%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ081^3 : 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 : 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 : 300s
% DateTime : Wed Feb 25 09:28:26 AM UTC 2026
% Result : Theorem 1.67s 1.32s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 256 ( 66 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 218 ( 59 ~; 38 |; 11 &; 99 @)
% ( 2 <=>; 7 =>; 0 <=; 2 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 44 !; 8 ?; 52 :)
% 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(func_def_11,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f111,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f43,f82,f110]) ).
thf(f110,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f109]) ).
thf(f109,plain,
( $false
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f108,f98]) ).
thf(f98,plain,
( ! [X0: $i] :
( ( knight @ X0 )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ! [X0: $i] :
( ( ( knight @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f39,f35]) ).
thf(f35,plain,
! [X0: $i] :
( ( ( knave @ X0 )
= $true )
| ( ( knight @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: $i] :
( ( knight @ X0 )
!= ( knave @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i] :
( ( knight @ X0 )
!= ( knave @ X0 ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i] :
( ( knave @ X0 )
<~> ( knight @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( knave @ X0 )
<~> ( knight @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',knights_xor_knaves) ).
thf(f39,plain,
( ! [X1: $i] :
( $true
!= ( knave @ X1 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl0_1
<=> ! [X1: $i] :
( $true
!= ( knave @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f108,plain,
( ( $true
!= ( knight @ zoey ) )
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f77,f39]) ).
thf(f77,plain,
( ( ( knave @ mel )
= $true )
| ( $true
!= ( knight @ zoey ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $true
!= ( knight @ zoey ) )
| ( ( knave @ mel )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f31,f33]) ).
thf(f33,plain,
( ( says @ zoey @ ( knave @ mel ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( says @ zoey @ ( knave @ mel ) )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
says @ zoey @ ( knave @ mel ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
says @ zoey @ ( knave @ mel ),
file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',zoey_speaks) ).
thf(f31,plain,
! [X0: $o,X1: $i] :
( ( ( says @ X1 @ X0 )
!= $true )
| ( $true
!= ( knight @ X1 ) )
| ( $true = X0 ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: $o,X1: $i] :
( ( $true
!= ( knight @ X1 ) )
| ( $true = X0 )
| ( ( says @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $o,X0: $i] :
( ( ( knight @ X0 )
!= $true )
| ( $true = X1 )
| ( ( says @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( says @ X0 @ X1 )
!= $true )
| ( ( knight @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i,X1: $o] :
( ( ( ( says @ X0 @ X1 )
= $true )
& ( ( knight @ X0 )
= $true ) )
=> ( $true = X1 ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $o] :
( ( ( knight @ X0 )
& ( says @ X0 @ X1 ) )
=> X1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $o] :
( ( ( knight @ X0 )
& ( says @ X0 @ X1 ) )
=> X1 ),
file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',knights_tell_truth) ).
thf(f82,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f80,f42]) ).
thf(f42,plain,
( ! [X0: $i] :
( ( knight @ X0 )
!= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl0_2
<=> ! [X0: $i] :
( ( knight @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
= ( knight @ zoey ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true != $true )
| ( $true
= ( knight @ zoey ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f56,f35]) ).
thf(f56,plain,
( ( ( knave @ zoey )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true != $true )
| ( ( knave @ zoey )
!= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f34,f52]) ).
thf(f52,plain,
( ( ( says @ zoey @ $true )
= $true )
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f51,f42]) ).
thf(f51,plain,
( ( ( knight @ mel )
= $true )
| ( ( says @ zoey @ $true )
= $true ) ),
inference(superposition,[status(thm)],[f33,f35]) ).
thf(f34,plain,
! [X0: $i] :
( ( $true
!= ( says @ X0 @ $true ) )
| ( ( knave @ X0 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $i,X1: $o] :
( ( $true != X1 )
| ( ( knave @ X0 )
!= $true )
| ( ( says @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $i,X1: $o] :
( ( $true != X1 )
| ( ( knave @ X0 )
!= $true )
| ( ( says @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i,X1: $o] :
( ( $true != X1 )
| ( ( says @ X0 @ X1 )
!= $true )
| ( ( knave @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i,X1: $o] :
( ( ( ( says @ X0 @ X1 )
= $true )
& ( ( knave @ X0 )
= $true ) )
=> ( $true != X1 ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $o] :
( ( ( ( says @ X0 @ X1 )
= $true )
& ( ( knave @ X0 )
= $true ) )
=> ( $true != X1 ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
& ( knave @ X0 ) )
=> ~ X1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
& ( knave @ X0 ) )
=> ~ X1 ),
file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',knaves_lie) ).
