TSTP Solution File: NUN023^2 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUN023^2 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n009.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 : 300s
% DateTime : Thu Aug 31 12:50:02 EDT 2023
% Result : Theorem 1.39s 1.64s
% Output : Proof 1.39s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_s,type,
s: $i > $i ).
thf(ty_ite,type,
ite: $o > $i > $i > $i ).
thf(ty_zero,type,
zero: $i ).
thf(ty_h,type,
h: $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( h @ X1 )
= ( ite @ ( X1 = zero ) @ ( s @ zero ) @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( ite @ $false @ ( s @ zero ) @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( ite @ ~ $false @ X1 @ X2 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( h @ zero )
= ( ite @ ~ $false @ ( s @ zero ) @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ite @ sP5 @ ( s @ zero ) @ ( ite @ ~ sP5 @ zero @ ( s @ zero ) ) )
= ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero )
= ( ite @ ~ sP5 @ zero @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ite
@ ( ( s @ zero )
= zero )
@ ( s @ zero )
@ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( ite @ sP5 @ X1 @ X2 )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( ite @ ~ sP5 @ ( s @ zero ) @ X1 )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ( s @ zero )
= zero )
= ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( s @ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( ite @ ~ sP5 @ zero @ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( h @ ( s @ zero ) )
= ( ite @ sP12 @ ( s @ zero ) @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( h @ ( s @ zero ) )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ite @ ~ sP5 @ ( s @ zero ) @ zero )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $i] :
( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( ite @ sP5 @ ( s @ zero ) @ ( ite @ ~ sP5 @ zero @ ( s @ zero ) ) )
= ( ite @ ~ sP5 @ zero @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( ite @ ~ sP5 @ zero @ X1 )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( ite @ ~ sP5 @ zero @ zero )
= ( h @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( h @ zero )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP22
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( ite @ ~ sP5 @ zero @ ( s @ zero ) )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(n10,conjecture,
( ~ ( ~ ( sP24
=> ~ sP16 )
=> ~ sP1 )
=> ~ sP18 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( sP24
=> ~ sP16 )
=> ~ sP1 )
=> ~ sP18 ),
inference(assume_negation,[status(cth)],[n10]) ).
thf(h1,assumption,
~ ( ~ ( sP24
=> ~ sP16 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP18,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP24
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
sP24,
introduced(assumption,[]) ).
thf(h6,assumption,
sP16,
introduced(assumption,[]) ).
thf(1,plain,
( sP6
| ~ sP25
| sP5
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP19
| sP8
| ~ sP6
| ~ sP25 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| sP21
| ~ sP7
| sP5 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(4,plain,
( sP11
| ~ sP12
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP7
| sP5
| ~ sP12
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP14
| sP15
| sP5
| ~ sP8 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP13
| sP15
| ~ sP21
| sP5 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| sP22
| sP5
| ~ sP17 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(10,plain,
~ sP5,
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP3
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP20
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP23
| ~ sP22
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP18
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP20
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP3
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP24
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP16
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,h5,h6,h4,h2]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,23,h5,h6]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,24,h3,h4]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,25,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( sP24
=> ~ sP16 )
=> ~ sP1 )
=> ~ sP18 ),
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN023^2 : TPTP v8.1.2. Released v6.4.0.
% 0.06/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n009.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 : 300
% 0.12/0.33 % DateTime : Sun Aug 27 08:55:05 EDT 2023
% 0.12/0.33 % CPUTime :
% 1.39/1.64 % SZS status Theorem
% 1.39/1.64 % Mode: cade22grackle2xfee4
% 1.39/1.64 % Steps: 33034
% 1.39/1.64 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------