TSTP Solution File: SEU829^1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU829^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.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 : Tue Jul 19 12:15:17 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 21 unt; 6 typ; 3 def)
% Number of atoms : 453 ( 161 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 257 ( 74 ~; 83 |; 0 &; 97 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 44 ^ 58 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i > $o ).
thf(tp_powerset,type,
powerset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_sK1_SV1,type,
sK1_SV1: $i > $o ).
thf(tp_sK2_SY11,type,
sK2_SY11: $i ).
thf(tp_sK3_SV5,type,
sK3_SV5: $i ).
thf(tp_subseteq,type,
subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(emptyset,definition,
( emptyset
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset) ).
thf(powerset,definition,
( powerset
= ( ^ [X: $i > $o,Y: $i > $o] : ( subseteq @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset) ).
thf(subseteq,definition,
( subseteq
= ( ^ [X: $i > $o,Y: $i > $o] :
! [U: $i] :
( ( X @ U )
=> ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subseteq) ).
thf(1,conjecture,
( ( powerset @ emptyset )
= ( ^ [X: $i > $o] : ( X = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ( powerset @ emptyset )
= ( ^ [X: $i > $o] : ( X = emptyset ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ^ [SY0: $i > $o] :
! [SY3: $i] :
( ( SY0 @ SY3 )
=> $false ) )
= ( ^ [SY4: $i > $o] :
( SY4
= ( ^ [X: $i] : $false ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,emptyset,powerset,subseteq]) ).
thf(4,plain,
( ( ( ( ^ [SY0: $i > $o] :
! [SY3: $i] :
( ( SY0 @ SY3 )
=> $false ) )
!= ( ^ [SY4: $i > $o] :
( SY4
= ( ^ [X: $i] : $false ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ( ( ^ [SY0: $i > $o] :
! [SY3: $i] :
~ ( SY0 @ SY3 ) )
!= ( ^ [SY4: $i > $o] :
( SY4
= ( ^ [X: $i] : $false ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ( ^ [SY0: $i > $o] :
! [SY3: $i] :
~ ( SY0 @ SY3 ) )
!= ( ^ [SY4: $i > $o] :
( SY4
= ( ^ [X: $i] : $false ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ( ^ [SY0: $i > $o] :
! [SY3: $i] :
~ ( SY0 @ SY3 ) )
= ( ^ [SY4: $i > $o] :
( SY4
= ( ^ [X: $i] : $false ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SV1: $i > $o] :
( ( ! [SY9: $i] :
~ ( SV1 @ SY9 ) )
= ( SV1
= ( ^ [X: $i] : $false ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[7]) ).
thf(9,plain,
( ( ( ^ [SY0: $i > $o] :
! [SY3: $i] :
~ ( SY0 @ SY3 ) )
= ( ^ [SY4: $i > $o] :
( SY4
= ( ^ [X: $i] : $false ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ( ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 ) )
= ( sK1_SV1
= ( ^ [X: $i] : $false ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(11,plain,
( ( ~ ( ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 )
| ( sK1_SV1
= ( ^ [X: $i] : $false ) ) )
| ~ ( ~ ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 )
| ( sK1_SV1
!= ( ^ [X: $i] : $false ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(12,plain,
( ( ( ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 ) )
= ( sK1_SV1
= ( ^ [X: $i] : $false ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 )
| ( sK1_SV1
= ( ^ [X: $i] : $false ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( ~ ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 )
| ( sK1_SV1
!= ( ^ [X: $i] : $false ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 )
| ( sK1_SV1
= ( ^ [X: $i] : $false ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 )
| ( sK1_SV1
!= ( ^ [X: $i] : $false ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ( ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 ) )
= $true )
| ( ( sK1_SV1
= ( ^ [X: $i] : $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ( ~ ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 ) )
= $true )
| ( ( ( sK1_SV1
!= ( ^ [X: $i] : $false ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV2: $i] :
( ( ( ~ ( sK1_SV1 @ SV2 ) )
= $true )
| ( ( sK1_SV1
= ( ^ [X: $i] : $false ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ( ! [SY11: $i] :
~ ( sK1_SV1 @ SY11 ) )
= $false )
| ( ( ( sK1_SV1
!= ( ^ [X: $i] : $false ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV2: $i] :
( ( ( sK1_SV1 @ SV2 )
= $false )
| ( ( sK1_SV1
= ( ^ [X: $i] : $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ( ~ ( sK1_SV1 @ sK2_SY11 ) )
= $false )
| ( ( ( sK1_SV1
!= ( ^ [X: $i] : $false ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(23,plain,
! [SV2: $i] :
( ( ( ! [SV3: $i] :
( ( sK1_SV1 @ SV3 )
= $false ) )
= $true )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV2: $i] :
( ( ( sK1_SV1
= ( ^ [X: $i] : $false ) )
= $true )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ( sK1_SV1 @ sK2_SY11 )
= $true )
| ( ( ( sK1_SV1
