%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ081^1 : TPTP v9.2.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 09:28:25 AM UTC 2026
% Result : Theorem 1.84s 1.53s
% Output : Refutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 74 ( 5 unt; 0 typ; 5 def)
% Number of atoms : 672 ( 169 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 500 ( 99 ~; 110 |; 19 &; 240 @)
% ( 7 <=>; 17 =>; 0 <=; 8 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 44 !; 8 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
says: $i > $o > $o ).
thf(func_def_6,type,
is_a: $i > $i > $o ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f102,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f73,f78,f79,f86,f87,f94,f96,f101]) ).
thf(f101,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f100,f65,f57]) ).
thf(f57,definition,
( spl0_1
<=> ( ( is_a @ zoey @ knave )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f65,definition,
( spl0_3
<=> ( ( is_a @ mel @ knave )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f100,plain,
( ( ( is_a @ zoey @ knave )
!= $true )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( ( is_a @ zoey @ knave )
!= $true )
| ( $true != $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f43,f97]) ).
thf(f97,plain,
( ( $true
= ( says @ zoey @ $true ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f32,f66]) ).
thf(f66,plain,
( ( ( is_a @ mel @ knave )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f32,plain,
( ( says @ zoey @ ( is_a @ mel @ knave ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( says @ zoey @ ( is_a @ mel @ knave ) )
= $true ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
says @ zoey @ ( is_a @ mel @ knave ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
says @ zoey @ ( is_a @ mel @ knave ),
file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_5) ).
thf(f43,plain,
! [X0: $i] :
( ( ( says @ X0 @ $true )
!= $true )
| ( ( is_a @ X0 @ knave )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i,X1: $o] :
( ( ( is_a @ X0 @ knave )
!= $true )
| ( $true != X1 )
| ( ( says @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knave )
!= $true )
| ! [X1: $o] :
( ( $true != X1 )
| ( ( says @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knave )
= $true )
=> ! [X1: $o] :
( ( ( says @ X0 @ X1 )
= $true )
=> ( $true != X1 ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knave )
= $true )
=> ! [X1: $o] :
( ( ( says @ X0 @ X1 )
= $true )
=> ( $true != X1 ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i] :
( ( is_a @ X0 @ knave )
=> ! [X1: $o] :
( ( says @ X0 @ X1 )
=> ~ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i] :
( ( is_a @ X0 @ knave )
=> ! [X1: $o] :
( ( says @ X0 @ X1 )
=> ~ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_3) ).
thf(f96,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f95,f61,f65,f57]) ).
thf(f61,definition,
( spl0_2
<=> ( knight = knave ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f95,plain,
( ( ( is_a @ zoey @ knave )
!= $true )
| ( ( is_a @ mel @ knave )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f81,f63]) ).
thf(f63,plain,
( ( knight = knave )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f81,plain,
( ( ( is_a @ mel @ knave )
= $true )
| ( ( is_a @ zoey @ knight )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true != $true )
| ( ( is_a @ zoey @ knight )
!= $true )
| ( ( is_a @ mel @ knave )
= $true ) ),
inference(superposition,[status(thm)],[f35,f32]) ).
thf(f35,plain,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
!= $true )
| ( ( is_a @ X0 @ knight )
!= $true )
| ( $true = X1 ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: $i] :
( ! [X1: $o] :
( ( ( says @ X0 @ X1 )
!= $true )
| ( $true = X1 ) )
| ( ( is_a @ X0 @ knight )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knight )
= $true )
=> ! [X1: $o] :
( ( ( says @ X0 @ X1 )
= $true )
=> ( $true = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( is_a @ X0 @ knight )
=> ! [X1: $o] :
( ( says @ X0 @ X1 )
=> X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i] :
( ( is_a @ X0 @ knight )
=> ! [X1: $o] :
( ( says @ X0 @ X1 )
=> X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_2) ).
thf(f94,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f93,f70,f61,f57]) ).
thf(f70,definition,
( spl0_4
<=> ( ( is_a @ zoey @ knight )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f93,plain,
( ( ( is_a @ zoey @ knave )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f71,f63]) ).
thf(f71,plain,
( ( ( is_a @ zoey @ knight )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f87,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f84,f70,f57]) ).
thf(f84,plain,
( ( ( is_a @ zoey @ knave )
= $true )
| ( ( is_a @ zoey @ knight )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ( is_a @ zoey @ knave )
= $true )
| ( $true != $true )
| ( ( is_a @ zoey @ knight )
= $true ) ),
inference(superposition,[status(thm)],[f34,f37]) ).
thf(f37,plain,
( ( is_a @ zoey @ islander )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( is_a @ mel @ islander )
= $true )
& ( ( is_a @ zoey @ islander )
= $true ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( ( is_a @ zoey @ islander )
& ( is_a @ mel @ islander ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( is_a @ zoey @ islander )
& ( is_a @ mel @ islander ) ),
file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_4) ).
thf(f34,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ islander )
!= $true )
| ( ( is_a @ X0 @ knave )
= $true )
| ( ( is_a @ X0 @ knight )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knave )
= $true )
| ( ( is_a @ X0 @ islander )
!= $true )
| ( ( is_a @ X0 @ knight )
= $true ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knight )
= $true )
| ( ( is_a @ X0 @ knave )
= $true )
| ( ( is_a @ X0 @ islander )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ islander )
= $true )
=> ( ( ( is_a @ X0 @ knight )
= $true )
| ( ( is_a @ X0 @ knave )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i] :
( ( is_a @ X0 @ islander )
=> ( ( is_a @ X0 @ knight )
| ( is_a @ X0 @ knave ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( is_a @ X0 @ islander )
=> ( ( is_a @ X0 @ knight )
| ( is_a @ X0 @ knave ) ) ),
file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_1) ).
