TSTP Solution File: PUZ001-2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : PUZ001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 18:19:14 EDT 2022
% Result : Unsatisfiable 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 93 ( 61 unt; 9 typ; 0 def)
% Number of atoms : 319 ( 120 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 311 ( 53 ~; 63 |; 0 &; 195 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 67 ( 0 ^ 67 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aunt_agatha,type,
aunt_agatha: $i ).
thf(tp_butler,type,
butler: $i ).
thf(tp_charles,type,
charles: $i ).
thf(tp_every_one_but,type,
every_one_but: $i > $i ).
thf(tp_hates,type,
hates: $i > $i > $o ).
thf(tp_killed,type,
killed: $i > $i > $o ).
thf(tp_lives_at_dreadsbury,type,
lives_at_dreadsbury: $i > $o ).
thf(tp_richer,type,
richer: $i > $i > $o ).
thf(tp_someone,type,
someone: $i ).
thf(1,axiom,
aunt_agatha != butler,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',agatha_is_not_the_butler) ).
thf(2,axiom,
! [Person: $i] :
~ ( hates @ Person @ ( every_one_but @ Person ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noone_hates_everyone) ).
thf(3,axiom,
! [Person: $i] :
( ~ ( hates @ aunt_agatha @ Person )
| ( hates @ butler @ Person ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',butler_and_agatha_hate_the_same_people) ).
thf(4,axiom,
! [Person: $i] :
( ( richer @ Person @ aunt_agatha )
| ( hates @ butler @ Person ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',butler_hates_poor_people) ).
thf(5,axiom,
! [Person: $i] :
( ( Person = butler )
| ( hates @ aunt_agatha @ Person ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',agatha_likes_only_butler) ).
thf(6,axiom,
! [Person: $i] :
( ~ ( hates @ aunt_agatha @ Person )
| ~ ( hates @ charles @ Person ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',charles_and_agatha_hate_different_people) ).
thf(7,axiom,
! [Killer: $i,Victim: $i] :
( ~ ( killed @ Killer @ Victim )
| ~ ( richer @ Killer @ Victim ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',killer_poorer_than_victim) ).
thf(8,axiom,
! [Killer: $i,Victim: $i] :
( ~ ( killed @ Killer @ Victim )
| ( hates @ Killer @ Victim ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',killer_hates_victim) ).
thf(9,axiom,
! [Person: $i] :
( ~ ( lives_at_dreadsbury @ Person )
| ( Person = aunt_agatha )
| ( Person = butler )
| ( Person = charles ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noone_else_lives_at_mansion) ).
thf(10,axiom,
lives_at_dreadsbury @ charles,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',charles_lives_at_mansion) ).
thf(11,axiom,
lives_at_dreadsbury @ butler,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',butler_lives_at_mansion) ).
thf(12,axiom,
lives_at_dreadsbury @ aunt_agatha,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',agatha_lives_at_mansion) ).
thf(13,axiom,
killed @ someone @ aunt_agatha,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',someone_killed_agatha) ).
thf(14,axiom,
lives_at_dreadsbury @ someone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',someone_in_mansion) ).
thf(15,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(16,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[15]) ).
thf(17,negated_conjecture,
~ ( killed @ aunt_agatha @ aunt_agatha ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_agatha_killed_herself) ).
thf(18,plain,
$false = $false,
inference(unfold_def,[status(thm)],[16]) ).
