%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PUZ081^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:36:53 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 79 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 470 ( 129 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 461 ( 120 ~; 106 |; 13 &; 216 @)
% ( 0 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 0 ^; 98 !; 8 ?; 106 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_knave,type,
knave: $i > $o ).
thf(tp_knight,type,
knight: $i > $o ).
thf(tp_mel,type,
mel: $i ).
thf(tp_says,type,
says: $i > $o > $o ).
thf(tp_zoey,type,
zoey: $i ).
thf(1,axiom,
( says @ mel
@ ( ~ ( knave @ zoey )
& ~ ( knave @ mel ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mel_speaks) ).
thf(2,axiom,
says @ zoey @ ( knave @ mel ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zoey_speaks) ).
thf(3,axiom,
! [P: $i,S: $o] :
( ( ( knave @ P )
& ( says @ P @ S ) )
=> ~ S ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_lie) ).
thf(4,axiom,
! [P: $i,S: $o] :
( ( ( knight @ P )
& ( says @ P @ S ) )
=> S ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_tell_truth) ).
thf(5,axiom,
! [P: $i] :
( ( knight @ P )
<~> ( knave @ P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_xor_knaves) ).
thf(6,conjecture,
? [Knight: $i,Knave: $i] :
( ( knight @ Knight )
& ( knave @ Knave ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',who_is_knight_and_knave) ).
thf(7,negated_conjecture,
( ( ? [Knight: $i,Knave: $i] :
( ( knight @ Knight )
& ( knave @ Knave ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ? [Knight: $i,Knave: $i] :
( ( knight @ Knight )
& ( knave @ Knave ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( says @ mel
@ ( ~ ( knave @ zoey )
& ~ ( knave @ mel ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( says @ zoey @ ( knave @ mel ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [P: $i,S: $o] :
( ( ( knave @ P )
& ( says @ P @ S ) )
=> ~ S ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [P: $i,S: $o] :
( ( ( knight @ P )
& ( says @ P @ S ) )
=> S ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [P: $i] :
( ( knight @ P )
<~> ( knave @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ~ ? [Knight: $i,Knave: $i] :
( ( knight @ Knight )
& ( knave @ Knave ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [Knave: $i] :
~ ( knave @ Knave )
| ! [Knight: $i] :
~ ( knight @ Knight ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [P: $i,S: $o] :
( ~ ( knave @ P )
| ~ ( says @ P @ S )
| ~ S ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(17,plain,
( ( ! [P: $i,S: $o] :
( ~ ( knight @ P )
| ~ ( says @ P @ S )
| S ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(18,plain,
( ( ! [P: $i] :
( ~ ( knave @ P )
| ~ ( knight @ P ) )
& ! [P: $i] :
( ( knave @ P )
| ( knight @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(19,plain,
( ( ! [P: $i] :
( ~ ( knave @ P )
| ~ ( knight @ P ) )
& ! [P: $i] :
( ( knave @ P )
| ( knight @ P ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [P: $i,S: $o] :
( ~ ( knight @ P )
| ~ ( says @ P @ S )
| S ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(21,plain,
( ( ! [P: $i,S: $o] :
( ~ ( knave @ P )
| ~ ( says @ P @ S )
| ~ S ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(22,plain,
( ( says @ zoey @ ( knave @ mel ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( says @ mel
@ ( ~ ( knave @ zoey )
& ~ ( knave @ mel ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [Knave: $i] :
~ ( knave @ Knave )
| ! [Knight: $i] :
~ ( knight @ Knight ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(25,plain,
( ( says @ mel
@ ~ ( ~ ~ ( knave @ zoey )
| ~ ~ ( knave @ mel ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( knave @ SX0 )
| ~ ( knight @ SX0 ) )
| ~ ! [SX0: $i] :
( ( knave @ SX0 )