thf(f86,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f85,f65,f75]) ).
thf(f75,definition,
( spl0_5
<=> ( ( is_a @ mel @ knight )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f85,plain,
( ( ( is_a @ mel @ knave )
= $true )
| ( ( is_a @ mel @ knight )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( ( is_a @ mel @ knight )
= $true )
| ( ( is_a @ mel @ knave )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f34,f38]) ).
thf(f38,plain,
( ( is_a @ mel @ islander )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f79,plain,
( ~ spl0_5
| spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f52,f70,f61,f75]) ).
thf(f52,plain,
( ( knight = knave )
| ( ( is_a @ mel @ knight )
!= $true )
| ( ( is_a @ zoey @ knight )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( is_a @ zoey @ knight )
!= $true )
| ( ( is_a @ mel @ knight )
!= $true )
| ( knight = knave )
| ( knight = knave ) ),
inference(equality_resolution,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i] :
( ( knight = knave )
| ( knave = X1 )
| ( knight != X1 )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( ( is_a @ zoey @ knight )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $i,X1: $i] :
( ( knave = X0 )
| ( knight != X0 )
| ( knave = X1 )
| ( knight != X1 )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( $true
!= ( is_a @ zoey @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $i,X1: $i] :
( ( ( ( knave = X0 )
| ( knight != X0 ) )
& ( ( knight = X0 )
| ( knave != X0 ) ) )
| ( ( ( knave = X1 )
| ( knight != X1 ) )
& ( ( knight = X1 )
| ( knave != X1 ) ) )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( $true
!= ( is_a @ zoey @ X0 ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i,X0: $i] :
( ( ( ( knave = X1 )
| ( knight != X1 ) )
& ( ( knight = X1 )
| ( knave != X1 ) ) )
| ( ( ( knave = X0 )
| ( knight != X0 ) )
& ( ( knight = X0 )
| ( knave != X0 ) ) )
| ( $true
!= ( is_a @ mel @ X0 ) )
| ( $true
!= ( is_a @ zoey @ X1 ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i,X0: $i] :
( ( ( knave = X1 )
<=> ( knight = X1 ) )
| ( ( knave = X0 )
<=> ( knight = X0 ) )
| ( $true
!= ( is_a @ mel @ X0 ) )
| ( $true
!= ( is_a @ zoey @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ? [X1: $i,X0: $i] :
( ( $true
= ( is_a @ mel @ X0 ) )
& ( $true
= ( is_a @ zoey @ X1 ) )
& ( ( knight = X1 )
<~> ( knave = X1 ) )
& ( ( knight = X0 )
<~> ( knave = X0 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ? [X0: $i,X1: $i] :
( ( is_a @ mel @ X0 )
& ( ( knave = X1 )
<~> ( knight = X1 ) )
& ( is_a @ zoey @ X1 )
& ( ( knave = X0 )
<~> ( knight = X0 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ? [X2: $i,X3: $i] :
( ( is_a @ mel @ X2 )
& ( ( knave = X3 )
<~> ( knight = X3 ) )
& ( is_a @ zoey @ X3 )
& ( ( knave = X2 )
<~> ( knight = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
? [X2: $i,X3: $i] :
( ( is_a @ mel @ X2 )
& ( ( knave = X3 )
<~> ( knight = X3 ) )
& ( is_a @ zoey @ X3 )
& ( ( knave = X2 )
<~> ( knight = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',query) ).
thf(f78,plain,
( ~ spl0_5
| ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f53,f61,f57,f75]) ).
thf(f53,plain,
( ( knight = knave )
| ( ( is_a @ mel @ knight )
!= $true )
| ( ( is_a @ zoey @ knave )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( is_a @ zoey @ knave )
!= $true )
| ( knight = knave )
| ( ( is_a @ mel @ knight )
!= $true )
| ( knight = knave ) ),
inference(equality_resolution,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( ( knight = knave )
| ( knave = X1 )
| ( knight != X1 )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( ( is_a @ zoey @ knave )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i,X1: $i] :
( ( knight = X0 )
| ( knave != X0 )
| ( knave = X1 )
| ( knight != X1 )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( $true
!= ( is_a @ zoey @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f73,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f54,f65,f70,f61]) ).
thf(f54,plain,
( ( knight = knave )
| ( ( is_a @ zoey @ knight )
!= $true )
| ( ( is_a @ mel @ knave )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( knight = knave )
| ( ( is_a @ zoey @ knight )
!= $true )
| ( ( is_a @ mel @ knave )
!= $true )
| ( knight = knave ) ),
inference(equality_resolution,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( ( knight = knave )
| ( knight = X1 )
| ( knave != X1 )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( ( is_a @ zoey @ knight )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i,X1: $i] :
( ( knave = X0 )
| ( knight != X0 )
| ( knight = X1 )
| ( knave != X1 )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( $true
!= ( is_a @ zoey @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ081^1 : TPTP v9.2.1. Released v3.6.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:32:17 EST 2026
% 0.20/0.35 % CPUTime :
% 0.20/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.50 ---- Original DTF file ---
% 0.29/0.50 thf(spec,logic,$$dhol).
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 % File : PUZ081^1 : TPTP v9.2.1. Released v3.6.0.
% 0.29/0.50 % Domain : Puzzles
% 0.29/0.50 % Problem : 1 of http://philosophy.hku.hk/think/logic/knight.php
% 0.29/0.50 % Version : [Ben08] axioms : Especial.
% 0.29/0.50 % English : A very special island is inhabited only by knights and knaves.
