TSTP Solution File: NUN023^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUN023^2 : 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 : n023.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 2.23s 2.54s
% Output : Proof 2.23s
% 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] :
( ( h @ X1 )
= ( ite @ ( X1 = zero ) @ ( s @ zero ) @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( h @ zero )
= ( ite @ ( zero = zero ) @ ( s @ zero ) @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( zero = zero )
=> ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ zero )
= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( ( s @ zero )
!= zero )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ X1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( s @ zero )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ( ( s @ ( s @ zero ) )
!= zero )
=> ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ X1
@ X2 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] :
( ( X1
@ ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ zero ) )
=> ! [X2: $i] :
( ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ zero )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( h @ ( s @ zero ) )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( zero = zero )
=> ( ( ite @ ( zero = zero ) @ X1 @ X2 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ( ( h @ zero )
= ( s @ zero ) )
=> ~ sP8 )
=> ! [X1: $i] :
( ( ( h @ zero )
= X1 )
=> ( ( X1
= ( s @ zero ) )
=> ~ sP8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero )
= X1 )
=> ( ( h @ ( s @ zero ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ zero )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP5
=> ( ( s @ zero )
!= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $o] :
( ( X1
@ ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero ) )
=> ! [X2: $i] :
( ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i] :
( ( ( s @ zero )
!= zero )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ X1
@ X2 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP12
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( ( s @ ( s @ zero ) )
!= zero )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
=> ~ ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( h @ ( s @ zero ) )
= ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i > $o] :
( ( X2 @ X1 )
=> ! [X3: $i] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( ( s @ ( s @ zero ) )
!= zero )
=> ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ X1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( ( h @ zero )
= X1 )
=> ( ( X1
= ( s @ zero ) )
=> ~ sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP20
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( ( s @ zero )
!= zero )
=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero )
= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP16
=> ! [X1: $i] :
( ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ ( s @ zero )
@ zero )
= X1 )
=> ( X1 = zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP2
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( s @ ( s @ zero ) )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i > $i] :
( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( ( h @ zero )
= ( s @ zero ) )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( zero = zero )
=> ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ X1 )
= ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP1
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ( ( ite @ sP28 @ ( s @ zero ) @ zero )
= X1 )
=> ( X1 = zero ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP33
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP16
=> ( zero = zero ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( s @ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i > $o] :
( ( X1 @ ( h @ zero ) )
=> ! [X2: $i] :
( ( ( h @ zero )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( zero = zero ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP5
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ( h @ X1 )
= ( ite @ ( X1 = zero ) @ ( s @ zero ) @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(n10,conjecture,
sP32 ).
thf(h0,negated_conjecture,
~ sP32,
inference(assume_negation,[status(cth)],[n10]) ).
thf(1,plain,
( ~ sP35
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP31
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| ~ sP41
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP17
| ~ sP12
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP27
| ~ sP2
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP23
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP10
| ~ sP30
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP39
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP37
| ~ sP16
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP34
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP26
| ~ sP16
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP7
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP22
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP18
| sP28
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP21
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP6
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP40
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP29
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP36
| ~ sP33
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP11
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP24
| ~ sP20
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP14
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP40
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP15
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP4
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP25
| sP38
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP21
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( sP19
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP19
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
sP21,
inference(eq_ind,[status(thm)],]) ).
thf(33,plain,
( ~ sP43
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP43
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( sP1
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP1
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP42
| ~ sP5
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
sP5,
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP13
| ~ sP5
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP29
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP29
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( sP32
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP32
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,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,h0]) ).
thf(0,theorem,
sP32,
inference(contra,[status(thm),contra(discharge,[h0])],[44,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN023^2 : 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
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 2 02:44:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.23/2.54 % SZS status Theorem
% 2.23/2.54 % Mode: mode506
% 2.23/2.54 % Inferences: 59629
% 2.23/2.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------