TSTP Solution File: PUZ081^3 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PUZ081^3 : TPTP v8.1.0. Released v3.6.0.
% 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 18:24:41 EDT 2022
% Result : Theorem 2.92s 3.10s
% Output : Proof 2.92s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_knave,type,
knave: $i > $o ).
thf(ty_knight,type,
knight: $i > $o ).
thf(ty_says,type,
says: $i > $o > $o ).
thf(ty_mel,type,
mel: $i ).
thf(ty_zoey,type,
zoey: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( knight @ X1 )
!= ( knave @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( knave @ zoey ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( knight @ zoey )
= sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ sP2
=> ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( says @ zoey @ ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( knight @ zoey )
=> ~ ( knave @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( knight @ zoey )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( knight @ zoey )
=> ~ ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $o] :
( ~ ( sP2
=> ~ ( says @ zoey @ X1 ) )
=> ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( says @ mel @ ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ( knight @ mel )
=> ~ sP10 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( knight @ mel ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( sP2
=> ~ sP5 )
=> ~ ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( knight @ zoey ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $o] :
( ~ ( sP14
=> ~ ( says @ zoey @ X1 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $o] :
( ~ ( ( knight @ X1 )
=> ~ ( says @ X1 @ X2 ) )
=> X2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP7
=> ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i] :
( ( knight @ X1 )
=> ~ ( knave @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP12
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP12
= ( knave @ mel ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( knave @ mel ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $o] :
( ~ ( sP12
=> ~ ( says @ mel @ X1 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $o] :
( ~ ( ( knave @ X1 )
=> ~ ( says @ X1 @ X2 ) )
=> ~ X2 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP2
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(who_is_knight_and_knave,conjecture,
~ sP18 ).
thf(h0,negated_conjecture,
sP18,
inference(assume_negation,[status(cth)],[who_is_knight_and_knave]) ).
thf(1,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP14
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| sP14
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP20
| sP12
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP1
| ~ sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP18
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP23
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP13
| sP24
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP24
| ~ sP2
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP16
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP15
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP17
| sP7
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP7
| ~ sP14
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP16
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP22
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP11
| sP19
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP19
| ~ sP12
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(mel_speaks,axiom,
sP10 ).
thf(zoey_speaks,axiom,
sP5 ).
thf(knaves_lie,axiom,
sP23 ).
thf(knights_tell_truth,axiom,
sP16 ).
thf(knights_xor_knaves,axiom,
sP1 ).
thf(21,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,mel_speaks,zoey_speaks,knaves_lie,knights_tell_truth,knights_xor_knaves,h0]) ).
thf(0,theorem,
~ sP18,
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : PUZ081^3 : TPTP v8.1.0. Released v3.6.0.
% 0.03/0.12 % 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 : Sun May 29 01:33:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.92/3.10 % SZS status Theorem
% 2.92/3.10 % Mode: mode506
% 2.92/3.10 % Inferences: 28522
% 2.92/3.10 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------