% 0.29/0.50 % Knights always tell the truth, and knaves always lie. You meet two
% 0.29/0.50 % inhabitants: Zoey and Mel. Zoey tells you that Mel is a knave. Mel
% 0.29/0.50 % says, `Neither Zoey nor I are knaves'. Who is a knight and who is
% 0.29/0.50 % a knave?
% 0.29/0.50
% 0.29/0.50 % Refs : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% 0.29/0.50 % Source : [Ben08]
% 0.29/0.50 % Names : Knights+Knaves_1b [Ben08]
% 0.29/0.50
% 0.29/0.50 % Status : Theorem
% 0.29/0.50 % 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, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.29/0.50 % Syntax : Number of formulae : 14 ( 0 unt; 7 typ; 0 def)
% 0.29/0.50 % Number of atoms : 20 ( 4 equ; 0 cnn)
% 0.29/0.50 % Maximal formula atoms : 6 ( 2 avg)
% 0.29/0.50 % Number of connectives : 47 ( 2 ~; 2 |; 4 &; 32 @)
% 0.29/0.50 % ( 0 <=>; 5 =>; 0 <=; 2 <~>)
% 0.29/0.50 % Maximal formula depth : 8 ( 6 avg)
% 0.29/0.50 % Number of types : 2 ( 0 usr)
% 0.29/0.50 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.50 % Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% 0.29/0.50 % Number of variables : 7 ( 0 ^; 5 !; 2 ?; 7 :)
% 0.29/0.50 % SPC : TH0_THM_EQU_NAR
% 0.29/0.50
% 0.29/0.50 % Comments : See http://philosophy.hku.hk/think/logic/knight.php
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 %----Type declarations
% 0.29/0.50 thf(islander,type,
% 0.29/0.50 islander: $i ).
% 0.29/0.50
% 0.29/0.50 thf(knight,type,
% 0.29/0.50 knight: $i ).
% 0.29/0.50
% 0.29/0.50 thf(knave,type,
% 0.29/0.50 knave: $i ).
% 0.29/0.50
% 0.29/0.50 thf(says,type,
% 0.29/0.50 says: $i > $o > $o ).
% 0.29/0.50
% 0.29/0.50 thf(zoey,type,
% 0.29/0.50 zoey: $i ).
% 0.29/0.50
% 0.29/0.50 thf(mel,type,
% 0.29/0.50 mel: $i ).
% 0.29/0.50
% 0.29/0.50 thf(is_a,type,
% 0.29/0.50 is_a: $i > $i > $o ).
% 0.29/0.50
% 0.29/0.50 %----A very special island is inhabited only by knights and knaves.
% 0.29/0.50 thf(kk_6_1,axiom,
% 0.29/0.50 ! [X: $i] :
% 0.29/0.50 ( ( is_a @ X @ islander )
% 0.29/0.50 => ( ( is_a @ X @ knight )
% 0.29/0.50 | ( is_a @ X @ knave ) ) ) ).
% 0.29/0.50
% 0.29/0.50 %----Knights always tell the truth
% 0.29/0.50 thf(kk_6_2,axiom,
% 0.29/0.50 ! [X: $i] :
% 0.29/0.50 ( ( is_a @ X @ knight )
% 0.29/0.50 => ! [A: $o] :
% 0.29/0.50 ( ( says @ X @ A )
% 0.29/0.50 => A ) ) ).
% 0.29/0.50
% 0.29/0.50 %----Knaves always lie
% 0.29/0.50 thf(kk_6_3,axiom,
% 0.29/0.50 ! [X: $i] :
% 0.29/0.50 ( ( is_a @ X @ knave )
% 0.29/0.50 => ! [A: $o] :
% 0.29/0.50 ( ( says @ X @ A )
% 0.29/0.50 => ~ A ) ) ).
% 0.29/0.50
% 0.29/0.50 %----Zoey and Mel are islanders
% 0.29/0.50 thf(kk_6_4,axiom,
% 0.29/0.50 ( ( is_a @ zoey @ islander )
% 0.29/0.50 & ( is_a @ mel @ islander ) ) ).
% 0.29/0.50
% 0.29/0.50 %----Zoey says Mel is a knave
% 0.29/0.50 thf(kk_6_5,axiom,
% 0.29/0.50 says @ zoey @ ( is_a @ mel @ knave ) ).
% 0.29/0.50
% 0.29/0.50 %----Mel says 'Neither Zoey nor I are knaves'
% 0.29/0.50 thf(kk_6_6,axiom,
% 0.29/0.50 ( says @ mel
% 0.29/0.50 @ ~ ( ( is_a @ zoey @ knave )
% 0.29/0.50 | ( is_a @ mel @ knave ) ) ) ).
% 0.29/0.50
% 0.29/0.50 %----Who is a knight and who is a knave?
% 0.29/0.50 thf(query,conjecture,
% 0.29/0.50 ? [Y: $i,Z: $i] :
% 0.29/0.50 ( ( ( Y = knight )
% 0.29/0.50 <~> ( Y = knave ) )
% 0.29/0.50 & ( ( Z = knight )
% 0.29/0.50 <~> ( Z = knave ) )
% 0.29/0.50 & ( is_a @ mel @ Y )
% 0.29/0.50 & ( is_a @ zoey @ Z ) ) ).
% 0.29/0.50
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 ------------------------
% 1.64/1.49 ---- Embedded in THF ---
% 1.64/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.49 %%% Generated on Tue Feb 24 11:32:18 EST 2026
% 1.64/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.49 %%% Logic specification used:
% 1.64/1.49 %%% thf(spec, logic, $$dhol).
