%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ081^2 : TPTP v9.2.1. Bugfixed v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 : Wed Feb 25 09:28:26 AM UTC 2026
% Result : Theorem 1.64s 1.38s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 3 unt; 0 typ; 4 def)
% Number of atoms : 281 ( 84 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 206 ( 67 ~; 59 |; 16 &; 58 @)
% ( 4 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 0 ^; 21 !; 8 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
knight: $i > $o ).
thf(func_def_3,type,
knave: $i > $o ).
thf(func_def_4,type,
says: $i > $o > $o ).
thf(f78,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f58,f63,f68,f69,f73,f77]) ).
thf(f77,plain,
( spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f76]) ).
thf(f76,plain,
( $false
| spl0_2
| spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f75,f62]) ).
thf(f62,plain,
( ( $true
!= ( knight @ zoey ) )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f60,definition,
( spl0_3
<=> ( $true
= ( knight @ zoey ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f75,plain,
( ( $true
= ( knight @ zoey ) )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( $true
= ( knight @ zoey ) )
| ( $true != $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f57,f48]) ).
thf(f48,plain,
! [X0: $i] :
( ( ( knave @ X0 )
= $true )
| ( ( knight @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $i] :
( ( knight @ X0 )
!= ( knave @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i] :
( ( knight @ X0 )
!= ( knave @ X0 ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i] :
( ( knight @ X0 )
<~> ( knave @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( knight @ X0 )
<~> ( knave @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.8jub0XKdEo/DTF2THF_29097.p',knights_xor_knaves) ).
thf(f57,plain,
( ( ( knave @ zoey )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl0_2
<=> ( ( knave @ zoey )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f73,plain,
( spl0_1
| spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| spl0_1
| spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f71,f67]) ).
thf(f67,plain,
( ( $true
!= ( knight @ mel ) )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl0_4
<=> ( $true
= ( knight @ mel ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f71,plain,
( ( $true
= ( knight @ mel ) )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true != $true )
| ( $true
= ( knight @ mel ) )
| spl0_1 ),
inference(superposition,[status(thm)],[f53,f48]) ).
thf(f53,plain,
( ( ( knave @ mel )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl0_1
<=> ( ( knave @ mel )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f69,plain,
( ~ spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f42,f60,f65]) ).
thf(f42,plain,
( ( $true
!= ( knight @ mel ) )
| ( $true
!= ( knight @ zoey ) ) ),
inference(equality_resolution,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i > $o] :
( ( $true
!= ( knight @ mel ) )
| ( knight != X0 )
| ( $true
!= ( X0 @ zoey ) ) ),
inference(equality_resolution,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( $true
!= ( X1 @ mel ) )
| ( knight != X1 )
| ( knight != X0 )
| ( $true
!= ( X0 @ zoey ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( $true
!= ( X1 @ mel ) )
| ( ( knight != X1 )
& ( knave != X1 ) )
| ( ( knave != X0 )
& ( knight != X0 ) )
| ( $true
!= ( X0 @ zoey ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i > $o,X0: $i > $o] :
( ( ( X0 @ mel )
!= $true )
| ( ( knight != X0 )
& ( knave != X0 ) )
| ( ( knave != X1 )
& ( knight != X1 ) )
| ( ( X1 @ zoey )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ? [X0: $i > $o,X1: $i > $o] :
( ( ( knight = X0 )
| ( knave = X0 ) )
& ( ( X0 @ mel )
= $true )
& ( ( X1 @ zoey )
= $true )
& ( ( knave = X1 )
| ( knight = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ? [X0: $i > $o,X1: $i > $o] :
( ( X0 @ mel )
& ( ( knight = X0 )
| ( knave = X0 ) )
& ( ( knave = X1 )
| ( knight = X1 ) )
& ( X1 @ zoey ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ? [X3: $i > $o,X2: $i > $o] :
( ( X3 @ mel )
& ( ( knight = X3 )
| ( knave = X3 ) )
& ( ( knave = X2 )
| ( knight = X2 ) )
& ( X2 @ zoey ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
? [X3: $i > $o,X2: $i > $o] :
( ( X3 @ mel )
& ( ( knight = X3 )
| ( knave = X3 ) )
& ( ( knave = X2 )
| ( knight = X2 ) )
& ( X2 @ zoey ) ),
file('/export/starexec/sandbox2/tmp/tmp.8jub0XKdEo/DTF2THF_29097.p',what_are_zoey_and_mel) ).