thf(19,plain,
( ( ( aunt_agatha != butler ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(20,plain,
( ( ! [Person: $i] :
~ ( hates @ Person @ ( every_one_but @ Person ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [Person: $i] :
( ~ ( hates @ aunt_agatha @ Person )
| ( hates @ butler @ Person ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Person: $i] :
( ( richer @ Person @ aunt_agatha )
| ( hates @ butler @ Person ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,plain,
( ( ! [Person: $i] :
( ( Person = butler )
| ( hates @ aunt_agatha @ Person ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(24,plain,
( ( ! [Person: $i] :
( ~ ( hates @ aunt_agatha @ Person )
| ~ ( hates @ charles @ Person ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(25,plain,
( ( ! [Killer: $i,Victim: $i] :
( ~ ( killed @ Killer @ Victim )
| ~ ( richer @ Killer @ Victim ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [Killer: $i,Victim: $i] :
( ~ ( killed @ Killer @ Victim )
| ( hates @ Killer @ Victim ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [Person: $i] :
( ~ ( lives_at_dreadsbury @ Person )
| ( Person = aunt_agatha )
| ( Person = butler )
| ( Person = charles ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(28,plain,
( ( lives_at_dreadsbury @ charles )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(29,plain,
( ( lives_at_dreadsbury @ butler )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(30,plain,
( ( lives_at_dreadsbury @ aunt_agatha )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(31,plain,
( ( killed @ someone @ aunt_agatha )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(32,plain,
( ( lives_at_dreadsbury @ someone )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(33,plain,
( ( ~ ( killed @ aunt_agatha @ aunt_agatha ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(34,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(35,plain,
( ( ( aunt_agatha != butler ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(36,plain,
( ( ! [Person: $i] :
( ( hates @ butler @ Person )
| ( richer @ Person @ aunt_agatha ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(37,plain,
( ( ~ ( killed @ aunt_agatha @ aunt_agatha ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(38,plain,
( ( lives_at_dreadsbury @ someone )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(39,plain,
( ( killed @ someone @ aunt_agatha )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(40,plain,
( ( lives_at_dreadsbury @ aunt_agatha )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(41,plain,
( ( lives_at_dreadsbury @ butler )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(42,plain,
( ( lives_at_dreadsbury @ charles )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( ! [Person: $i] :
( ~ ( lives_at_dreadsbury @ Person )
| ( Person = aunt_agatha )
| ( Person = butler )
| ( Person = charles ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(44,plain,
( ( ! [Killer: $i,Victim: $i] :
( ~ ( killed @ Killer @ Victim )
| ( hates @ Killer @ Victim ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(45,plain,
( ( ! [Killer: $i,Victim: $i] :
( ~ ( killed @ Killer @ Victim )
| ~ ( richer @ Killer @ Victim ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(46,plain,
( ( ! [Person: $i] :
( ~ ( hates @ aunt_agatha @ Person )
| ~ ( hates @ charles @ Person ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [Person: $i] :
( ( Person = butler )
| ( hates @ aunt_agatha @ Person ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(48,plain,
( ( ! [Person: $i] :
( ( hates @ butler @ Person )
| ( richer @ Person @ aunt_agatha ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(49,plain,
( ( ! [Person: $i] :
( ~ ( hates @ aunt_agatha @ Person )
| ( hates @ butler @ Person ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(50,plain,
( ( ! [Person: $i] :
~ ( hates @ Person @ ( every_one_but @ Person ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(51,plain,
( ( ( aunt_agatha != butler ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(52,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(53,plain,
( ( killed @ aunt_agatha @ aunt_agatha )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(54,plain,
! [SV1: $i] :
( ( ~ ( lives_at_dreadsbury @ SV1 )
| ( SV1 = aunt_agatha )
| ( SV1 = butler )
| ( SV1 = charles ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(55,plain,
! [SV2: $i] :
( ( ! [SY10: $i] :
( ~ ( killed @ SV2 @ SY10 )
| ( hates @ SV2 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(56,plain,
! [SV3: $i] :