% 1.64/1.49
% 1.64/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2DTF17085.p
% See solution above
% 1.64/1.49 ------------------------
% 1.84/1.50 ---- Cleaned THF ---
% 1.84/1.50 thf(islander,type,
% 1.84/1.50 islander: $i ).
% 1.84/1.50
% 1.84/1.50 thf(knight,type,
% 1.84/1.50 knight: $i ).
% 1.84/1.50
% 1.84/1.50 thf(knave,type,
% 1.84/1.50 knave: $i ).
% 1.84/1.50
% 1.84/1.50 thf(says,type,
% 1.84/1.50 says: $i > $o > $o ).
% 1.84/1.50
% 1.84/1.50 thf(zoey,type,
% 1.84/1.50 zoey: $i ).
% 1.84/1.50
% 1.84/1.50 thf(mel,type,
% 1.84/1.50 mel: $i ).
% 1.84/1.50
% 1.84/1.50 thf(is_a,type,
% 1.84/1.50 is_a: $i > $i > $o ).
% 1.84/1.50
% 1.84/1.50 thf(kk_6_1,axiom,
% 1.84/1.50 ! [X: $i] :
% 1.84/1.50 ( ( is_a @ X @ islander )
% 1.84/1.50 => ( ( is_a @ X @ knight )
% 1.84/1.50 | ( is_a @ X @ knave ) ) ) ).
% 1.84/1.50
% 1.84/1.50 thf(kk_6_2,axiom,
% 1.84/1.50 ! [X: $i] :
% 1.84/1.50 ( ( is_a @ X @ knight )
% 1.84/1.50 => ! [A: $o] :
% 1.84/1.50 ( ( says @ X @ A )
% 1.84/1.50 => A ) ) ).
% 1.84/1.50
% 1.84/1.50 thf(kk_6_3,axiom,
% 1.84/1.50 ! [X: $i] :
% 1.84/1.50 ( ( is_a @ X @ knave )
% 1.84/1.50 => ! [A: $o] :
% 1.84/1.50 ( ( says @ X @ A )
% 1.84/1.50 => ~ A ) ) ).
% 1.84/1.50
% 1.84/1.50 thf(kk_6_4,axiom,
% 1.84/1.50 ( ( is_a @ zoey @ islander )
% 1.84/1.50 & ( is_a @ mel @ islander ) ) ).
% 1.84/1.50
% 1.84/1.50 thf(kk_6_5,axiom,
% 1.84/1.50 says @ zoey @ ( is_a @ mel @ knave ) ).
% 1.84/1.50
% 1.84/1.50 thf(kk_6_6,axiom,
% 1.84/1.50 ( says @ mel
% 1.84/1.50 @ ~ ( ( is_a @ zoey @ knave )
% 1.84/1.50 | ( is_a @ mel @ knave ) ) ) ).
% 1.84/1.50
% 1.84/1.50 thf(query,conjecture,
% 1.84/1.50 ? [Y: $i,Z: $i] :
% 1.84/1.50 ( ( ( Y = knight )
% 1.84/1.50 <~> ( Y = knave ) )
% 1.84/1.50 & ( ( Z = knight )
% 1.84/1.50 <~> ( Z = knave ) )
% 1.84/1.50 & ( is_a @ mel @ Y )
% 1.84/1.50 & ( is_a @ zoey @ Z ) ) ).
% 1.84/1.50 ------------------------
% 1.84/1.52 % (17185)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17085 for (2999ds/2Mi)
% 1.84/1.52 % (17183)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_17085 for (2999ds/4Mi)
% 1.84/1.52 % (17182)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17085 for (2999ds/183Mi)
% 1.84/1.52 % (17184)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_17085 for (2999ds/27Mi)
% 1.84/1.52 % (17186)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_17085 for (2999ds/2Mi)
% 1.84/1.52 % (17187)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_17085 for (2999ds/275Mi)
% 1.84/1.52 % (17188)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17085 for (2999ds/18Mi)
% 1.84/1.52 % (17185)Instruction limit reached!
% 1.84/1.52 % (17185)------------------------------
% 1.84/1.52 % (17185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.52 % (17185)Termination reason: Unknown
% 1.84/1.52 % (17185)Termination phase: Saturation
% 1.84/1.52
% 1.84/1.52 % (17185)Memory used [KB]: 5500
% 1.84/1.52 % (17186)Instruction limit reached!
% 1.84/1.52 % (17186)------------------------------
% 1.84/1.52 % (17186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.52 % (17186)Termination reason: Unknown
% 1.84/1.52 % (17186)Termination phase: Saturation
% 1.84/1.52
% 1.84/1.52 % (17186)Memory used [KB]: 1023
% 1.84/1.52 % (17186)Time elapsed: 0.003 s
% 1.84/1.52 % (17186)Instructions burned: 3 (million)
% 1.84/1.52 % (17186)------------------------------
% 1.84/1.52 % (17186)------------------------------
% 1.84/1.52 % (17185)Time elapsed: 0.003 s
% 1.84/1.52 % (17185)Instructions burned: 3 (million)
% 1.84/1.52 % (17185)------------------------------
% 1.84/1.52 % (17185)------------------------------
% 1.84/1.52 % (17187)Refutation not found, incomplete strategy
% 1.84/1.52 % (17187)------------------------------
% 1.84/1.52 % (17187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.52 % (17187)Termination reason: Refutation not found, incomplete strategy
% 1.84/1.52
% 1.84/1.52
% 1.84/1.52 % (17187)Memory used [KB]: 5500
% 1.84/1.52 % (17187)Time elapsed: 0.003 s
% 1.84/1.52 % (17187)Instructions burned: 3 (million)
% 1.84/1.52 % (17183)Instruction limit reached!