thf(f68,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f40,f65,f55]) ).
thf(f40,plain,
( ( $true
!= ( knight @ mel ) )
| ( ( knave @ zoey )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $i > $o] :
( ( $true
!= ( knight @ mel ) )
| ( knave != X0 )
| ( $true
!= ( X0 @ zoey ) ) ),
inference(equality_resolution,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( $true
!= ( X1 @ mel ) )
| ( knight != X1 )
| ( knave != X0 )
| ( $true
!= ( X0 @ zoey ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f63,plain,
( ~ spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f46,f51,f60]) ).
thf(f46,plain,
( ( ( knave @ mel )
!= $true )
| ( $true
!= ( knight @ zoey ) ) ),
inference(equality_resolution,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: $i > $o] :
( ( ( knave @ mel )
!= $true )
| ( knight != X0 )
| ( $true
!= ( X0 @ zoey ) ) ),
inference(equality_resolution,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( $true
!= ( X1 @ mel ) )
| ( knave != X1 )
| ( knight != X0 )
| ( $true
!= ( X0 @ zoey ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f58,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f44,f55,f51]) ).
thf(f44,plain,
( ( ( knave @ mel )
!= $true )
| ( ( knave @ zoey )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: $i > $o] :
( ( ( knave @ mel )
!= $true )
| ( knave != X0 )
| ( $true
!= ( X0 @ zoey ) ) ),
inference(equality_resolution,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( $true
!= ( X1 @ mel ) )
| ( knave != X1 )
| ( knave != X0 )
| ( $true
!= ( X0 @ zoey ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ081^2 : TPTP v9.2.1. Bugfixed v7.1.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n005.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:32:29 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : PUZ081^2 : TPTP v9.2.1. Bugfixed v7.1.0.
% 0.31/0.46 % Domain : Puzzles
% 0.31/0.46 % Problem : 1 of http://philosophy.hku.hk/think/logic/knight.php
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : A very special island is inhabited only by knights and knaves.
% 0.31/0.46 % Knights always tell the truth, and knaves always lie. You meet two
% 0.31/0.46 % inhabitants: Zoey and Mel. Zoey tells you that Mel is a knave. Mel
% 0.31/0.46 % says, `Neither Zoey nor I are knaves'. Who is a knight and who is
% 0.31/0.46 % a knave?
% 0.31/0.46
% 0.31/0.46 % Refs :
% 0.31/0.46 % Source : [TPTP]
% 0.31/0.46 % Names :
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0
% 0.31/0.46 % Syntax : Number of formulae : 11 ( 0 unt; 5 typ; 0 def)
% 0.31/0.46 % Number of atoms : 19 ( 4 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 3 avg)
% 0.31/0.46 % Number of connectives : 31 ( 3 ~; 2 |; 6 &; 17 @)
% 0.31/0.46 % ( 0 <=>; 2 =>; 0 <=; 1 <~>)
% 0.31/0.46 % Maximal formula depth : 7 ( 6 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 7 ( 0 ^; 5 !; 2 ?; 7 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : See http://philosophy.hku.hk/think/logic/knight.php
% 0.31/0.46 % : This version finds the types of Zoey and Mel
% 0.31/0.46 % Bugfixes : v7.1.0 - Fixed the conjecture.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 %----Type declarations
% 0.31/0.46 thf(mel_type,type,
% 0.31/0.46 mel: $i ).
% 0.31/0.46
% 0.31/0.46 thf(zoey_type,type,
% 0.31/0.46 zoey: $i ).
% 0.31/0.46
% 0.31/0.46 thf(knight_type,type,
% 0.31/0.46 knight: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(knave_type,type,
% 0.31/0.46 knave: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(says_type,type,
% 0.31/0.46 says: $i > $o > $o ).
