TSTP Solution File: SET639+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET639+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 : n021.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 03:03:51 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 186 ( 111 unt; 10 typ; 0 def)
% Number of atoms : 1020 ( 349 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 1886 ( 375 ~; 316 |; 29 &;1145 @)
% ( 12 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 463 ( 0 ^ 463 !; 0 ?; 463 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY21,type,
sK2_SY21: $i ).
thf(tp_sK3_D,type,
sK3_D: $i > $i > $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(2,axiom,
! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
thf(3,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(5,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(6,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(7,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
thf(8,axiom,
! [B: $i] :
~ ( member @ B @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
thf(9,axiom,
! [B: $i,C: $i] :
( ( subset @ B @ C )
=> ( ( intersection @ B @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_intersection) ).
thf(10,conjecture,
! [B: $i,C: $i] :
( ( ( subset @ B @ C )
& ( ( intersection @ C @ B )
= empty_set ) )
=> ( B = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th121) ).
thf(11,negated_conjecture,
( ( ! [B: $i,C: $i] :
( ( ( subset @ B @ C )
& ( ( intersection @ C @ B )
= empty_set ) )
=> ( B = empty_set ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [B: $i,C: $i] :
( ( ( subset @ B @ C )
& ( ( intersection @ C @ B )
= empty_set ) )
=> ( B = empty_set ) ) )
= $false ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
=> ( ( intersection @ B @ C )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(22,plain,
( ( ! [SY21: $i] :
( ( ( subset @ sK1_B @ SY21 )
& ( ( intersection @ SY21 @ sK1_B )
= empty_set ) )
=> ( sK1_B = empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ( ( subset @ sK1_B @ sK2_SY21 )
& ( ( intersection @ sK2_SY21 @ sK1_B )
= empty_set ) )
=> ( sK1_B = empty_set ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( subset @ sK1_B @ sK2_SY21 )
= $true ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(25,plain,
( ( ( intersection @ sK2_SY21 @ sK1_B )
= empty_set )
= $true ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(26,plain,
( ( sK1_B = empty_set )
= $false ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(27,plain,
( ( ( sK1_B != empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(28,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK3_D @ C @ B ) @ B )
| ~ ( member @ ( sK3_D @ C @ B ) @ C ) )
& ( ( member @ ( sK3_D @ C @ B ) @ B )
| ( member @ ( sK3_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(29,plain,
( ( ! [B: $i] :
( ( member @ ( sK4_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(30,plain,
( ( ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ~ ( subset @ C @ B )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(31,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK5_D @ C @ B ) @ B )
& ~ ( member @ ( sK5_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)],[18]) ).
thf(32,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C )
| ( member @ D @ ( intersection @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(33,plain,
( ( ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ( ( intersection @ B @ C )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(34,plain,
( ( ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ( ( intersection @ B @ C )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(36,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C )
| ( member @ D @ ( intersection @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(37,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK5_D @ C @ B ) @ B )
& ~ ( member @ ( sK5_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)],[31]) ).
thf(38,plain,
( ( ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ~ ( subset @ C @ B )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(40,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(41,plain,
( ( ! [B: $i] :
( ( member @ ( sK4_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(42,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK3_D @ C @ B ) @ B )
| ~ ( member @ ( sK3_D @ C @ B ) @ C ) )
& ( ( member @ ( sK3_D @ C @ B ) @ B )
| ( member @ ( sK3_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( ( intersection @ sK2_SY21 @ sK1_B )
= empty_set )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(44,plain,
( ( subset @ sK1_B @ sK2_SY21 )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(45,plain,
( ( ( sK1_B != empty_set ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(46,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(47,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( member @ ( sK4_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(48,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(49,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK5_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)],[37]) ).
thf(50,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(51,plain,
! [SV1: $i] :
( ( ! [SY22: $i] :
( ~ ( subset @ SV1 @ SY22 )
| ( ( intersection @ SV1 @ SY22 )
= SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(52,plain,
! [SV2: $i] :
( ( ~ ( member @ SV2 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(53,plain,
! [SV3: $i] :
( ( ! [SY23: $i] :
( ( intersection @ SV3 @ SY23 )
= ( intersection @ SY23 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
! [SV4: $i] :
( ( subset @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(55,plain,
( ( sK1_B = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(56,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(57,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK4_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(58,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY24: $i,SY25: $i] :
( ~ ( member @ SY25 @ SV5 )
| ~ ( member @ SY25 @ SY24 )
| ( member @ SY25 @ ( intersection @ SV5 @ SY24 ) ) )
| ~ ~ ( ~ ! [SY26: $i,SY27: $i] :
( ~ ( member @ SY27 @ ( intersection @ SV5 @ SY26 ) )
| ( member @ SY27 @ SV5 ) )
| ~ ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ ( intersection @ SV5 @ SY28 ) )
| ( member @ SY29 @ SY28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(59,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK5_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)],[49]) ).