% 1.84/1.52 % (17183)------------------------------
% 1.84/1.52 % (17183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.52 % (17187)------------------------------
% 1.84/1.52 % (17187)------------------------------
% 1.84/1.52 % (17183)Termination reason: Unknown
% 1.84/1.52 % (17183)Termination phase: Saturation
% 1.84/1.52
% 1.84/1.52 % (17183)Memory used [KB]: 5500
% 1.84/1.52 % (17183)Time elapsed: 0.004 s
% 1.84/1.52 % (17183)Instructions burned: 4 (million)
% 1.84/1.52 % (17183)------------------------------
% 1.84/1.52 % (17183)------------------------------
% 1.84/1.53 % (17184)First to succeed.
% 1.84/1.53 % (17182)Also succeeded, but the first one will report.
% 1.84/1.53 % (17184)Refutation found. Thanks to Tanya!
% 1.84/1.53 % SZS status Theorem for DTF2THF_17085
% 1.84/1.53 % SZS output start Proof for DTF2THF_17085
% 1.84/1.53 thf(func_def_3, type, says: $i > $o > $o).
% 1.84/1.53 thf(func_def_6, type, is_a: $i > $i > $o).
% 1.84/1.53 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.84/1.53 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 1.84/1.53 thf(f102,plain,(
% 1.84/1.53 $false),
% 1.84/1.53 inference(avatar_sat_refutation,[status(thm)],[f73,f78,f79,f86,f87,f94,f96,f101])).
% 1.84/1.53 thf(f101,plain,(
% 1.84/1.53 ~spl0_1 | ~spl0_3),
% 1.84/1.53 inference(avatar_split_clause,[status(thm)],[f100,f65,f57])).
% 1.84/1.53 thf(f57,definition,(
% 1.84/1.53 spl0_1 <=> ((is_a @ zoey @ knave) = $true)),
% 1.84/1.53 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.84/1.53 thf(f65,definition,(
% 1.84/1.53 spl0_3 <=> ((is_a @ mel @ knave) = $true)),
% 1.84/1.53 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.84/1.53 thf(f100,plain,(
% 1.84/1.53 ((is_a @ zoey @ knave) != $true) | ~spl0_3),
% 1.84/1.53 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.84/1.53 thf(f99,plain,(
% 1.84/1.53 ((is_a @ zoey @ knave) != $true) | ($true != $true) | ~spl0_3),
% 1.84/1.53 inference(superposition,[status(thm)],[f43,f97])).
% 1.84/1.53 thf(f97,plain,(
% 1.84/1.53 ($true = (says @ zoey @ $true)) | ~spl0_3),
% 1.84/1.53 inference(backward_demodulation,[status(thm)],[f32,f66])).
% 1.84/1.53 thf(f66,plain,(
% 1.84/1.53 ((is_a @ mel @ knave) = $true) | ~spl0_3),
% 1.84/1.53 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.84/1.53 thf(f32,plain,(
% 1.84/1.53 ((says @ zoey @ (is_a @ mel @ knave)) = $true)),
% 1.84/1.53 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.53 thf(f19,plain,(
% 1.84/1.53 ((says @ zoey @ (is_a @ mel @ knave)) = $true)),
% 1.84/1.53 inference(fool_elimination,[status(thm)],[f18])).
% 1.84/1.53 thf(f18,plain,(
% 1.84/1.53 (says @ zoey @ (is_a @ mel @ knave))),
% 1.84/1.53 inference(rectify,[status(thm)],[f5])).
% 1.84/1.53 thf(f5,axiom,(
% 1.84/1.53 (says @ zoey @ (is_a @ mel @ knave))),
% 1.84/1.53 file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_5)).
% 1.84/1.53 thf(f43,plain,(
% 1.84/1.53 ( ! [X0 : $i] : (((says @ X0 @ $true) != $true) | ((is_a @ X0 @ knave) != $true)) )),
% 1.84/1.53 inference(equality_resolution,[status(thm)],[f36])).
% 1.84/1.53 thf(f36,plain,(
% 1.84/1.53 ( ! [X0 : $i,X1 : $o] : (((is_a @ X0 @ knave) != $true) | ($true != X1) | ((says @ X0 @ X1) != $true)) )),
% 1.84/1.53 inference(cnf_transformation,[status(thm)],[f25])).
% 1.84/1.53 thf(f25,plain,(
% 1.84/1.53 ! [X0 : $i] : (((is_a @ X0 @ knave) != $true) | ! [X1 : $o] : (($true != X1) | ((says @ X0 @ X1) != $true)))),
% 1.84/1.53 inference(ennf_transformation,[status(thm)],[f24])).
% 1.84/1.53 thf(f24,plain,(
% 1.84/1.53 ! [X0 : $i] : (((is_a @ X0 @ knave) = $true) => ! [X1 : $o] : (((says @ X0 @ X1) = $true) => ($true != X1)))),
% 1.84/1.53 inference(flattening,[status(thm)],[f17])).
% 1.84/1.53 thf(f17,plain,(
% 1.84/1.53 ! [X0 : $i] : (((is_a @ X0 @ knave) = $true) => ! [X1 : $o] : (((says @ X0 @ X1) = $true) => ~($true = X1)))),
% 1.84/1.53 inference(fool_elimination,[status(thm)],[f16])).
% 1.84/1.53 thf(f16,plain,(
% 1.84/1.53 ! [X0 : $i] : ((is_a @ X0 @ knave) => ! [X1 : $o] : ((says @ X0 @ X1) => ~X1))),
% 1.84/1.53 inference(rectify,[status(thm)],[f3])).
% 1.84/1.53 thf(f3,axiom,(
% 1.84/1.53 ! [X0 : $i] : ((is_a @ X0 @ knave) => ! [X1 : $o] : ((says @ X0 @ X1) => ~X1))),
% 1.84/1.53 file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_3)).