% 0.31/0.46
% 0.31/0.46 %----A very special island is inhabited only by knights and knaves.
% 0.31/0.46 thf(knights_xor_knaves,axiom,
% 0.31/0.46 ! [P: $i] :
% 0.31/0.46 ( ( knight @ P )
% 0.31/0.46 <~> ( knave @ P ) ) ).
% 0.31/0.46
% 0.31/0.46 %----Knights always tell the truth
% 0.31/0.46 thf(knights_tell_truth,axiom,
% 0.31/0.46 ! [P: $i,S: $o] :
% 0.31/0.46 ( ( ( knight @ P )
% 0.31/0.46 & ( says @ P @ S ) )
% 0.31/0.46 => S ) ).
% 0.31/0.46
% 0.31/0.46 %----Knaves always lie
% 0.31/0.46 thf(knaves_lie,axiom,
% 0.31/0.46 ! [P: $i,S: $o] :
% 0.31/0.46 ( ( ( knave @ P )
% 0.31/0.46 & ( says @ P @ S ) )
% 0.31/0.46 => ~ S ) ).
% 0.31/0.46
% 0.31/0.46 %----Zoey says 'Mel is a knave'
% 0.31/0.46 thf(zoey_speaks,axiom,
% 0.31/0.46 says @ zoey @ ( knave @ mel ) ).
% 0.31/0.46
% 0.31/0.46 %----Mel says 'Neither Zoey nor I are knaves.'
% 0.31/0.46 thf(mel_speaks,axiom,
% 0.31/0.46 ( says @ mel
% 0.31/0.46 @ ( ~ ( knave @ zoey )
% 0.31/0.46 & ~ ( knave @ mel ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %----What are Zoey and Mel
% 0.31/0.46 thf(what_are_zoey_and_mel,conjecture,
% 0.31/0.46 ? [TZ: $i > $o,TM: $i > $o] :
% 0.31/0.46 ( ( ( TZ = knight )
% 0.31/0.46 | ( TZ = knave ) )
% 0.31/0.46 & ( ( TM = knight )
% 0.31/0.46 | ( TM = knave ) )
% 0.31/0.46 & ( TZ @ zoey )
% 0.31/0.46 & ( TM @ mel ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.64/1.34 ---- Embedded in THF ---
% 1.64/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.34 %%% Generated on Tue Feb 24 11:32:30 EST 2026
% 1.64/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.34 %%% Logic specification used:
% 1.64/1.34 %%% thf(spec, logic, $$dhol).
% 1.64/1.34
% 1.64/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.8jub0XKdEo/DTF2DTF29097.p
% See solution above
% 1.64/1.34 ------------------------
% 1.64/1.35 ---- Cleaned THF ---
% 1.64/1.35 thf(mel_type,type,
% 1.64/1.35 mel: $i ).
% 1.64/1.35
% 1.64/1.35 thf(zoey_type,type,
% 1.64/1.35 zoey: $i ).
% 1.64/1.35
% 1.64/1.35 thf(knight_type,type,
% 1.64/1.35 knight: $i > $o ).
% 1.64/1.35
% 1.64/1.35 thf(knave_type,type,
% 1.64/1.35 knave: $i > $o ).
% 1.64/1.35
% 1.64/1.35 thf(says_type,type,
% 1.64/1.35 says: $i > $o > $o ).
% 1.64/1.35
% 1.64/1.35 thf(knights_xor_knaves,axiom,
% 1.64/1.35 ! [P: $i] :
% 1.64/1.35 ( ( knight @ P )
% 1.64/1.35 <~> ( knave @ P ) ) ).
% 1.64/1.35
% 1.64/1.35 thf(knights_tell_truth,axiom,
% 1.64/1.35 ! [P: $i,S: $o] :
% 1.64/1.35 ( ( ( knight @ P )
% 1.64/1.35 & ( says @ P @ S ) )
% 1.64/1.35 => S ) ).
% 1.64/1.35
% 1.64/1.35 thf(knaves_lie,axiom,
% 1.64/1.35 ! [P: $i,S: $o] :
% 1.64/1.35 ( ( ( knave @ P )
% 1.64/1.35 & ( says @ P @ S ) )
% 1.64/1.35 => ~ S ) ).