thf(f43,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f41,f38]) ).
thf(f32,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( knave @ X1 ) )
| ( ( knight @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( knave @ X1 ) )
| ( ( knight @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ? [X0: $i,X1: $i] :
( ( $true
= ( knave @ X1 ) )
& ( ( knight @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ? [X0: $i,X1: $i] :
( ( knight @ X0 )
& ( knave @ X1 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ? [X2: $i,X3: $i] :
( ( knight @ X2 )
& ( knave @ X3 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
? [X2: $i,X3: $i] :
( ( knight @ X2 )
& ( knave @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',who_is_knight_and_knave) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ081^3 : 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
% 0.17/0.34 % Computer : n025.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 11:32:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : PUZ081^3 : TPTP v9.2.1. Released v3.6.0.
% 0.20/0.46 % Domain : Puzzles
% 0.20/0.46 % Problem : 1 of http://philosophy.hku.hk/think/logic/knight.php
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : A very special island is inhabited only by knights and knaves.
% 0.20/0.46 % Knights always tell the truth, and knaves always lie. You meet two
% 0.20/0.46 % inhabitants: Zoey and Mel. Zoey tells you that Mel is a knave. Mel
% 0.20/0.46 % says, `Neither Zoey nor I are knaves'. Who is a knight and who is
% 0.20/0.46 % a knave?
% 0.20/0.46
% 0.20/0.46 % Refs :
% 0.20/0.46 % Source : [TPTP]
% 0.20/0.46 % Names :
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.17 v6.1.0, 0.33 v5.5.0, 0.00 v5.3.0, 0.50 v5.2.0, 0.25 v5.1.0, 0.00 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 11 ( 0 unt; 5 typ; 0 def)
% 0.20/0.46 % Number of atoms : 13 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 3 ( 2 avg)
% 0.31/0.46 % Number of connectives : 27 ( 3 ~; 0 |; 4 &; 17 @)
% 0.31/0.46 % ( 0 <=>; 2 =>; 0 <=; 1 <~>)
% 0.31/0.46 % Maximal formula depth : 7 ( 5 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 5 ( 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_NEQ_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 a knight and a knave
% 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(who_is_knight_and_knave,conjecture,
% 0.31/0.46 ? [Knight: $i,Knave: $i] :
% 0.31/0.46 ( ( knight @ Knight )
% 0.31/0.46 & ( knave @ Knave ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.50/1.28 ---- Embedded in THF ---
% 1.50/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.28 %%% Generated on Tue Feb 24 11:32:43 EST 2026
% 1.50/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.28 %%% Logic specification used:
% 1.50/1.28 %%% thf(spec, logic, $$dhol).
% 1.50/1.28
% 1.50/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2DTF26500.p
% See solution above
% 1.50/1.28 ------------------------
% 1.50/1.29 ---- Cleaned THF ---
% 1.50/1.29 thf(mel_type,type,
% 1.50/1.29 mel: $i ).
% 1.50/1.29
% 1.50/1.29 thf(zoey_type,type,
% 1.50/1.29 zoey: $i ).
% 1.50/1.29
% 1.50/1.29 thf(knight_type,type,
% 1.50/1.29 knight: $i > $o ).
% 1.50/1.29
% 1.50/1.29 thf(knave_type,type,
% 1.50/1.29 knave: $i > $o ).
% 1.50/1.29
% 1.50/1.29 thf(says_type,type,
% 1.50/1.29 says: $i > $o > $o ).
% 1.50/1.29
% 1.50/1.29 thf(knights_xor_knaves,axiom,
% 1.50/1.29 ! [P: $i] :
% 1.50/1.29 ( ( knight @ P )
% 1.50/1.29 <~> ( knave @ P ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(knights_tell_truth,axiom,
% 1.50/1.29 ! [P: $i,S: $o] :
% 1.50/1.29 ( ( ( knight @ P )
% 1.50/1.29 & ( says @ P @ S ) )
% 1.50/1.29 => S ) ).
% 1.50/1.29
% 1.50/1.29 thf(knaves_lie,axiom,
% 1.50/1.29 ! [P: $i,S: $o] :
% 1.50/1.29 ( ( ( knave @ P )
% 1.50/1.29 & ( says @ P @ S ) )
% 1.50/1.29 => ~ S ) ).
