69/4.93 % Inferences: 89811
% 4.69/4.93 % SZS output start Proof
% See solution above
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