% 1.64/1.35
% 1.64/1.35 thf(zoey_speaks,axiom,
% 1.64/1.35 says @ zoey @ ( knave @ mel ) ).
% 1.64/1.35
% 1.64/1.35 thf(mel_speaks,axiom,
% 1.64/1.35 ( says @ mel
% 1.64/1.35 @ ( ~ ( knave @ zoey )
% 1.64/1.35 & ~ ( knave @ mel ) ) ) ).
% 1.64/1.35
% 1.64/1.35 thf(what_are_zoey_and_mel,conjecture,
% 1.64/1.35 ? [TZ: $i > $o,TM: $i > $o] :
% 1.64/1.35 ( ( ( TZ = knight )
% 1.64/1.35 | ( TZ = knave ) )
% 1.64/1.35 & ( ( TM = knight )
% 1.64/1.35 | ( TM = knave ) )
% 1.64/1.35 & ( TZ @ zoey )
% 1.64/1.35 & ( TM @ mel ) ) ).
% 1.64/1.35 ------------------------
% 1.64/1.36 % (29323)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29097 for (2999ds/2Mi)
% 1.64/1.36 % (29323)Instruction limit reached!
% 1.64/1.36 % (29323)------------------------------
% 1.64/1.36 % (29323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (29323)Termination reason: Unknown
% 1.64/1.36 % (29323)Termination phase: Saturation
% 1.64/1.36
% 1.64/1.36 % (29323)Memory used [KB]: 5500
% 1.64/1.36 % (29323)Time elapsed: 0.002 s
% 1.64/1.36 % (29323)Instructions burned: 2 (million)
% 1.64/1.36 % (29323)------------------------------
% 1.64/1.36 % (29323)------------------------------
% 1.64/1.37 % (29321)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_29097 for (2999ds/4Mi)
% 1.64/1.37 % (29320)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29097 for (2999ds/183Mi)
% 1.64/1.37 % (29322)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_29097 for (2999ds/27Mi)
% 1.64/1.37 % (29324)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_29097 for (2999ds/2Mi)
% 1.64/1.37 % (29325)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_29097 for (2999ds/275Mi)
% 1.64/1.37 % (29326)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29097 for (2999ds/18Mi)
% 1.64/1.37 % (29324)Instruction limit reached!
% 1.64/1.37 % (29324)------------------------------
% 1.64/1.37 % (29324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (29324)Termination reason: Unknown
% 1.64/1.37 % (29324)Termination phase: Unused predicate definition removal
% 1.64/1.37
% 1.64/1.37 % (29324)Memory used [KB]: 895
% 1.64/1.37 % (29324)Time elapsed: 0.003 s
% 1.64/1.37 % (29324)Instructions burned: 2 (million)
% 1.64/1.37 % (29324)------------------------------
% 1.64/1.37 % (29324)------------------------------
% 1.64/1.37 % (29325)Refutation not found, incomplete strategy
% 1.64/1.37 % (29325)------------------------------
% 1.64/1.37 % (29325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (29325)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.37
% 1.64/1.37
% 1.64/1.37 % (29325)Memory used [KB]: 5500
% 1.64/1.37 % (29325)Time elapsed: 0.004 s
% 1.64/1.37 % (29325)Instructions burned: 3 (million)
% 1.64/1.37 % (29325)------------------------------
% 1.64/1.37 % (29325)------------------------------
% 1.64/1.37 % (29320)First to succeed.
% 1.64/1.37 % (29321)Instruction limit reached!
% 1.64/1.37 % (29321)------------------------------
% 1.64/1.37 % (29321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (29321)Termination reason: Unknown
% 1.64/1.37 % (29321)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (29321)Memory used [KB]: 5500
% 1.64/1.37 % (29321)Time elapsed: 0.005 s
% 1.64/1.37 % (29321)Instructions burned: 4 (million)
% 1.64/1.37 % (29321)------------------------------
% 1.64/1.37 % (29321)------------------------------
% 1.64/1.37 % (29322)Also succeeded, but the first one will report.