( ( ! [SY11: $i] :
( ~ ( killed @ SV3 @ SY11 )
| ~ ( richer @ SV3 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(57,plain,
! [SV4: $i] :
( ( ~ ( hates @ aunt_agatha @ SV4 )
| ~ ( hates @ charles @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV5: $i] :
( ( ( SV5 = butler )
| ( hates @ aunt_agatha @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(59,plain,
! [SV6: $i] :
( ( ( hates @ butler @ SV6 )
| ( richer @ SV6 @ aunt_agatha ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV7: $i] :
( ( ~ ( hates @ aunt_agatha @ SV7 )
| ( hates @ butler @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(61,plain,
! [SV8: $i] :
( ( ~ ( hates @ SV8 @ ( every_one_but @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(62,plain,
( ( aunt_agatha = butler )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(63,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV1: $i] :
( ( ( ~ ( lives_at_dreadsbury @ SV1 ) )
= $true )
| ( ( ( SV1 = aunt_agatha )
| ( SV1 = butler )
| ( SV1 = charles ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ( killed @ SV2 @ SV9 )
| ( hates @ SV2 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV10: $i,SV3: $i] :
( ( ~ ( killed @ SV3 @ SV10 )
| ~ ( richer @ SV3 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV4: $i] :
( ( ( ~ ( hates @ aunt_agatha @ SV4 ) )
= $true )
| ( ( ~ ( hates @ charles @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(68,plain,
! [SV5: $i] :
( ( ( SV5 = butler )
= $true )
| ( ( hates @ aunt_agatha @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV6: $i] :
( ( ( hates @ butler @ SV6 )
= $true )
| ( ( richer @ SV6 @ aunt_agatha )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV7: $i] :
( ( ( ~ ( hates @ aunt_agatha @ SV7 ) )
= $true )
| ( ( hates @ butler @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV8: $i] :
( ( hates @ SV8 @ ( every_one_but @ SV8 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV1: $i] :
( ( ( lives_at_dreadsbury @ SV1 )
= $false )
| ( ( ( SV1 = aunt_agatha )
| ( SV1 = butler )
| ( SV1 = charles ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( killed @ SV2 @ SV9 ) )
= $true )
| ( ( hates @ SV2 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV10: $i,SV3: $i] :
( ( ( ~ ( killed @ SV3 @ SV10 ) )
= $true )
| ( ( ~ ( richer @ SV3 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV4: $i] :
( ( ( hates @ aunt_agatha @ SV4 )
= $false )
| ( ( ~ ( hates @ charles @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV7: $i] :
( ( ( hates @ aunt_agatha @ SV7 )
= $false )
| ( ( hates @ butler @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV1: $i] :
( ( ( SV1 = aunt_agatha )
= $true )
| ( ( ( SV1 = butler )
| ( SV1 = charles ) )
= $true )
| ( ( lives_at_dreadsbury @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV9: $i,SV2: $i] :
( ( ( killed @ SV2 @ SV9 )
= $false )
| ( ( hates @ SV2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV10: $i,SV3: $i] :
( ( ( killed @ SV3 @ SV10 )
= $false )
| ( ( ~ ( richer @ SV3 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV4: $i] :
( ( ( hates @ charles @ SV4 )
= $false )
| ( ( hates @ aunt_agatha @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV1: $i] :
( ( ( SV1 = butler )
= $true )
| ( ( SV1 = charles )
= $true )
| ( ( SV1 = aunt_agatha )
= $true )
| ( ( lives_at_dreadsbury @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV10: $i,SV3: $i] :
( ( ( richer @ SV3 @ SV10 )
= $false )
| ( ( killed @ SV3 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,82,81,80,78,76,71,69,68,63,62,53,42,41,40,39]) ).
thf(84,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : PUZ001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun May 29 03:04:03 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 15
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:15,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:17,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.38
% 0.19/0.38 ********************************
% 0.19/0.38 * All subproblems solved! *
% 0.19/0.38 ********************************
% 0.19/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:83,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.38
% 0.19/0.38 %**** Beginning of derivation protocol ****
% 0.19/0.38 % SZS output start CNFRefutation
% See solution above
% 0.19/0.38
% 0.19/0.38 %**** End of derivation protocol ****
% 0.19/0.38 %**** no. of clauses in derivation: 84 ****
% 0.19/0.38 %**** clause counter: 83 ****
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:83,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------