% 1.84/1.53 thf(f96,plain,(
% 1.84/1.53 ~spl0_1 | spl0_3 | ~spl0_2),
% 1.84/1.53 inference(avatar_split_clause,[status(thm)],[f95,f61,f65,f57])).
% 1.84/1.53 thf(f61,definition,(
% 1.84/1.53 spl0_2 <=> (knight = knave)),
% 1.84/1.53 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.84/1.53 thf(f95,plain,(
% 1.84/1.53 ((is_a @ zoey @ knave) != $true) | ((is_a @ mel @ knave) = $true) | ~spl0_2),
% 1.84/1.53 inference(forward_demodulation,[status(thm)],[f81,f63])).
% 1.84/1.53 thf(f63,plain,(
% 1.84/1.53 (knight = knave) | ~spl0_2),
% 1.84/1.53 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.84/1.53 thf(f81,plain,(
% 1.84/1.53 ((is_a @ mel @ knave) = $true) | ((is_a @ zoey @ knight) != $true)),
% 1.84/1.53 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.84/1.53 thf(f80,plain,(
% 1.84/1.53 ($true != $true) | ((is_a @ zoey @ knight) != $true) | ((is_a @ mel @ knave) = $true)),
% 1.84/1.53 inference(superposition,[status(thm)],[f35,f32])).
% 1.84/1.53 thf(f35,plain,(
% 1.84/1.53 ( ! [X0 : $i,X1 : $o] : (((says @ X0 @ X1) != $true) | ((is_a @ X0 @ knight) != $true) | ($true = X1)) )),
% 1.84/1.53 inference(cnf_transformation,[status(thm)],[f27])).
% 1.84/1.53 thf(f27,plain,(
% 1.84/1.53 ! [X0 : $i] : (! [X1 : $o] : (((says @ X0 @ X1) != $true) | ($true = X1)) | ((is_a @ X0 @ knight) != $true))),
% 1.84/1.53 inference(ennf_transformation,[status(thm)],[f15])).
% 1.84/1.53 thf(f15,plain,(
% 1.84/1.53 ! [X0 : $i] : (((is_a @ X0 @ knight) = $true) => ! [X1 : $o] : (((says @ X0 @ X1) = $true) => ($true = X1)))),
% 1.84/1.53 inference(fool_elimination,[status(thm)],[f14])).
% 1.84/1.53 thf(f14,plain,(
% 1.84/1.53 ! [X0 : $i] : ((is_a @ X0 @ knight) => ! [X1 : $o] : ((says @ X0 @ X1) => X1))),
% 1.84/1.53 inference(rectify,[status(thm)],[f2])).
% 1.84/1.53 thf(f2,axiom,(
% 1.84/1.53 ! [X0 : $i] : ((is_a @ X0 @ knight) => ! [X1 : $o] : ((says @ X0 @ X1) => X1))),
% 1.84/1.53 file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_2)).
% 1.84/1.53 thf(f94,plain,(
% 1.84/1.53 spl0_1 | ~spl0_2 | ~spl0_4),
% 1.84/1.53 inference(avatar_split_clause,[status(thm)],[f93,f70,f61,f57])).
% 1.84/1.53 thf(f70,definition,(
% 1.84/1.53 spl0_4 <=> ((is_a @ zoey @ knight) = $true)),
% 1.84/1.53 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.84/1.53 thf(f93,plain,(
% 1.84/1.53 ((is_a @ zoey @ knave) = $true) | (~spl0_2 | ~spl0_4)),
% 1.84/1.53 inference(forward_demodulation,[status(thm)],[f71,f63])).
% 1.84/1.53 thf(f71,plain,(
% 1.84/1.53 ((is_a @ zoey @ knight) = $true) | ~spl0_4),
% 1.84/1.53 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.84/1.53 thf(f87,plain,(
% 1.84/1.53 spl0_1 | spl0_4),
% 1.84/1.53 inference(avatar_split_clause,[status(thm)],[f84,f70,f57])).
% 1.84/1.53 thf(f84,plain,(
% 1.84/1.53 ((is_a @ zoey @ knave) = $true) | ((is_a @ zoey @ knight) = $true)),
% 1.84/1.53 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.84/1.53 thf(f82,plain,(
% 1.84/1.53 ((is_a @ zoey @ knave) = $true) | ($true != $true) | ((is_a @ zoey @ knight) = $true)),
% 1.84/1.53 inference(superposition,[status(thm)],[f34,f37])).
% 1.84/1.53 thf(f37,plain,(
% 1.84/1.53 ((is_a @ zoey @ islander) = $true)),
% 1.84/1.53 inference(cnf_transformation,[status(thm)],[f21])).
% 1.84/1.53 thf(f21,plain,(
% 1.84/1.53 ((is_a @ mel @ islander) = $true) & ((is_a @ zoey @ islander) = $true)),
% 1.84/1.53 inference(fool_elimination,[status(thm)],[f20])).
% 1.84/1.53 thf(f20,plain,(
% 1.84/1.53 (is_a @ zoey @ islander) & (is_a @ mel @ islander)),
% 1.84/1.53 inference(rectify,[status(thm)],[f4])).
% 1.84/1.53 thf(f4,axiom,(
% 1.84/1.53 (is_a @ zoey @ islander) & (is_a @ mel @ islander)),
% 1.84/1.53 file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_4)).
% 1.84/1.53 thf(f34,plain,(
% 1.84/1.53 ( ! [X0 : $i] : (((is_a @ X0 @ islander) != $true) | ((is_a @ X0 @ knave) = $true) | ((is_a @ X0 @ knight) = $true)) )),
% 1.84/1.53 inference(cnf_transformation,[status(thm)],[f29])).