% 1.64/1.37 % (29327)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29097 for (2999ds/3Mi)
% 1.64/1.38 % (29320)Refutation found. Thanks to Tanya!
% 1.64/1.38 % SZS status Theorem for DTF2THF_29097
% 1.64/1.38 % SZS output start Proof for DTF2THF_29097
% 1.64/1.38 thf(func_def_2, type, knight: $i > $o).
% 1.64/1.38 thf(func_def_3, type, knave: $i > $o).
% 1.64/1.38 thf(func_def_4, type, says: $i > $o > $o).
% 1.64/1.38 thf(f78,plain,(
% 1.64/1.38 $false),
% 1.64/1.38 inference(avatar_sat_refutation,[status(thm)],[f58,f63,f68,f69,f73,f77])).
% 1.64/1.38 thf(f77,plain,(
% 1.64/1.38 spl0_2 | spl0_3),
% 1.64/1.38 inference(avatar_contradiction_clause,[status(thm)],[f76])).
% 1.64/1.38 thf(f76,plain,(
% 1.64/1.38 $false | (spl0_2 | spl0_3)),
% 1.64/1.38 inference(subsumption_resolution,[status(thm)],[f75,f62])).
% 1.64/1.38 thf(f62,plain,(
% 1.64/1.38 ($true != (knight @ zoey)) | spl0_3),
% 1.64/1.38 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.64/1.38 thf(f60,definition,(
% 1.64/1.38 spl0_3 <=> ($true = (knight @ zoey))),
% 1.64/1.38 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.64/1.38 thf(f75,plain,(
% 1.64/1.38 ($true = (knight @ zoey)) | spl0_2),
% 1.64/1.38 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.64/1.38 thf(f74,plain,(
% 1.64/1.38 ($true = (knight @ zoey)) | ($true != $true) | spl0_2),
% 1.64/1.38 inference(superposition,[status(thm)],[f57,f48])).
% 1.64/1.38 thf(f48,plain,(
% 1.64/1.38 ( ! [X0 : $i] : (((knave @ X0) = $true) | ((knight @ X0) = $true)) )),
% 1.64/1.38 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.64/1.38 thf(f35,plain,(
% 1.64/1.38 ( ! [X0 : $i] : (((knight @ X0) != (knave @ X0))) )),
% 1.64/1.38 inference(cnf_transformation,[status(thm)],[f20])).
% 1.64/1.38 thf(f20,plain,(
% 1.64/1.38 ! [X0 : $i] : ((knight @ X0) != (knave @ X0))),
% 1.64/1.38 inference(fool_elimination,[status(thm)],[f19])).
% 1.64/1.38 thf(f19,plain,(
% 1.64/1.38 ! [X0 : $i] : ((knight @ X0) <~> (knave @ X0))),
% 1.64/1.38 inference(rectify,[status(thm)],[f1])).
% 1.64/1.38 thf(f1,axiom,(
% 1.64/1.38 ! [X0 : $i] : ((knight @ X0) <~> (knave @ X0))),
% 1.64/1.38 file('/export/starexec/sandbox2/tmp/tmp.8jub0XKdEo/DTF2THF_29097.p',knights_xor_knaves)).
% 1.64/1.38 thf(f57,plain,(
% 1.64/1.38 ((knave @ zoey) != $true) | spl0_2),
% 1.64/1.38 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.64/1.38 thf(f55,definition,(
% 1.64/1.38 spl0_2 <=> ((knave @ zoey) = $true)),
% 1.64/1.38 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.64/1.38 thf(f73,plain,(
% 1.64/1.38 spl0_1 | spl0_4),
% 1.64/1.38 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.64/1.38 thf(f72,plain,(
% 1.64/1.38 $false | (spl0_1 | spl0_4)),
% 1.64/1.38 inference(subsumption_resolution,[status(thm)],[f71,f67])).