% 1.50/1.29
% 1.50/1.29 thf(zoey_speaks,axiom,
% 1.50/1.29 says @ zoey @ ( knave @ mel ) ).
% 1.50/1.29
% 1.50/1.29 thf(mel_speaks,axiom,
% 1.50/1.29 ( says @ mel
% 1.50/1.29 @ ( ~ ( knave @ zoey )
% 1.50/1.29 & ~ ( knave @ mel ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf(who_is_knight_and_knave,conjecture,
% 1.50/1.29 ? [Knight: $i,Knave: $i] :
% 1.50/1.29 ( ( knight @ Knight )
% 1.50/1.29 & ( knave @ Knave ) ) ).
% 1.50/1.29 ------------------------
% 1.67/1.30 % (26832)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_26500 for (3000ds/275Mi)
% 1.67/1.30 % (26830)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26500 for (3000ds/2Mi)
% 1.67/1.30 % (26832)Refutation not found, incomplete strategy
% 1.67/1.30 % (26832)------------------------------
% 1.67/1.30 % (26832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.30 % (26832)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.30
% 1.67/1.30
% 1.67/1.30 % (26832)Memory used [KB]: 5500
% 1.67/1.30 % (26832)Time elapsed: 0.002 s
% 1.67/1.30 % (26832)Instructions burned: 2 (million)
% 1.67/1.30 % (26832)------------------------------
% 1.67/1.30 % (26832)------------------------------
% 1.67/1.30 % (26830)Instruction limit reached!
% 1.67/1.30 % (26830)------------------------------
% 1.67/1.30 % (26830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.30 % (26830)Termination reason: Unknown
% 1.67/1.30 % (26830)Termination phase: Saturation
% 1.67/1.30
% 1.67/1.30 % (26830)Memory used [KB]: 5500
% 1.67/1.30 % (26830)Time elapsed: 0.002 s
% 1.67/1.30 % (26830)Instructions burned: 2 (million)
% 1.67/1.30 % (26830)------------------------------
% 1.67/1.30 % (26830)------------------------------
% 1.67/1.31 % (26828)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_26500 for (3000ds/4Mi)
% 1.67/1.31 % (26827)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26500 for (3000ds/183Mi)
% 1.67/1.31 % (26829)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_26500 for (3000ds/27Mi)
% 1.67/1.31 % (26833)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26500 for (3000ds/18Mi)
% 1.67/1.31 % (26831)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_26500 for (3000ds/2Mi)
% 1.67/1.31 % (26831)Instruction limit reached!
% 1.67/1.31 % (26831)------------------------------
% 1.67/1.31 % (26831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (26831)Termination reason: Unknown
% 1.67/1.31 % (26831)Termination phase: Saturation
% 1.67/1.31
% 1.67/1.31 % (26831)Memory used [KB]: 1023
% 1.67/1.31 % (26831)Time elapsed: 0.003 s
% 1.67/1.31 % (26831)Instructions burned: 2 (million)
% 1.67/1.31 % (26831)------------------------------
% 1.67/1.31 % (26831)------------------------------
% 1.67/1.31 % (26828)Instruction limit reached!
% 1.67/1.31 % (26828)------------------------------
% 1.67/1.31 % (26828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (26828)Termination reason: Unknown
% 1.67/1.31 % (26828)Termination phase: Saturation
% 1.67/1.31
% 1.67/1.31 % (26828)Memory used [KB]: 5500
% 1.67/1.31 % (26828)Time elapsed: 0.005 s
% 1.67/1.31 % (26828)Instructions burned: 4 (million)
% 1.67/1.31 % (26828)------------------------------
% 1.67/1.31 % (26828)------------------------------
% 1.67/1.31 % (26835)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_26500 for (2999ds/37Mi)
% 1.67/1.31 % (26834)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26500 for (2999ds/3Mi)
% 1.67/1.32 % (26827)First to succeed.
% 1.67/1.32 % (26834)Instruction limit reached!
% 1.67/1.32 % (26834)------------------------------
% 1.67/1.32 % (26834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (26834)Termination reason: Unknown
% 1.67/1.32 % (26834)Termination phase: Saturation
% 1.67/1.32
% 1.67/1.32 % (26834)Memory used [KB]: 5500
% 1.67/1.32 % (26834)Time elapsed: 0.003 s
% 1.67/1.32 % (26834)Instructions burned: 3 (million)
% 1.67/1.32 % (26834)------------------------------
% 1.67/1.32 % (26834)------------------------------
% 1.67/1.32 % (26829)Also succeeded, but the first one will report.