thf(60,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV6: $i,SV1: $i] :
( ( ~ ( subset @ SV1 @ SV6 )
| ( ( intersection @ SV1 @ SV6 )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV2: $i] :
( ( member @ SV2 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV7: $i,SV3: $i] :
( ( ( intersection @ SV3 @ SV7 )
= ( intersection @ SV7 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(64,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(65,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(66,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK4_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(67,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(68,plain,
! [SV5: $i] :
( ( ~ ! [SY24: $i,SY25: $i] :
( ~ ( member @ SY25 @ SV5 )
| ~ ( member @ SY25 @ SY24 )
| ( member @ SY25 @ ( intersection @ SV5 @ SY24 ) ) )
| ~ ~ ( ~ ! [SY26: $i,SY27: $i] :
( ~ ( member @ SY27 @ ( intersection @ SV5 @ SY26 ) )
| ( member @ SY27 @ SV5 ) )
| ~ ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ ( intersection @ SV5 @ SY28 ) )
| ( member @ SY29 @ SY28 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(69,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(70,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(71,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(72,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(73,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV6 ) )
= $true )
| ( ( ( intersection @ SV1 @ SV6 )
= SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK3_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ( member @ ( sK4_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(77,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(78,plain,
! [SV5: $i] :
( ( ~ ! [SY24: $i,SY25: $i] :
( ~ ( member @ SY25 @ SV5 )
| ~ ( member @ SY25 @ SY24 )
| ( member @ SY25 @ ( intersection @ SV5 @ SY24 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(79,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ! [SY26: $i,SY27: $i] :
( ~ ( member @ SY27 @ ( intersection @ SV5 @ SY26 ) )
| ( member @ SY27 @ SV5 ) )
| ~ ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ ( intersection @ SV5 @ SY28 ) )
| ( member @ SY29 @ SY28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(80,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(82,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(83,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(84,plain,
! [SV6: $i,SV1: $i] :
( ( ( subset @ SV1 @ SV6 )
= $false )
| ( ( ( intersection @ SV1 @ SV6 )
= SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(85,plain,
! [SV8: $i] :
( ( ! [SY30: $i] :
( ~ ( ~ ( ~ ( member @ ( sK3_D @ SY30 @ SV8 ) @ SV8 )
| ~ ( member @ ( sK3_D @ SY30 @ SV8 ) @ SY30 ) )
| ~ ( ( member @ ( sK3_D @ SY30 @ SV8 ) @ SV8 )
| ( member @ ( sK3_D @ SY30 @ SV8 ) @ SY30 ) ) )
| ( SV8 = SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(86,plain,
! [SV9: $i] :
( ( ! [SY31: $i] :
( ( SV9 != SY31 )
| ~ ( ~ ! [SY32: $i] :
( ~ ( member @ SY32 @ SV9 )
| ( member @ SY32 @ SY31 ) )
| ~ ! [SY33: $i] :
( ~ ( member @ SY33 @ SY31 )
| ( member @ SY33 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(87,plain,
! [SV10: $i] :
( ( ( member @ ( sK4_C @ SV10 ) @ SV10 )
| ( empty @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV11: $i] :
( ( ~ ( empty @ SV11 )
| ! [SY34: $i] :
~ ( member @ SY34 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(89,plain,
! [SV5: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ~ ( member @ SY25 @ SV5 )
| ~ ( member @ SY25 @ SY24 )
| ( member @ SY25 @ ( intersection @ SV5 @ SY24 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(90,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY26: $i,SY27: $i] :
( ~ ( member @ SY27 @ ( intersection @ SV5 @ SY26 ) )
| ( member @ SY27 @ SV5 ) )
| ~ ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ ( intersection @ SV5 @ SY28 ) )
| ( member @ SY29 @ SY28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(91,plain,
! [SV12: $i] :
( ( ! [SY35: $i] :
( ~ ( ~ ( member @ ( sK5_D @ SY35 @ SV12 ) @ SV12 )
| ~ ~ ( member @ ( sK5_D @ SY35 @ SV12 ) @ SY35 ) )
| ( subset @ SV12 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(92,plain,
! [SV13: $i] :
( ( ! [SY36: $i] :
( ~ ( subset @ SV13 @ SY36 )
| ! [SY37: $i] :
( ~ ( member @ SY37 @ SV13 )
| ( member @ SY37 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(93,plain,
! [SV14: $i] :
( ( ! [SY38: $i] :
( ~ ( subset @ SV14 @ SY38 )
| ~ ( subset @ SY38 @ SV14 )
| ( SV14 = SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(94,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(95,plain,
! [SV8: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) )
| ~ ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) ) )
| ( SV8 = SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(96,plain,
! [SV16: $i,SV9: $i] :
( ( ( SV9 != SV16 )
| ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV9 )
| ( member @ SY39 @ SV16 ) )
| ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV16 )
| ( member @ SY40 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(97,plain,
! [SV10: $i] :
( ( ( member @ ( sK4_C @ SV10 ) @ SV10 )
= $true )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(98,plain,
! [SV11: $i] :
( ( ( ~ ( empty @ SV11 ) )
= $true )
| ( ( ! [SY34: $i] :
~ ( member @ SY34 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV17: $i,SV5: $i] :
( ( ! [SY41: $i] :
( ~ ( member @ SY41 @ SV5 )
| ~ ( member @ SY41 @ SV17 )
| ( member @ SY41 @ ( intersection @ SV5 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV5: $i] :
( ( ~ ! [SY26: $i,SY27: $i] :
( ~ ( member @ SY27 @ ( intersection @ SV5 @ SY26 ) )
| ( member @ SY27 @ SV5 ) )
| ~ ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ ( intersection @ SV5 @ SY28 ) )
| ( member @ SY29 @ SY28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV12: $i,SV18: $i] :
( ( ~ ( ~ ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV12 )
| ~ ~ ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV18 ) )
| ( subset @ SV12 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV19: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV19 )
| ! [SY42: $i] :
( ~ ( member @ SY42 @ SV13 )
| ( member @ SY42 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV20: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV20 )
| ~ ( subset @ SV20 @ SV14 )
| ( SV14 = SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(104,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(105,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(106,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) )
| ~ ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) ) ) )
= $true )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV16: $i,SV9: $i] :
( ( ( ( SV9 != SV16 ) )
= $true )
| ( ( ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV9 )
| ( member @ SY39 @ SV16 ) )
| ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV16 )
| ( member @ SY40 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
= $false )
| ( ( ! [SY34: $i] :
~ ( member @ SY34 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV17: $i,SV5: $i,SV21: $i] :
( ( ~ ( member @ SV21 @ SV5 )
| ~ ( member @ SV21 @ SV17 )
| ( member @ SV21 @ ( intersection @ SV5 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV5: $i] :
( ( ~ ! [SY26: $i,SY27: $i] :
( ~ ( member @ SY27 @ ( intersection @ SV5 @ SY26 ) )
| ( member @ SY27 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(111,plain,
! [SV5: $i] :
( ( ~ ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ ( intersection @ SV5 @ SY28 ) )
| ( member @ SY29 @ SY28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(112,plain,
! [SV12: $i,SV18: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV12 )
| ~ ~ ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV18 ) ) )
= $true )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV19: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV19 ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ( member @ SY42 @ SV13 )
| ( member @ SY42 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV20: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV20 )
| ~ ( subset @ SV20 @ SV14 ) )
= $true )
| ( ( SV14 = SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(117,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) )
| ~ ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) ) )
= $false )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV16: $i,SV9: $i] :
( ( ( SV9 = SV16 )
= $false )
| ( ( ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV9 )
| ( member @ SY39 @ SV16 ) )
| ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV16 )
| ( member @ SY40 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV11: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV11 ) )
= $true )
| ( ( empty @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV17: $i,SV5: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV5 )
| ~ ( member @ SV21 @ SV17 ) )
= $true )
| ( ( member @ SV21 @ ( intersection @ SV5 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV5: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ( member @ SY27 @ ( intersection @ SV5 @ SY26 ) )
| ( member @ SY27 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(122,plain,
! [SV5: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ ( intersection @ SV5 @ SY28 ) )
| ( member @ SY29 @ SY28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(123,plain,
! [SV12: $i,SV18: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV12 )
| ~ ~ ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV18 ) )
= $false )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(124,plain,
! [SV19: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV19 )
= $false )
| ( ( ! [SY42: $i] :
( ~ ( member @ SY42 @ SV13 )
| ( member @ SY42 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(125,plain,
