TSTP Solution File: PUZ081^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PUZ081^2 : TPTP v8.1.0. Bugfixed v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 18:24:41 EDT 2022
% Result : Theorem 33.24s 33.48s
% Output : Proof 33.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 83
% Syntax : Number of formulae : 88 ( 16 unt; 6 typ; 1 def)
% Number of atoms : 251 ( 32 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 269 ( 100 ~; 45 |; 0 &; 48 @)
% ( 37 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 42 con; 0-2 aty)
% Number of variables : 13 ( 1 ^ 12 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_knave,type,
knave: $i > $o ).
thf(ty_knight,type,
knight: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_says,type,
says: $i > $o > $o ).
thf(ty_mel,type,
mel: $i ).
thf(ty_zoey,type,
zoey: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
( ( knight @ X1 )
!= ( knight @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( knight @ X1 )
!= ( knave @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( knight @ mel ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o] :
( ~ ( ( knight @ zoey )
=> ~ ( says @ zoey @ X1 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( says @ mel @ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( ( knight != knight )
=> ( knight = knave ) )
=> ~ ( ( knave != knight )
=> ( knave = knave ) ) )
=> ~ ( knight @ zoey ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP2
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( says @ zoey @ ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( knave @ zoey )
=> ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ( knight != knight )
=> ( knight = knave ) )
=> ~ ( ( knave != knight )
=> ( knave = knave ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( knight @ zoey )
= ( knave @ zoey ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( knave @ mel )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $o] :
( ~ ( sP2
=> ~ ( says @ mel @ X1 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( knight @ X1 )
= ( knight @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( knight != knight )
=> ( knight = knave ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( says @ mel @ ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( knight = knight ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP6
=> ~ ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i > $o] :
( ~ ( ~ ( sP15
=> ~ ( ( X1 != knight )
=> ( X1 = knave ) ) )
=> ~ ( knight @ zoey ) )
=> ~ ( X1 @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( zoey = zoey ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP2
= ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( mel = mel ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( knave = knave ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( knight @ zoey ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( knave != knight )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $o] :
( ~ ( ( knight @ X1 )
=> ~ ( says @ X1 @ X2 ) )
=> X2 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( knight @ eigen__4 )
= ( knight @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( ~ sP9 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ~ ( ( ( X1 != knight )
=> ( X1 = knave ) )
=> ~ ( ( X2 != knight )
=> ( X2 = knave ) ) )
=> ~ ( X1 @ zoey ) )
=> ~ ( X2 @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( says @ zoey @ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i > $o] :
( ~ ( ~ ( sP25
=> ~ ( ( X1 != knight )
=> ( X1 = knave ) ) )
=> ~ ( knave @ zoey ) )
=> ~ ( X1 @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( knave @ mel ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP24
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ ( ~ ( sP25
=> ~ sP25 )
=> ~ ( knave @ zoey ) )
=> ~ sP32 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( knave @ zoey ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ ( sP25
=> ~ sP25 )
=> ~ sP35 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP25
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(what_are_zoey_and_mel,conjecture,
~ sP29 ).
thf(h1,negated_conjecture,
sP29,
inference(assume_negation,[status(cth)],[what_are_zoey_and_mel]) ).
thf(1,plain,
( ~ sP10
| ~ sP15
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP10
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP18
| sP6
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
sP27,
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP14
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(6,plain,
( sP17
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP15
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP19
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP29
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
sP23,
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP25
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP37
| ~ sP25
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP36
| sP37
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP34
| sP36
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP31
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP29
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP7
| ~ sP2
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP13
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP16
| sP5
| ~ sP22
| ~ sP28 ),
inference(mating_rule,[status(thm)],]) ).
thf(20,plain,
sP22,
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP21
| sP2
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP33
| ~ sP24
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP4
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( sP12
| sP32
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP8
| sP30
| ~ sP20
| ~ sP12 ),
inference(mating_rule,[status(thm)],]) ).
thf(26,plain,
( sP28
| ~ sP9
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
sP20,
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP11
| sP24
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP9
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP1
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP26
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP1
| ~ sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP26
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
~ sP3,
inference(prop_rule,[status(thm)],]) ).
thf(mel_speaks,axiom,
sP16 ).
thf(zoey_speaks,axiom,
sP8 ).
thf(knights_tell_truth,axiom,
sP26 ).
thf(knights_xor_knaves,axiom,
sP1 ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,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,mel_speaks,zoey_speaks,knights_tell_truth,knights_xor_knaves,h1]) ).
thf(36,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[35,h0]) ).
thf(0,theorem,
~ sP29,
inference(contra,[status(thm),contra(discharge,[h1])],[35,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ081^2 : TPTP v8.1.0. Bugfixed v7.1.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat May 28 21:39:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 33.24/33.48 % SZS status Theorem
% 33.24/33.48 % Mode: mode448
% 33.24/33.48 % Inferences: 416
% 33.24/33.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------