| ( knight @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(27,plain,
! [SV1: $i] :
( ( ! [SY7: $o] :
( ~ ( knight @ SV1 )
| ~ ( says @ SV1 @ SY7 )
| SY7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV2: $i] :
( ( ! [SY8: $o] :
( ~ ( knave @ SV2 )
| ~ ( says @ SV2 @ SY8 )
| ~ SY8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
( ( ( ! [Knave: $i] :
~ ( knave @ Knave ) )
= $true )
| ( ( ! [Knight: $i] :
~ ( knight @ Knight ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ! [SX0: $i] :
( ~ ( knave @ SX0 )
| ~ ( knight @ SX0 ) )
| ~ ! [SX0: $i] :
( ( knave @ SX0 )
| ( knight @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $o,SV1: $i] :
( ( ~ ( knight @ SV1 )
| ~ ( says @ SV1 @ SV3 )
| SV3 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: $i] :
( ( ~ ( knight @ SV1 )
| ~ ( says @ SV1 @ $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV1: $i] :
( ( ~ ( knight @ SV1 )
| ~ ( says @ SV1 @ $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV4: $o,SV2: $i] :
( ( ~ ( knave @ SV2 )
| ~ ( says @ SV2 @ SV4 )
| ~ SV4 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV2: $i] :
( ( ~ ( knave @ SV2 )
| ~ ( says @ SV2 @ $true )
| ~ $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV2: $i] :
( ( ~ ( knave @ SV2 )
| ~ ( says @ SV2 @ $false )
| ~ $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV5: $i] :
( ( ( ~ ( knave @ SV5 ) )
= $true )
| ( ( ! [Knight: $i] :
~ ( knight @ Knight ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
( ( ~ ! [SX0: $i] :
( ~ ( knave @ SX0 )
| ~ ( knight @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(39,plain,
( ( ~ ! [SX0: $i] :
( ( knave @ SX0 )
| ( knight @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(40,plain,
! [SV3: $o,SV1: $i] :
( ( ( ~ ( knight @ SV1 )
| ~ ( says @ SV1 @ SV3 ) )
= $true )
| ( SV3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV1: $i] :
( ( ( ~ ( knight @ SV1 )
| ~ ( says @ SV1 @ $true ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV1: $i] :
( ( ( ~ ( knight @ SV1 )
| ~ ( says @ SV1 @ $false ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV4: $o,SV2: $i] :
( ( ( ~ ( knave @ SV2 )
| ~ ( says @ SV2 @ SV4 ) )
= $true )
| ( ( ~ SV4 ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( ~ ( knave @ SV2 )
| ~ ( says @ SV2 @ $true ) )
= $true )
| ( ( ~ $true ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(45,plain,
! [SV2: $i] :
( ( ( ~ ( knave @ SV2 )
| ~ ( says @ SV2 @ $false ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(46,plain,
! [SV5: $i] :
( ( ( knave @ SV5 )
= $false )
| ( ( ! [Knight: $i] :
~ ( knight @ Knight ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(47,plain,
( ( ! [SX0: $i] :
( ~ ( knave @ SX0 )
| ~ ( knight @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(48,plain,
( ( ! [SX0: $i] :
( ( knave @ SX0 )
| ( knight @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(49,plain,
! [SV3: $o,SV1: $i] :
( ( ( ~ ( knight @ SV1 ) )
= $true )
| ( ( ~ ( says @ SV1 @ SV3 ) )
= $true )
| ( SV3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV1: $i] :
( ( ( ~ ( knight @ SV1 ) )
= $true )
| ( ( ~ ( says @ SV1 @ $true ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV1: $i] :
( ( ( ~ ( knight @ SV1 ) )
= $true )
| ( ( ~ ( says @ SV1 @ $false ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV4: $o,SV2: $i] :
( ( ( ~ ( knave @ SV2 ) )
= $true )
| ( ( ~ ( says @ SV2 @ SV4 ) )
= $true )
| ( ( ~ SV4 ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(53,plain,
! [SV2: $i] :
( ( ( ~ ( knave @ SV2 ) )
= $true )
| ( ( ~ ( says @ SV2 @ $true ) )
= $true )
| ( ( ~ $true ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV2: $i] :
( ( ( ~ ( knave @ SV2 ) )
= $true )
| ( ( ~ ( says @ SV2 @ $false ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV5: $i,SV6: $i] :
( ( ( ~ ( knight @ SV6 ) )
= $true )
| ( ( knave @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV7: $i] :