% 1.67/1.32 % (26833)Also succeeded, but the first one will report.
% 1.67/1.32 % (26827)Refutation found. Thanks to Tanya!
% 1.67/1.32 % SZS status Theorem for DTF2THF_26500
% 1.67/1.32 % SZS output start Proof for DTF2THF_26500
% 1.67/1.32 thf(func_def_2, type, knight: $i > $o).
% 1.67/1.32 thf(func_def_3, type, knave: $i > $o).
% 1.67/1.32 thf(func_def_4, type, says: $i > $o > $o).
% 1.67/1.32 thf(func_def_11, type, ph1: !>[X0: $tType]:(X0)).
% 1.67/1.32 thf(f111,plain,(
% 1.67/1.32 $false),
% 1.67/1.32 inference(avatar_sat_refutation,[status(thm)],[f43,f82,f110])).
% 1.67/1.32 thf(f110,plain,(
% 1.67/1.32 ~spl0_1),
% 1.67/1.32 inference(avatar_contradiction_clause,[status(thm)],[f109])).
% 1.67/1.32 thf(f109,plain,(
% 1.67/1.32 $false | ~spl0_1),
% 1.67/1.32 inference(subsumption_resolution,[status(thm)],[f108,f98])).
% 1.67/1.32 thf(f98,plain,(
% 1.67/1.32 ( ! [X0 : $i] : (((knight @ X0) = $true)) ) | ~spl0_1),
% 1.67/1.32 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.67/1.32 thf(f94,plain,(
% 1.67/1.32 ( ! [X0 : $i] : (((knight @ X0) = $true) | ($true != $true)) ) | ~spl0_1),
% 1.67/1.32 inference(superposition,[status(thm)],[f39,f35])).
% 1.67/1.32 thf(f35,plain,(
% 1.67/1.32 ( ! [X0 : $i] : (((knave @ X0) = $true) | ((knight @ X0) = $true)) )),
% 1.67/1.32 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.67/1.32 thf(f30,plain,(
% 1.67/1.32 ( ! [X0 : $i] : (((knight @ X0) != (knave @ X0))) )),
% 1.67/1.32 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.32 thf(f18,plain,(
% 1.67/1.32 ! [X0 : $i] : ((knight @ X0) != (knave @ X0))),
% 1.67/1.32 inference(fool_elimination,[status(thm)],[f17])).
% 1.67/1.32 thf(f17,plain,(
% 1.67/1.32 ! [X0 : $i] : ((knave @ X0) <~> (knight @ X0))),
% 1.67/1.32 inference(rectify,[status(thm)],[f1])).
% 1.67/1.32 thf(f1,axiom,(
% 1.67/1.32 ! [X0 : $i] : ((knave @ X0) <~> (knight @ X0))),
% 1.67/1.32 file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',knights_xor_knaves)).
% 1.67/1.32 thf(f39,plain,(
% 1.67/1.32 ( ! [X1 : $i] : (($true != (knave @ X1))) ) | ~spl0_1),
% 1.67/1.32 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.67/1.32 thf(f38,definition,(
% 1.67/1.32 spl0_1 <=> ! [X1 : $i] : ($true != (knave @ X1))),
% 1.67/1.32 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.67/1.32 thf(f108,plain,(
% 1.67/1.32 ($true != (knight @ zoey)) | ~spl0_1),
% 1.67/1.32 inference(subsumption_resolution,[status(thm)],[f77,f39])).
% 1.67/1.32 thf(f77,plain,(
% 1.67/1.32 ((knave @ mel) = $true) | ($true != (knight @ zoey))),
% 1.67/1.32 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.67/1.32 thf(f76,plain,(
% 1.67/1.32 ($true != (knight @ zoey)) | ((knave @ mel) = $true) | ($true != $true)),
% 1.67/1.32 inference(superposition,[status(thm)],[f31,f33])).
% 1.67/1.32 thf(f33,plain,(
% 1.67/1.32 ((says @ zoey @ (knave @ mel)) = $true)),
% 1.67/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.67/1.32 thf(f10,plain,(
% 1.67/1.32 ((says @ zoey @ (knave @ mel)) = $true)),
% 1.67/1.32 inference(fool_elimination,[status(thm)],[f9])).
