TSTP Solution File: PUZ132+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : PUZ132+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 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 : 600s
% DateTime : Mon Jul 18 18:19:40 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 96 ( 64 unt; 11 typ; 0 def)
% Number of atoms : 310 ( 93 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 230 ( 32 ~; 36 |; 3 &; 151 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 50 ( 0 ^ 44 !; 6 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_beautiful,type,
beautiful: $i > $o ).
thf(tp_capital,type,
capital: $i > $o ).
thf(tp_capital_city,type,
capital_city: $i > $i ).
thf(tp_city,type,
city: $i > $o ).
thf(tp_country,type,
country: $i > $o ).
thf(tp_has_crime,type,
has_crime: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_A,type,
sK2_A: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_usa,type,
usa: $i ).
thf(tp_washington,type,
washington: $i ).
thf(1,axiom,
! [X: $i] :
( ( country @ X )
=> ( beautiful @ ( capital_city @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beautiful_capital_axiom) ).
thf(2,axiom,
( ( capital_city @ usa )
= washington ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',usa_capital_axiom) ).
thf(3,axiom,
! [X: $i] :
( ( city @ X )
=> ( has_crime @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crime_axiom) ).
thf(4,axiom,
! [A: $i] :
( ( country @ A )
=> ( capital @ ( capital_city @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',country_capital_type) ).
thf(5,axiom,
country @ usa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',usa_type) ).
thf(6,axiom,
capital @ washington,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',washington_type) ).
thf(7,axiom,
? [A: $i] : ( country @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',country_type) ).
thf(8,axiom,
! [A: $i] :
( ( capital @ A )
=> ( city @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',capital_city_type) ).
thf(9,axiom,
? [A: $i] : ( city @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',city_type) ).
thf(10,axiom,
? [A: $i] : ( capital @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',capital_type) ).
thf(11,conjecture,
( ( beautiful @ washington )
& ( has_crime @ washington ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',washington_conjecture) ).
thf(12,negated_conjecture,
( ( ( beautiful @ washington )
& ( has_crime @ washington ) )
= $false ),
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,plain,
( ( ( beautiful @ washington )
& ( has_crime @ washington ) )
= $false ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [X: $i] :
( ( country @ X )
=> ( beautiful @ ( capital_city @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ( capital_city @ usa )
= washington )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( city @ X )
=> ( has_crime @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( country @ A )
=> ( capital @ ( capital_city @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( country @ usa )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( capital @ washington )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( ? [A: $i] : ( country @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( capital @ A )
=> ( city @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ? [A: $i] : ( city @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ? [A: $i] : ( capital @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( beautiful @ washington )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[13]) ).
thf(25,plain,
( ( has_crime @ washington )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[13]) ).
thf(26,plain,
( ( ~ ( beautiful @ washington ) )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( has_crime @ washington ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(28,plain,
( ( ! [X: $i] :
( ~ ( country @ X )
| ( beautiful @ ( capital_city @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(29,plain,
( ( ! [X: $i] :
( ~ ( city @ X )
| ( has_crime @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(30,plain,
( ( ! [A: $i] :
( ~ ( country @ A )
| ( capital @ ( capital_city @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(31,plain,
( ( country @ sK1_A )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(32,plain,
( ( ! [A: $i] :
( ~ ( capital @ A )
| ( city @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(33,plain,
( ( city @ sK2_A )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(34,plain,
( ( capital @ sK3_A )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(35,plain,
( ( capital @ sK3_A )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(36,plain,
( ( city @ sK2_A )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(37,plain,
( ( ! [A: $i] :
( ~ ( capital @ A )
| ( city @ A ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(38,plain,
( ( country @ sK1_A )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(39,plain,
( ( capital @ washington )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(40,plain,
( ( country @ usa )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(41,plain,
( ( ! [A: $i] :
( ~ ( country @ A )
| ( capital @ ( capital_city @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(42,plain,
( ( ! [X: $i] :
( ~ ( city @ X )
| ( has_crime @ X ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(43,plain,
( ( ( capital_city @ usa )
= washington )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(44,plain,
( ( ! [X: $i] :
( ~ ( country @ X )