% 1.84/1.53 thf(f29,plain,(
% 1.84/1.53 ! [X0 : $i] : (((is_a @ X0 @ knave) = $true) | ((is_a @ X0 @ islander) != $true) | ((is_a @ X0 @ knight) = $true))),
% 1.84/1.53 inference(flattening,[status(thm)],[f28])).
% 1.84/1.53 thf(f28,plain,(
% 1.84/1.53 ! [X0 : $i] : ((((is_a @ X0 @ knight) = $true) | ((is_a @ X0 @ knave) = $true)) | ((is_a @ X0 @ islander) != $true))),
% 1.84/1.53 inference(ennf_transformation,[status(thm)],[f23])).
% 1.84/1.53 thf(f23,plain,(
% 1.84/1.53 ! [X0 : $i] : (((is_a @ X0 @ islander) = $true) => (((is_a @ X0 @ knight) = $true) | ((is_a @ X0 @ knave) = $true)))),
% 1.84/1.53 inference(fool_elimination,[status(thm)],[f22])).
% 1.84/1.53 thf(f22,plain,(
% 1.84/1.53 ! [X0 : $i] : ((is_a @ X0 @ islander) => ((is_a @ X0 @ knight) | (is_a @ X0 @ knave)))),
% 1.84/1.53 inference(rectify,[status(thm)],[f1])).
% 1.84/1.53 thf(f1,axiom,(
% 1.84/1.53 ! [X0 : $i] : ((is_a @ X0 @ islander) => ((is_a @ X0 @ knight) | (is_a @ X0 @ knave)))),
% 1.84/1.53 file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',kk_6_1)).
% 1.84/1.53 thf(f86,plain,(
% 1.84/1.53 spl0_5 | spl0_3),
% 1.84/1.53 inference(avatar_split_clause,[status(thm)],[f85,f65,f75])).
% 1.84/1.53 thf(f75,definition,(
% 1.84/1.53 spl0_5 <=> ((is_a @ mel @ knight) = $true)),
% 1.84/1.53 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.84/1.53 thf(f85,plain,(
% 1.84/1.53 ((is_a @ mel @ knave) = $true) | ((is_a @ mel @ knight) = $true)),
% 1.84/1.53 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.84/1.53 thf(f83,plain,(
% 1.84/1.53 ((is_a @ mel @ knight) = $true) | ((is_a @ mel @ knave) = $true) | ($true != $true)),
% 1.84/1.53 inference(superposition,[status(thm)],[f34,f38])).
% 1.84/1.53 thf(f38,plain,(
% 1.84/1.53 ((is_a @ mel @ islander) = $true)),
% 1.84/1.53 inference(cnf_transformation,[status(thm)],[f21])).
% 1.84/1.53 thf(f79,plain,(
% 1.84/1.53 ~spl0_5 | spl0_2 | ~spl0_4),
% 1.84/1.53 inference(avatar_split_clause,[status(thm)],[f52,f70,f61,f75])).
% 1.84/1.53 thf(f52,plain,(
% 1.84/1.53 (knight = knave) | ((is_a @ mel @ knight) != $true) | ((is_a @ zoey @ knight) != $true)),
% 1.84/1.53 inference(duplicate_literal_removal,[status(thm)],[f45])).
% 1.84/1.53 thf(f45,plain,(
% 1.84/1.53 ((is_a @ zoey @ knight) != $true) | ((is_a @ mel @ knight) != $true) | (knight = knave) | (knight = knave)),
% 1.84/1.53 inference(equality_resolution,[status(thm)],[f44])).
% 1.84/1.53 thf(f44,plain,(
% 1.84/1.53 ( ! [X1 : $i] : ((knight = knave) | (knave = X1) | (knight != X1) | ($true != (is_a @ mel @ X1)) | ((is_a @ zoey @ knight) != $true)) )),
% 1.84/1.53 inference(equality_resolution,[status(thm)],[f42])).
% 1.84/1.53 thf(f42,plain,(
% 1.84/1.53 ( ! [X0 : $i,X1 : $i] : ((knave = X0) | (knight != X0) | (knave = X1) | (knight != X1) | ($true != (is_a @ mel @ X1)) | ($true != (is_a @ zoey @ X0))) )),
% 1.84/1.53 inference(cnf_transformation,[status(thm)],[f31])).
% 1.84/1.53 thf(f31,plain,(
% 1.84/1.53 ! [X0 : $i,X1 : $i] : ((((knave = X0) | (knight != X0)) & ((knight = X0) | (knave != X0))) | (((knave = X1) | (knight != X1)) & ((knight = X1) | (knave != X1))) | ($true != (is_a @ mel @ X1)) | ($true != (is_a @ zoey @ X0)))),
% 1.84/1.53 inference(rectify,[status(thm)],[f30])).
% 1.84/1.53 thf(f30,plain,(
% 1.84/1.53 ! [X1 : $i,X0 : $i] : ((((knave = X1) | (knight != X1)) & ((knight = X1) | (knave != X1))) | (((knave = X0) | (knight != X0)) & ((knight = X0) | (knave != X0))) | ($true != (is_a @ mel @ X0)) | ($true != (is_a @ zoey @ X1)))),
% 1.84/1.53 inference(nnf_transformation,[status(thm)],[f26])).
% 1.84/1.53 thf(f26,plain,(
% 1.84/1.53 ! [X1 : $i,X0 : $i] : (((knave = X1) <=> (knight = X1)) | ((knave = X0) <=> (knight = X0)) | ($true != (is_a @ mel @ X0)) | ($true != (is_a @ zoey @ X1)))),
% 1.84/1.53 inference(ennf_transformation,[status(thm)],[f11])).