% 1.67/1.32 thf(f9,plain,(
% 1.67/1.32 (says @ zoey @ (knave @ mel))),
% 1.67/1.32 inference(rectify,[status(thm)],[f4])).
% 1.67/1.32 thf(f4,axiom,(
% 1.67/1.32 (says @ zoey @ (knave @ mel))),
% 1.67/1.32 file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',zoey_speaks)).
% 1.67/1.32 thf(f31,plain,(
% 1.67/1.32 ( ! [X0 : $o,X1 : $i] : (((says @ X1 @ X0) != $true) | ($true != (knight @ X1)) | ($true = X0)) )),
% 1.67/1.32 inference(cnf_transformation,[status(thm)],[f27])).
% 1.67/1.32 thf(f27,plain,(
% 1.67/1.32 ! [X0 : $o,X1 : $i] : (($true != (knight @ X1)) | ($true = X0) | ((says @ X1 @ X0) != $true))),
% 1.67/1.32 inference(rectify,[status(thm)],[f24])).
% 1.67/1.32 thf(f24,plain,(
% 1.67/1.32 ! [X1 : $o,X0 : $i] : (((knight @ X0) != $true) | ($true = X1) | ((says @ X0 @ X1) != $true))),
% 1.67/1.32 inference(flattening,[status(thm)],[f23])).
% 1.67/1.32 thf(f23,plain,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : (($true = X1) | (((says @ X0 @ X1) != $true) | ((knight @ X0) != $true)))),
% 1.67/1.32 inference(ennf_transformation,[status(thm)],[f20])).
% 1.67/1.32 thf(f20,plain,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : ((((says @ X0 @ X1) = $true) & ((knight @ X0) = $true)) => ($true = X1))),
% 1.67/1.32 inference(fool_elimination,[status(thm)],[f19])).
% 1.67/1.32 thf(f19,plain,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : (((knight @ X0) & (says @ X0 @ X1)) => X1)),
% 1.67/1.32 inference(rectify,[status(thm)],[f2])).
% 1.67/1.32 thf(f2,axiom,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : (((knight @ X0) & (says @ X0 @ X1)) => X1)),
% 1.67/1.32 file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',knights_tell_truth)).
% 1.67/1.32 thf(f82,plain,(
% 1.67/1.32 ~spl0_2),
% 1.67/1.32 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.67/1.32 thf(f81,plain,(
% 1.67/1.32 $false | ~spl0_2),
% 1.67/1.32 inference(subsumption_resolution,[status(thm)],[f80,f42])).
% 1.67/1.32 thf(f42,plain,(
% 1.67/1.32 ( ! [X0 : $i] : (((knight @ X0) != $true)) ) | ~spl0_2),
% 1.67/1.32 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.67/1.32 thf(f41,definition,(
% 1.67/1.32 spl0_2 <=> ! [X0 : $i] : ((knight @ X0) != $true)),
% 1.67/1.32 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.67/1.32 thf(f80,plain,(
% 1.67/1.32 ($true = (knight @ zoey)) | ~spl0_2),
% 1.67/1.32 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.67/1.32 thf(f79,plain,(
% 1.67/1.32 ($true != $true) | ($true = (knight @ zoey)) | ~spl0_2),
% 1.67/1.32 inference(superposition,[status(thm)],[f56,f35])).
% 1.67/1.32 thf(f56,plain,(
% 1.67/1.32 ((knave @ zoey) != $true) | ~spl0_2),
% 1.67/1.32 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.67/1.32 thf(f53,plain,(
% 1.67/1.32 ($true != $true) | ((knave @ zoey) != $true) | ~spl0_2),
% 1.67/1.32 inference(superposition,[status(thm)],[f34,f52])).
% 1.67/1.32 thf(f52,plain,(
% 1.67/1.32 ((says @ zoey @ $true) = $true) | ~spl0_2),
% 1.67/1.32 inference(subsumption_resolution,[status(thm)],[f51,f42])).
% 1.67/1.32 thf(f51,plain,(
% 1.67/1.32 ((knight @ mel) = $true) | ((says @ zoey @ $true) = $true)),
% 1.67/1.32 inference(superposition,[status(thm)],[f33,f35])).
% 1.67/1.32 thf(f34,plain,(
% 1.67/1.32 ( ! [X0 : $i] : (($true != (says @ X0 @ $true)) | ((knave @ X0) != $true)) )),
% 1.67/1.32 inference(equality_resolution,[status(thm)],[f29])).