! [SV20: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV20 ) )
= $true )
| ( ( ~ ( subset @ SV20 @ SV14 ) )
= $true )
| ( ( SV14 = SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(126,plain,
! [SV23: $i] :
( ( ! [SY43: $i] :
( ( SV23 != SY43 )
| ( subset @ SV23 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(127,plain,
! [SV24: $i] :
( ( ! [SY44: $i] :
( ( SV24 != SY44 )
| ( subset @ SY44 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(128,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) ) )
= $false )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(129,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) ) )
= $false )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(130,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV9 )
| ( member @ SY39 @ SV16 ) )
| ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV16 )
| ( member @ SY40 @ SV9 ) ) )
= $false )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV11: $i,SV22: $i] :
( ( ( member @ SV22 @ SV11 )
= $false )
| ( ( empty @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV17: $i,SV5: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV5 ) )
= $true )
| ( ( ~ ( member @ SV21 @ SV17 ) )
= $true )
| ( ( member @ SV21 @ ( intersection @ SV5 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV25: $i,SV5: $i] :
( ( ! [SY45: $i] :
( ~ ( member @ SY45 @ ( intersection @ SV5 @ SV25 ) )
| ( member @ SY45 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV26: $i,SV5: $i] :
( ( ! [SY46: $i] :
( ~ ( member @ SY46 @ ( intersection @ SV5 @ SV26 ) )
| ( member @ SY46 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV12: $i,SV18: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV12 ) )
= $false )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(136,plain,
! [SV12: $i,SV18: $i] :
( ( ( ~ ~ ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV18 ) )
= $false )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(137,plain,
! [SV19: $i,SV13: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV13 )
| ( member @ SV27 @ SV19 ) )
= $true )
| ( ( subset @ SV13 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(138,plain,
! [SV20: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV20 )
= $false )
| ( ( ~ ( subset @ SV20 @ SV14 ) )
= $true )
| ( ( SV14 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(139,plain,
! [SV28: $i,SV23: $i] :
( ( ( SV23 != SV28 )
| ( subset @ SV23 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(140,plain,
! [SV29: $i,SV24: $i] :
( ( ( SV24 != SV29 )
| ( subset @ SV29 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(141,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) )
= $true )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(142,plain,
! [SV8: $i,SV15: $i] :
( ( ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
| ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) )
= $true )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(143,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV9 )
| ( member @ SY39 @ SV16 ) ) )
= $false )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(144,plain,
! [SV9: $i,SV16: $i] :
( ( ( ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV16 )
| ( member @ SY40 @ SV9 ) ) )
= $false )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(145,plain,
! [SV17: $i,SV5: $i,SV21: $i] :
( ( ( member @ SV21 @ SV5 )
= $false )
| ( ( ~ ( member @ SV21 @ SV17 ) )
= $true )
| ( ( member @ SV21 @ ( intersection @ SV5 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(146,plain,
! [SV25: $i,SV5: $i,SV30: $i] :
( ( ~ ( member @ SV30 @ ( intersection @ SV5 @ SV25 ) )
| ( member @ SV30 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(147,plain,
! [SV26: $i,SV5: $i,SV31: $i] :
( ( ~ ( member @ SV31 @ ( intersection @ SV5 @ SV26 ) )
| ( member @ SV31 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(148,plain,
! [SV12: $i,SV18: $i] :
( ( ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV12 )
= $true )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(149,plain,
! [SV12: $i,SV18: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV18 ) )
= $true )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(150,plain,
! [SV19: $i,SV13: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV13 ) )
= $true )
| ( ( member @ SV27 @ SV19 )
= $true )
| ( ( subset @ SV13 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(151,plain,
! [SV14: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV14 )
= $false )
| ( ( subset @ SV14 @ SV20 )
= $false )
| ( ( SV14 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(152,plain,
! [SV28: $i,SV23: $i] :
( ( ( ( SV23 != SV28 ) )
= $true )
| ( ( subset @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(153,plain,
! [SV29: $i,SV24: $i] :
( ( ( ( SV24 != SV29 ) )
= $true )
| ( ( subset @ SV29 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(154,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 ) )
= $true )
| ( ( ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) )