% 1.64/1.38 thf(f67,plain,(
% 1.64/1.38 ($true != (knight @ mel)) | spl0_4),
% 1.64/1.38 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.64/1.38 thf(f65,definition,(
% 1.64/1.38 spl0_4 <=> ($true = (knight @ mel))),
% 1.64/1.38 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.64/1.38 thf(f71,plain,(
% 1.64/1.38 ($true = (knight @ mel)) | spl0_1),
% 1.64/1.38 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.64/1.38 thf(f70,plain,(
% 1.64/1.38 ($true != $true) | ($true = (knight @ mel)) | spl0_1),
% 1.64/1.38 inference(superposition,[status(thm)],[f53,f48])).
% 1.64/1.38 thf(f53,plain,(
% 1.64/1.38 ((knave @ mel) != $true) | spl0_1),
% 1.64/1.38 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.64/1.38 thf(f51,definition,(
% 1.64/1.38 spl0_1 <=> ((knave @ mel) = $true)),
% 1.64/1.38 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.64/1.38 thf(f69,plain,(
% 1.64/1.38 ~spl0_4 | ~spl0_3),
% 1.64/1.38 inference(avatar_split_clause,[status(thm)],[f42,f60,f65])).
% 1.64/1.38 thf(f42,plain,(
% 1.64/1.38 ($true != (knight @ mel)) | ($true != (knight @ zoey))),
% 1.64/1.38 inference(equality_resolution,[status(thm)],[f41])).
% 1.64/1.38 thf(f41,plain,(
% 1.64/1.38 ( ! [X0 : $i > $o] : (($true != (knight @ mel)) | (knight != X0) | ($true != (X0 @ zoey))) )),
% 1.64/1.38 inference(equality_resolution,[status(thm)],[f32])).
% 1.64/1.38 thf(f32,plain,(
% 1.64/1.38 ( ! [X0 : $i > $o,X1 : $i > $o] : (($true != (X1 @ mel)) | (knight != X1) | (knight != X0) | ($true != (X0 @ zoey))) )),
% 1.64/1.38 inference(cnf_transformation,[status(thm)],[f27])).
% 1.64/1.38 thf(f27,plain,(
% 1.64/1.38 ! [X0 : $i > $o,X1 : $i > $o] : (($true != (X1 @ mel)) | ((knight != X1) & (knave != X1)) | ((knave != X0) & (knight != X0)) | ($true != (X0 @ zoey)))),
% 1.64/1.38 inference(rectify,[status(thm)],[f22])).
% 1.64/1.38 thf(f22,plain,(
% 1.64/1.38 ! [X1 : $i > $o,X0 : $i > $o] : (((X0 @ mel) != $true) | ((knight != X0) & (knave != X0)) | ((knave != X1) & (knight != X1)) | ((X1 @ zoey) != $true))),
% 1.64/1.38 inference(ennf_transformation,[status(thm)],[f10])).
% 1.64/1.38 thf(f10,plain,(
% 1.64/1.38 ~? [X0 : $i > $o,X1 : $i > $o] : (((knight = X0) | (knave = X0)) & ((X0 @ mel) = $true) & ((X1 @ zoey) = $true) & ((knave = X1) | (knight = X1)))),
% 1.64/1.38 inference(fool_elimination,[status(thm)],[f9])).
% 1.64/1.38 thf(f9,plain,(
% 1.64/1.38 ~? [X0 : $i > $o,X1 : $i > $o] : ((X0 @ mel) & ((knight = X0) | (knave = X0)) & ((knave = X1) | (knight = X1)) & (X1 @ zoey))),
% 1.64/1.38 inference(rectify,[status(thm)],[f7])).
% 1.64/1.38 thf(f7,negated_conjecture,(
% 1.64/1.38 ~? [X3 : $i > $o,X2 : $i > $o] : ((X3 @ mel) & ((knight = X3) | (knave = X3)) & ((knave = X2) | (knight = X2)) & (X2 @ zoey))),
% 1.64/1.38 inference(negated_conjecture,[status(cth)],[f6])).
% 1.64/1.38 thf(f6,conjecture,(
% 1.64/1.38 ? [X3 : $i > $o,X2 : $i > $o] : ((X3 @ mel) & ((knight = X3) | (knave = X3)) & ((knave = X2) | (knight = X2)) & (X2 @ zoey))),
% 1.64/1.38 file('/export/starexec/sandbox2/tmp/tmp.8jub0XKdEo/DTF2THF_29097.p',what_are_zoey_and_mel)).