% 1.67/1.32 thf(f29,plain,(
% 1.67/1.32 ( ! [X0 : $i,X1 : $o] : (($true != X1) | ((knave @ X0) != $true) | ((says @ X0 @ X1) != $true)) )),
% 1.67/1.32 inference(cnf_transformation,[status(thm)],[f26])).
% 1.67/1.32 thf(f26,plain,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : (($true != X1) | ((knave @ X0) != $true) | ((says @ X0 @ X1) != $true))),
% 1.67/1.32 inference(flattening,[status(thm)],[f25])).
% 1.67/1.32 thf(f25,plain,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : (($true != X1) | (((says @ X0 @ X1) != $true) | ((knave @ X0) != $true)))),
% 1.67/1.32 inference(ennf_transformation,[status(thm)],[f21])).
% 1.67/1.32 thf(f21,plain,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : ((((says @ X0 @ X1) = $true) & ((knave @ X0) = $true)) => ($true != X1))),
% 1.67/1.32 inference(flattening,[status(thm)],[f16])).
% 1.67/1.32 thf(f16,plain,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : ((((says @ X0 @ X1) = $true) & ((knave @ X0) = $true)) => ~($true = X1))),
% 1.67/1.32 inference(fool_elimination,[status(thm)],[f15])).
% 1.67/1.32 thf(f15,plain,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : (((says @ X0 @ X1) & (knave @ X0)) => ~X1)),
% 1.67/1.32 inference(rectify,[status(thm)],[f3])).
% 1.67/1.32 thf(f3,axiom,(
% 1.67/1.32 ! [X0 : $i,X1 : $o] : (((says @ X0 @ X1) & (knave @ X0)) => ~X1)),
% 1.67/1.32 file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',knaves_lie)).
% 1.67/1.32 thf(f43,plain,(
% 1.67/1.32 spl0_1 | spl0_2),
% 1.67/1.32 inference(avatar_split_clause,[status(thm)],[f32,f41,f38])).
% 1.67/1.32 thf(f32,plain,(
% 1.67/1.32 ( ! [X0 : $i,X1 : $i] : (($true != (knave @ X1)) | ((knight @ X0) != $true)) )),
% 1.67/1.32 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.32 thf(f22,plain,(
% 1.67/1.32 ! [X0 : $i,X1 : $i] : (($true != (knave @ X1)) | ((knight @ X0) != $true))),
% 1.67/1.32 inference(ennf_transformation,[status(thm)],[f14])).
% 1.67/1.32 thf(f14,plain,(
% 1.67/1.32 ~? [X0 : $i,X1 : $i] : (($true = (knave @ X1)) & ((knight @ X0) = $true))),
% 1.67/1.32 inference(fool_elimination,[status(thm)],[f13])).
% 1.67/1.32 thf(f13,plain,(
% 1.67/1.32 ~? [X0 : $i,X1 : $i] : ((knight @ X0) & (knave @ X1))),
% 1.67/1.32 inference(rectify,[status(thm)],[f7])).
% 1.67/1.32 thf(f7,negated_conjecture,(
% 1.67/1.32 ~? [X2 : $i,X3 : $i] : ((knight @ X2) & (knave @ X3))),
% 1.67/1.32 inference(negated_conjecture,[status(cth)],[f6])).
% 1.67/1.32 thf(f6,conjecture,(
% 1.67/1.32 ? [X2 : $i,X3 : $i] : ((knight @ X2) & (knave @ X3))),
% 1.67/1.32 file('/export/starexec/sandbox/tmp/tmp.jNCbbrPoyJ/DTF2THF_26500.p',who_is_knight_and_knave)).
% 1.67/1.32 % SZS output end Proof for DTF2THF_26500
% 1.67/1.32 % (26827)------------------------------
% 1.67/1.32 % (26827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (26827)Termination reason: Refutation
% 1.67/1.32
% 1.67/1.32 % (26827)Memory used [KB]: 5500
% 1.67/1.32 % (26827)Time elapsed: 0.008 s
% 1.67/1.32 % (26827)Instructions burned: 6 (million)
% 1.67/1.32 % (26827)------------------------------
% 1.67/1.32 % (26827)------------------------------
% 1.67/1.32 % (26826)Success in time 0.021 s
%------------------------------------------------------------------------------