% 1.84/1.53 thf(f11,plain,(
% 1.84/1.53 ~? [X1 : $i,X0 : $i] : (($true = (is_a @ mel @ X0)) & ($true = (is_a @ zoey @ X1)) & ((knight = X1) <~> (knave = X1)) & ((knight = X0) <~> (knave = X0)))),
% 1.84/1.53 inference(fool_elimination,[status(thm)],[f10])).
% 1.84/1.53 thf(f10,plain,(
% 1.84/1.53 ~? [X0 : $i,X1 : $i] : ((is_a @ mel @ X0) & ((knave = X1) <~> (knight = X1)) & (is_a @ zoey @ X1) & ((knave = X0) <~> (knight = X0)))),
% 1.84/1.53 inference(rectify,[status(thm)],[f8])).
% 1.84/1.53 thf(f8,negated_conjecture,(
% 1.84/1.53 ~? [X2 : $i,X3 : $i] : ((is_a @ mel @ X2) & ((knave = X3) <~> (knight = X3)) & (is_a @ zoey @ X3) & ((knave = X2) <~> (knight = X2)))),
% 1.84/1.53 inference(negated_conjecture,[status(cth)],[f7])).
% 1.84/1.53 thf(f7,conjecture,(
% 1.84/1.53 ? [X2 : $i,X3 : $i] : ((is_a @ mel @ X2) & ((knave = X3) <~> (knight = X3)) & (is_a @ zoey @ X3) & ((knave = X2) <~> (knight = X2)))),
% 1.84/1.53 file('/export/starexec/sandbox/tmp/tmp.scXivEwtk7/DTF2THF_17085.p',query)).
% 1.84/1.53 thf(f78,plain,(
% 1.84/1.53 ~spl0_5 | ~spl0_1 | spl0_2),
% 1.84/1.53 inference(avatar_split_clause,[status(thm)],[f53,f61,f57,f75])).
% 1.84/1.53 thf(f53,plain,(
% 1.84/1.53 (knight = knave) | ((is_a @ mel @ knight) != $true) | ((is_a @ zoey @ knave) != $true)),
% 1.84/1.53 inference(duplicate_literal_removal,[status(thm)],[f49])).
% 1.84/1.53 thf(f49,plain,(
% 1.84/1.53 ((is_a @ zoey @ knave) != $true) | (knight = knave) | ((is_a @ mel @ knight) != $true) | (knight = knave)),
% 1.84/1.53 inference(equality_resolution,[status(thm)],[f48])).
% 1.84/1.53 thf(f48,plain,(
% 1.84/1.53 ( ! [X1 : $i] : ((knight = knave) | (knave = X1) | (knight != X1) | ($true != (is_a @ mel @ X1)) | ((is_a @ zoey @ knave) != $true)) )),
% 1.84/1.53 inference(equality_resolution,[status(thm)],[f40])).
% 1.84/1.53 thf(f40,plain,(
% 1.84/1.53 ( ! [X0 : $i,X1 : $i] : ((knight = X0) | (knave != X0) | (knave = X1) | (knight != X1) | ($true != (is_a @ mel @ X1)) | ($true != (is_a @ zoey @ X0))) )),
% 1.84/1.53 inference(cnf_transformation,[status(thm)],[f31])).
% 1.84/1.53 thf(f73,plain,(
% 1.84/1.53 spl0_2 | ~spl0_4 | ~spl0_3),
% 1.84/1.53 inference(avatar_split_clause,[status(thm)],[f54,f65,f70,f61])).
% 1.84/1.53 thf(f54,plain,(
% 1.84/1.53 (knight = knave) | ((is_a @ zoey @ knight) != $true) | ((is_a @ mel @ knave) != $true)),
% 1.84/1.53 inference(duplicate_literal_removal,[status(thm)],[f47])).
% 1.84/1.53 thf(f47,plain,(
% 1.84/1.53 (knight = knave) | ((is_a @ zoey @ knight) != $true) | ((is_a @ mel @ knave) != $true) | (knight = knave)),
% 1.84/1.53 inference(equality_resolution,[status(thm)],[f46])).
% 1.84/1.53 thf(f46,plain,(
% 1.84/1.53 ( ! [X1 : $i] : ((knight = knave) | (knight = X1) | (knave != X1) | ($true != (is_a @ mel @ X1)) | ((is_a @ zoey @ knight) != $true)) )),
% 1.84/1.53 inference(equality_resolution,[status(thm)],[f41])).
% 1.84/1.53 thf(f41,plain,(
% 1.84/1.53 ( ! [X0 : $i,X1 : $i] : ((knave = X0) | (knight != X0) | (knight = X1) | (knave != X1) | ($true != (is_a @ mel @ X1)) | ($true != (is_a @ zoey @ X0))) )),
% 1.84/1.53 inference(cnf_transformation,[status(thm)],[f31])).
% 1.84/1.53 % SZS output end Proof for DTF2THF_17085
% 1.84/1.53 % (17184)------------------------------
% 1.84/1.53 % (17184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.53 % (17184)Termination reason: Refutation
% 1.84/1.53
% 1.84/1.53 % (17184)Memory used [KB]: 5500
% 1.84/1.53 % (17184)Time elapsed: 0.007 s
% 1.84/1.53 % (17184)Instructions burned: 5 (million)
% 1.84/1.53 % (17184)------------------------------
% 1.84/1.53 % (17184)------------------------------
% 1.84/1.53 % (17181)Success in time 0.021 s
%------------------------------------------------------------------------------