% 1.64/1.38 thf(f68,plain,(
% 1.64/1.38 ~spl0_2 | ~spl0_4),
% 1.64/1.38 inference(avatar_split_clause,[status(thm)],[f40,f65,f55])).
% 1.64/1.38 thf(f40,plain,(
% 1.64/1.38 ($true != (knight @ mel)) | ((knave @ zoey) != $true)),
% 1.64/1.38 inference(equality_resolution,[status(thm)],[f39])).
% 1.64/1.38 thf(f39,plain,(
% 1.64/1.38 ( ! [X0 : $i > $o] : (($true != (knight @ mel)) | (knave != X0) | ($true != (X0 @ zoey))) )),
% 1.64/1.38 inference(equality_resolution,[status(thm)],[f33])).
% 1.64/1.38 thf(f33,plain,(
% 1.64/1.38 ( ! [X0 : $i > $o,X1 : $i > $o] : (($true != (X1 @ mel)) | (knight != X1) | (knave != X0) | ($true != (X0 @ zoey))) )),
% 1.64/1.38 inference(cnf_transformation,[status(thm)],[f27])).
% 1.64/1.38 thf(f63,plain,(
% 1.64/1.38 ~spl0_3 | ~spl0_1),
% 1.64/1.38 inference(avatar_split_clause,[status(thm)],[f46,f51,f60])).
% 1.64/1.38 thf(f46,plain,(
% 1.64/1.38 ((knave @ mel) != $true) | ($true != (knight @ zoey))),
% 1.64/1.38 inference(equality_resolution,[status(thm)],[f45])).
% 1.64/1.38 thf(f45,plain,(
% 1.64/1.38 ( ! [X0 : $i > $o] : (((knave @ mel) != $true) | (knight != X0) | ($true != (X0 @ zoey))) )),
% 1.64/1.38 inference(equality_resolution,[status(thm)],[f30])).
% 1.64/1.38 thf(f30,plain,(
% 1.64/1.38 ( ! [X0 : $i > $o,X1 : $i > $o] : (($true != (X1 @ mel)) | (knave != X1) | (knight != X0) | ($true != (X0 @ zoey))) )),
% 1.64/1.38 inference(cnf_transformation,[status(thm)],[f27])).
% 1.64/1.38 thf(f58,plain,(
% 1.64/1.38 ~spl0_1 | ~spl0_2),
% 1.64/1.38 inference(avatar_split_clause,[status(thm)],[f44,f55,f51])).
% 1.64/1.38 thf(f44,plain,(
% 1.64/1.38 ((knave @ mel) != $true) | ((knave @ zoey) != $true)),
% 1.64/1.38 inference(equality_resolution,[status(thm)],[f43])).
% 1.64/1.38 thf(f43,plain,(
% 1.64/1.38 ( ! [X0 : $i > $o] : (((knave @ mel) != $true) | (knave != X0) | ($true != (X0 @ zoey))) )),
% 1.64/1.38 inference(equality_resolution,[status(thm)],[f31])).
% 1.64/1.38 thf(f31,plain,(
% 1.64/1.38 ( ! [X0 : $i > $o,X1 : $i > $o] : (($true != (X1 @ mel)) | (knave != X1) | (knave != X0) | ($true != (X0 @ zoey))) )),
% 1.64/1.38 inference(cnf_transformation,[status(thm)],[f27])).
% 1.64/1.38 % SZS output end Proof for DTF2THF_29097
% 1.64/1.38 % (29320)------------------------------
% 1.64/1.38 % (29320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (29320)Termination reason: Refutation
% 1.64/1.38
% 1.64/1.38 % (29320)Memory used [KB]: 5500
% 1.64/1.38 % (29320)Time elapsed: 0.005 s
% 1.64/1.38 % (29320)Instructions burned: 3 (million)
% 1.64/1.38 % (29320)------------------------------
% 1.64/1.38 % (29320)------------------------------
% 1.64/1.38 % (29319)Success in time 0.021 s
%------------------------------------------------------------------------------