= $true )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(155,plain,
! [SV8: $i,SV15: $i] :
( ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
= $true )
| ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 )
= $true )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(156,plain,
! [SV16: $i,SV9: $i] :
( ( ( ! [SY39: $i] :
( ~ ( member @ SY39 @ SV9 )
| ( member @ SY39 @ SV16 ) ) )
= $true )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(157,plain,
! [SV9: $i,SV16: $i] :
( ( ( ! [SY40: $i] :
( ~ ( member @ SY40 @ SV16 )
| ( member @ SY40 @ SV9 ) ) )
= $true )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(158,plain,
! [SV5: $i,SV17: $i,SV21: $i] :
( ( ( member @ SV21 @ SV17 )
= $false )
| ( ( member @ SV21 @ SV5 )
= $false )
| ( ( member @ SV21 @ ( intersection @ SV5 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(159,plain,
! [SV25: $i,SV5: $i,SV30: $i] :
( ( ( ~ ( member @ SV30 @ ( intersection @ SV5 @ SV25 ) ) )
= $true )
| ( ( member @ SV30 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV26: $i,SV5: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ ( intersection @ SV5 @ SV26 ) ) )
= $true )
| ( ( member @ SV31 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV12: $i,SV18: $i] :
( ( ( member @ ( sK5_D @ SV18 @ SV12 ) @ SV18 )
= $false )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(162,plain,
! [SV19: $i,SV13: $i,SV27: $i] :
( ( ( member @ SV27 @ SV13 )
= $false )
| ( ( member @ SV27 @ SV19 )
= $true )
| ( ( subset @ SV13 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(163,plain,
! [SV28: $i,SV23: $i] :
( ( ( SV23 = SV28 )
= $false )
| ( ( subset @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(164,plain,
! [SV29: $i,SV24: $i] :
( ( ( SV24 = SV29 )
= $false )
| ( ( subset @ SV29 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(165,plain,
! [SV8: $i,SV15: $i] :
( ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
= $false )
| ( ( ~ ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 ) )
= $true )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(166,plain,
! [SV16: $i,SV9: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV9 )
| ( member @ SV32 @ SV16 ) )
= $true )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV9: $i,SV16: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV16 )
| ( member @ SV33 @ SV9 ) )
= $true )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV25: $i,SV5: $i,SV30: $i] :
( ( ( member @ SV30 @ ( intersection @ SV5 @ SV25 ) )
= $false )
| ( ( member @ SV30 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV26: $i,SV5: $i,SV31: $i] :
( ( ( member @ SV31 @ ( intersection @ SV5 @ SV26 ) )
= $false )
| ( ( member @ SV31 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV8: $i,SV15: $i] :
( ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV15 )
= $false )
| ( ( member @ ( sK3_D @ SV15 @ SV8 ) @ SV8 )
= $false )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(171,plain,
! [SV16: $i,SV9: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV9 ) )
= $true )
| ( ( member @ SV32 @ SV16 )
= $true )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(172,plain,
! [SV9: $i,SV16: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV16 ) )
= $true )
| ( ( member @ SV33 @ SV9 )
= $true )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(173,plain,
! [SV16: $i,SV9: $i,SV32: $i] :
( ( ( member @ SV32 @ SV9 )
= $false )
| ( ( member @ SV32 @ SV16 )
= $true )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(174,plain,
! [SV9: $i,SV16: $i,SV33: $i] :
( ( ( member @ SV33 @ SV16 )
= $false )
| ( ( member @ SV33 @ SV9 )
= $true )
| ( ( SV9 = SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(175,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[43,174,173,170,169,168,164,163,162,161,158,155,151,148,131,97,84,63,62,55,54,44]) ).
thf(176,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n021.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 : Sat Jul 9 21:02:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 9
% 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:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 0.19/0.42
% 0.19/0.42 ********************************
% 0.19/0.42 * All subproblems solved! *
% 0.19/0.42 ********************************
% 0.19/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,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:175,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.43
% 0.19/0.43 %**** Beginning of derivation protocol ****
% 0.19/0.43 % SZS output start CNFRefutation
% See solution above
% 0.19/0.43
% 0.19/0.43 %**** End of derivation protocol ****
% 0.19/0.43 %**** no. of clauses in derivation: 176 ****
% 0.19/0.43 %**** clause counter: 175 ****
% 0.19/0.43
% 0.19/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,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:175,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------