TSTP Solution File: SET062+3 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET062+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : Tue Jul 19 02:58:54 EDT 2022
% Result : Theorem 0.17s 0.36s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 42 unt; 7 typ; 0 def)
% Number of atoms : 293 ( 74 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 505 ( 98 ~; 72 |; 6 &; 323 @)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 121 ( 0 ^ 121 !; 0 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_C,type,
sK2_C: $i > $i ).
thf(tp_sK3_D,type,
sK3_D: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
thf(2,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(3,axiom,
! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(4,axiom,
! [B: $i] :
~ ( member @ B @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
thf(5,conjecture,
! [B: $i] : ( subset @ empty_set @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_empty_set_subset) ).
thf(6,negated_conjecture,
( ( ! [B: $i] : ( subset @ empty_set @ B ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [B: $i] : ( subset @ empty_set @ B ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( subset @ empty_set @ sK1_B )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(13,plain,
( ( ~ ( subset @ empty_set @ sK1_B ) )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [B: $i] :
( ( member @ ( sK2_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(15,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK3_D @ C @ B ) @ B )
& ~ ( member @ ( sK3_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(16,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK3_D @ C @ B ) @ B )
& ~ ( member @ ( sK3_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(19,plain,
( ( ! [B: $i] :
( ( member @ ( sK2_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ~ ( subset @ empty_set @ sK1_B ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( member @ ( sK2_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(24,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
( ( subset @ empty_set @ sK1_B )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK2_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK2_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(33,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ! [SX0: $i] :
( ( member @ ( sK2_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV3: $i] :
( ( ! [SY8: $i] :
( ~ ( ~ ( member @ ( sK3_D @ SY8 @ SV3 ) @ SV3 )
| ~ ~ ( member @ ( sK3_D @ SY8 @ SV3 ) @ SY8 ) )
| ( subset @ SV3 @ SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV4: $i] :
( ( ! [SY9: $i] :
( ~ ( subset @ SV4 @ SY9 )
| ! [SY10: $i] :
( ~ ( member @ SY10 @ SV4 )
| ( member @ SY10 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV5: $i] :
( ( ( member @ ( sK2_C @ SV5 ) @ SV5 )
| ( empty @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV6: $i] :
( ( ~ ( empty @ SV6 )
| ! [SY11: $i] :
~ ( member @ SY11 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV3: $i,SV7: $i] :
( ( ~ ( ~ ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV3 )
| ~ ~ ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV7 ) )
| ( subset @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( subset @ SV4 @ SV8 )
| ! [SY12: $i] :
( ~ ( member @ SY12 @ SV4 )
| ( member @ SY12 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV5: $i] :
( ( ( member @ ( sK2_C @ SV5 ) @ SV5 )
= $true )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $true )
| ( ( ! [SY11: $i] :
~ ( member @ SY11 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( ~ ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV3 )
| ~ ~ ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV7 ) ) )
= $true )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV8 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( member @ SY12 @ SV4 )
| ( member @ SY12 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV6: $i] :
( ( ( empty @ SV6 )
= $false )
| ( ( ! [SY11: $i] :
~ ( member @ SY11 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV3 )
| ~ ~ ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV7 ) )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV8: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV8 )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( member @ SY12 @ SV4 )
| ( member @ SY12 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV6: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV6 ) )
= $true )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV3 ) )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ~ ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV7 ) )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
! [SV8: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV4 )
| ( member @ SV10 @ SV8 ) )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV6: $i,SV9: $i] :
( ( ( member @ SV9 @ SV6 )
= $false )
| ( ( empty @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV3: $i,SV7: $i] :
( ( ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV7 ) )
= $true )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(57,plain,
! [SV8: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV4 ) )
= $true )
| ( ( member @ SV10 @ SV8 )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV3: $i,SV7: $i] :
( ( ( member @ ( sK3_D @ SV7 @ SV3 ) @ SV7 )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV8: $i,SV4: $i,SV10: $i] :
( ( ( member @ SV10 @ SV4 )
= $false )
| ( ( member @ SV10 @ SV8 )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,59,58,55,54,43,28,25]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET062+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.31 % Computer : n028.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Sun Jul 10 12:24:27 EDT 2022
% 0.17/0.31 % CPUTime :
% 0.17/0.32
% 0.17/0.32 No.of.Axioms: 4
% 0.17/0.32
% 0.17/0.32 Length.of.Defs: 0
% 0.17/0.32
% 0.17/0.32 Contains.Choice.Funs: false
% 0.17/0.32 (rf:0,axioms:4,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:6,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.17/0.36
% 0.17/0.36 ********************************
% 0.17/0.36 * All subproblems solved! *
% 0.17/0.36 ********************************
% 0.17/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:60,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.17/0.36
% 0.17/0.36 %**** Beginning of derivation protocol ****
% 0.17/0.36 % SZS output start CNFRefutation
% See solution above
% 0.17/0.36
% 0.17/0.36 %**** End of derivation protocol ****
% 0.17/0.36 %**** no. of clauses in derivation: 61 ****
% 0.17/0.36 %**** clause counter: 60 ****
% 0.17/0.36
% 0.17/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------