| ( beautiful @ ( capital_city @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(45,plain,
( ( ~ ( beautiful @ washington ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(46,plain,
! [SV1: $i] :
( ( ~ ( capital @ SV1 )
| ( city @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(47,plain,
! [SV2: $i] :
( ( ~ ( country @ SV2 )
| ( capital @ ( capital_city @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV3: $i] :
( ( ~ ( city @ SV3 )
| ( has_crime @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV4: $i] :
( ( ~ ( country @ SV4 )
| ( beautiful @ ( capital_city @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
( ( beautiful @ washington )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV1: $i] :
( ( ( ~ ( capital @ SV1 ) )
= $true )
| ( ( city @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV2: $i] :
( ( ( ~ ( country @ SV2 ) )
= $true )
| ( ( capital @ ( capital_city @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV3: $i] :
( ( ( ~ ( city @ SV3 ) )
= $true )
| ( ( has_crime @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV4: $i] :
( ( ( ~ ( country @ SV4 ) )
= $true )
| ( ( beautiful @ ( capital_city @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV1: $i] :
( ( ( capital @ SV1 )
= $false )
| ( ( city @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( country @ SV2 )
= $false )
| ( ( capital @ ( capital_city @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV3: $i] :
( ( ( city @ SV3 )
= $false )
| ( ( has_crime @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV4: $i] :
( ( ( country @ SV4 )
= $false )
| ( ( beautiful @ ( capital_city @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,58,57,56,55,50,43,40,39,38,36]) ).
thf(60,plain,
( ( capital @ sK3_A )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(61,plain,
( ( city @ sK2_A )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(62,plain,
( ( ! [A: $i] :
( ~ ( capital @ A )
| ( city @ A ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(63,plain,
( ( country @ sK1_A )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(64,plain,
( ( capital @ washington )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(65,plain,
( ( country @ usa )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(66,plain,
( ( ! [A: $i] :
( ~ ( country @ A )
| ( capital @ ( capital_city @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(67,plain,
( ( ! [X: $i] :
( ~ ( city @ X )
| ( has_crime @ X ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(68,plain,
( ( ( capital_city @ usa )
= washington )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(69,plain,
( ( ! [X: $i] :
( ~ ( country @ X )
| ( beautiful @ ( capital_city @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(70,plain,
( ( ~ ( has_crime @ washington ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(71,plain,
! [SV5: $i] :
( ( ~ ( capital @ SV5 )
| ( city @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV6: $i] :
( ( ~ ( country @ SV6 )
| ( capital @ ( capital_city @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV7: $i] :
( ( ~ ( city @ SV7 )
| ( has_crime @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV8: $i] :
( ( ~ ( country @ SV8 )
| ( beautiful @ ( capital_city @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(75,plain,
( ( has_crime @ washington )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV5: $i] :
( ( ( ~ ( capital @ SV5 ) )
= $true )
| ( ( city @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV6: $i] :
( ( ( ~ ( country @ SV6 ) )
= $true )
| ( ( capital @ ( capital_city @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV7: $i] :
( ( ( ~ ( city @ SV7 ) )
= $true )
| ( ( has_crime @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV8: $i] :
( ( ( ~ ( country @ SV8 ) )
= $true )
| ( ( beautiful @ ( capital_city @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV5: $i] :
( ( ( capital @ SV5 )
= $false )
| ( ( city @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV6: $i] :
( ( ( country @ SV6 )
= $false )
| ( ( capital @ ( capital_city @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV7: $i] :
( ( ( city @ SV7 )
= $false )
| ( ( has_crime @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV8: $i] :
( ( ( country @ SV8 )
= $false )
| ( ( beautiful @ ( capital_city @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,83,82,81,80,75,68,65,64,63,61]) ).
thf(85,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[84,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : PUZ132+1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n025.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 02:25:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 10
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (rf:0,axioms:10,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:12,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.39
% 0.13/0.39 ********************************
% 0.13/0.39 * All subproblems solved! *
% 0.13/0.39 ********************************
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:84,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39
% 0.13/0.39 %**** Beginning of derivation protocol ****
% 0.13/0.39 % SZS output start CNFRefutation
% See solution above
% 0.13/0.39
% 0.13/0.39 %**** End of derivation protocol ****
% 0.13/0.39 %**** no. of clauses in derivation: 85 ****
% 0.13/0.39 %**** clause counter: 84 ****
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:84,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------