( ( ~ ( knave @ SV7 )
| ~ ( knight @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV8: $i] :
( ( ( knave @ SV8 )
| ( knight @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV3: $o,SV1: $i] :
( ( ( knight @ SV1 )
= $false )
| ( ( ~ ( says @ SV1 @ SV3 ) )
= $true )
| ( SV3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV1: $i] :
( ( ( knight @ SV1 )
= $false )
| ( ( ~ ( says @ SV1 @ $true ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV1: $i] :
( ( ( knight @ SV1 )
= $false )
| ( ( ~ ( says @ SV1 @ $false ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV4: $o,SV2: $i] :
( ( ( knave @ SV2 )
= $false )
| ( ( ~ ( says @ SV2 @ SV4 ) )
= $true )
| ( ( ~ SV4 ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV2: $i] :
( ( ( knave @ SV2 )
= $false )
| ( ( ~ ( says @ SV2 @ $true ) )
= $true )
| ( ( ~ $true ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV2: $i] :
( ( ( knave @ SV2 )
= $false )
| ( ( ~ ( says @ SV2 @ $false ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV5: $i,SV6: $i] :
( ( ( knight @ SV6 )
= $false )
| ( ( knave @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV7: $i] :
( ( ( ~ ( knave @ SV7 ) )
= $true )
| ( ( ~ ( knight @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV8: $i] :
( ( ( knave @ SV8 )
= $true )
| ( ( knight @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV3: $o,SV1: $i] :
( ( ( says @ SV1 @ SV3 )
= $false )
| ( ( knight @ SV1 )
= $false )
| ( SV3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV1: $i] :
( ( ( says @ SV1 @ $true )
= $false )
| ( ( knight @ SV1 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV1: $i] :
( ( ( says @ SV1 @ $false )
= $false )
| ( ( knight @ SV1 )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV4: $o,SV2: $i] :
( ( ( says @ SV2 @ SV4 )
= $false )
| ( ( knave @ SV2 )
= $false )
| ( ( ~ SV4 ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV2: $i] :
( ( ( says @ SV2 @ $true )
= $false )
| ( ( knave @ SV2 )
= $false )
| ( ( ~ $true ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV2: $i] :
( ( ( says @ SV2 @ $false )
= $false )
| ( ( knave @ SV2 )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV7: $i] :
( ( ( knave @ SV7 )
= $false )
| ( ( ~ ( knight @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV2: $i,SV4: $o] :
( ( SV4 = $false )
| ( ( knave @ SV2 )
= $false )
| ( ( says @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV2: $i] :
( ( $true = $false )
| ( ( knave @ SV2 )
= $false )
| ( ( says @ SV2 @ $true )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV2: $i] :
( ( $false = $false )
| ( ( knave @ SV2 )
= $false )
| ( ( says @ SV2 @ $false )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV7: $i] :
( ( ( knight @ SV7 )
= $false )
| ( ( knave @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,77,76,75,74,69,68,67,66,64,25]) ).
thf(79,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ081^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 13:59:36 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.25
% 0.09/0.25 No.of.Axioms: 5
% 0.09/0.25
% 0.09/0.25 Length.of.Defs: 0
% 0.09/0.25
% 0.09/0.25 Contains.Choice.Funs: false
% 0.09/0.25 .
% 0.09/0.25
% 0.09/0.25 ********************************
% 0.09/0.25 * All subproblems solved! *
% 0.09/0.25 ********************************
% 0.09/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:78,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.25
% 0.09/0.25 %**** Beginning of derivation protocol ****
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25
% 0.09/0.25 %**** End of derivation protocol ****
% 0.09/0.25 %**** no. of clauses in derivation: 79 ****
% 0.09/0.25 %**** clause counter: 78 ****
% 0.09/0.25
% 0.09/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:78,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------