!= ( ^ [X: $i] : $false ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i,SV4: $i] :
( ( ( ( sK1_SV1 @ SV4 )
= $false )
= $true )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ( sK1_SV1
= ( ^ [X: $i] : $false ) )
= $false )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( ( sK1_SV1 @ SV4 )
| $false )
| ~ ( ~ ( sK1_SV1 @ SV4 )
| ~ $false ) )
= $true )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: $i,SV4: $i] :
( ( ( ( sK1_SV1 @ SV4 )
= $false )
= $true )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ! [SV5: $i] :
( ( sK1_SV1 @ SV5 )
= $false ) )
= $false )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ( sK1_SV1
= ( ^ [X: $i] : $false ) )
= $false )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( ( sK1_SV1 @ SV4 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( sK1_SV1 @ SV4 )
| ~ $false ) )
= $true )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ( ( sK1_SV1 @ sK3_SV5 )
= $false )
= $false )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(34,plain,
! [SV2: $i,SV4: $i] :
( ( ( ( sK1_SV1 @ SV4 )
| $false )
= $false )
| ( ( ~ ( ~ ( sK1_SV1 @ SV4 )
| ~ $false ) )
= $true )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( ( ~ ( ( sK1_SV1 @ sK3_SV5 )
| $false )
| ~ ( ~ ( sK1_SV1 @ sK3_SV5 )
| ~ $false ) )
= $false )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ( ( sK1_SV1 @ sK3_SV5 )
= $false )
= $false )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV2: $i,SV4: $i] :
( ( ( sK1_SV1 @ SV4 )
= $false )
| ( ( ~ ( ~ ( sK1_SV1 @ SV4 )
| ~ $false ) )
= $true )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV2: $i,SV4: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( sK1_SV1 @ SV4 )
| ~ $false ) )
= $true )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( ( ~ ( ( sK1_SV1 @ sK3_SV5 )
| $false ) )
= $false )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ( ~ ( ~ ( sK1_SV1 @ sK3_SV5 )
| ~ $false ) )
= $false )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( sK1_SV1 @ SV4 )
| ~ $false )
= $false )
| ( ( sK1_SV1 @ SV4 )
= $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( sK1_SV1 @ SV4 )
| ~ $false )
= $false )
| ( $false = $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
( ( ( ( sK1_SV1 @ sK3_SV5 )
| $false )
= $true )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
( ( ( ~ ( sK1_SV1 @ sK3_SV5 )
| ~ $false )
= $true )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( sK1_SV1 @ SV4 ) )
= $false )
| ( ( sK1_SV1 @ SV4 )
= $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ $false )
= $false )
| ( ( sK1_SV1 @ SV4 )
= $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( sK1_SV1 @ SV4 ) )
= $false )
| ( $false = $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV2: $i] :
( ( ( ~ $false )
= $false )
| ( $false = $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(49,plain,
( ( ( sK1_SV1 @ sK3_SV5 )
= $true )
| ( $false = $true )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( ( ~ ( sK1_SV1 @ sK3_SV5 ) )
= $true )
| ( ( ~ $false )
= $true )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV2: $i,SV4: $i] :
( ( ( sK1_SV1 @ SV4 )
= $true )
| ( ( sK1_SV1 @ SV4 )
= $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV2: $i,SV4: $i] :
( ( $false = $true )
| ( ( sK1_SV1 @ SV4 )
= $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV2: $i,SV4: $i] :
( ( ( sK1_SV1 @ SV4 )
= $true )
| ( $false = $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(54,plain,
! [SV2: $i] :
( ( $false = $true )
| ( $false = $false )
| ( ( sK1_SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(55,plain,
( ( ( sK1_SV1 @ sK3_SV5 )
= $false )
| ( ( ~ $false )
= $true )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(56,plain,
( ( $false = $false )
| ( ( sK1_SV1 @ sK3_SV5 )
= $false )
| ( ( sK1_SV1 @ sK2_SY11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(57,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[9,56,54,53,52,51,49,36,31,29,24,12]) ).
thf(58,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU829^1 : TPTP v8.1.0. Released v3.7.0.
% 0.13/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 03:26:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.35
% 0.19/0.35 No.of.Axioms: 0
% 0.19/0.35
% 0.19/0.35 Length.of.Defs: 439
% 0.19/0.35
% 0.19/0.35 Contains.Choice.Funs: false
% 0.19/0.35 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,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 Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:57,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.39
% 0.19/0.39 %**** Beginning of derivation protocol ****
% 0.19/0.39 % SZS output start CNFRefutation
% See solution above
% 0.19/0.39
% 0.19/0.39 %**** End of derivation protocol ****
% 0.19/0.39 %**** no. of clauses in derivation: 58 ****
% 0.19/0.39 %**** clause counter: 57 ****
% 0.19/0.39
% 0.19/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------