TSTP Solution File: SET628+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET628+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 : 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 : Tue Jul 19 03:03:43 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 243 ( 136 unt; 9 typ; 0 def)
% Number of atoms : 1389 ( 458 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 2467 ( 523 ~; 428 |; 27 &;1469 @)
% ( 14 <=>; 6 =>; 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 : 12 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 537 ( 0 ^ 535 !; 2 ?; 537 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_intersect,type,
intersect: $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_not_equal,type,
not_equal: $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_sK4_D,type,
sK4_D: $i > $i > $i ).
thf(1,axiom,
! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
thf(2,axiom,
! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(3,axiom,
! [B: $i,C: $i] :
( ( not_equal @ B @ C )
<=> ( B != C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(5,axiom,
! [B: $i] :
~ ( member @ B @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
thf(6,axiom,
! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
thf(7,conjecture,
! [B: $i] :
( ( intersect @ B @ B )
<=> ( not_equal @ B @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th110) ).
thf(8,negated_conjecture,
( ( ! [B: $i] :
( ( intersect @ B @ B )
<=> ( not_equal @ B @ empty_set ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [B: $i] :
( ( intersect @ B @ B )
<=> ( not_equal @ B @ empty_set ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [B: $i,C: $i] :
( ( not_equal @ B @ C )
<=> ( B != C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(16,plain,
( ( ( intersect @ sK1_B @ sK1_B )
<=> ( not_equal @ sK1_B @ empty_set ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(17,plain,
( ( ( intersect @ sK1_B @ sK1_B )
=> ( not_equal @ sK1_B @ empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(18,plain,
( ( ( not_equal @ sK1_B @ empty_set )
=> ( intersect @ sK1_B @ sK1_B ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(19,plain,
( ( ~ ( ( intersect @ sK1_B @ sK1_B )
=> ( not_equal @ sK1_B @ empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ( not_equal @ sK1_B @ empty_set )
=> ( intersect @ sK1_B @ sK1_B ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(21,plain,
( ( ( intersect @ sK1_B @ sK1_B )
& ~ ( not_equal @ sK1_B @ empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(22,plain,
( ( ( not_equal @ sK1_B @ empty_set )
& ~ ( intersect @ sK1_B @ sK1_B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(23,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)],[10]) ).
thf(24,plain,
( ( ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( intersect @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(25,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
| ( not_equal @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( not_equal @ B @ C )
| ( B != C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(26,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(27,plain,
( ( ! [B: $i,C: $i] :
( ! [D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C ) )
| ( intersect @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( ( member @ ( sK4_D @ C @ B ) @ B )
& ( member @ ( sK4_D @ C @ B ) @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(28,plain,
( ( ! [B: $i,C: $i] :
( ! [D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C ) )
| ( intersect @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( ( member @ ( sK4_D @ C @ B ) @ B )
& ( member @ ( sK4_D @ C @ B ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(29,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(30,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)],[26]) ).
thf(31,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
| ( not_equal @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( not_equal @ B @ C )
| ( B != C ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( intersect @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ! [B: $i] :
( ( member @ ( sK2_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ( intersect @ sK1_B @ sK1_B )
& ~ ( not_equal @ sK1_B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(35,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)],[33]) ).
thf(36,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(37,plain,
( ( ~ ( ~ ( intersect @ sK1_B @ sK1_B )
| ~ ~ ( not_equal @ sK1_B @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(38,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( not_equal @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( not_equal @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(39,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)],[30]) ).
thf(40,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(41,plain,
! [SV2: $i] :
( ( ! [SY14: $i] :
( ~ ( intersect @ SV2 @ SY14 )
| ( intersect @ SY14 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,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)],[35]) ).
thf(43,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(44,plain,
( ( ~ ( intersect @ sK1_B @ sK1_B )
| ~ ~ ( not_equal @ sK1_B @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(45,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( not_equal @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( not_equal @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
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 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( intersect @ SV2 @ SV3 )
| ( intersect @ SV3 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK2_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(50,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(51,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(52,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(53,plain,
( ( ~ ( intersect @ sK1_B @ sK1_B ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(54,plain,
( ( ~ ~ ( not_equal @ sK1_B @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(55,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( not_equal @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(56,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( not_equal @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(57,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)],[46]) ).
thf(58,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)],[46]) ).
thf(59,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( intersect @ SV2 @ SV3 ) )
= $true )
| ( ( intersect @ SV3 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(60,plain,
( ( ! [SX0: $i] :
( ( member @ ( sK2_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(61,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(63,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(64,plain,
( ( intersect @ sK1_B @ sK1_B )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(65,plain,
( ( ~ ( not_equal @ sK1_B @ empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(66,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( not_equal @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( not_equal @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(68,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)],[57]) ).
thf(69,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)],[58]) ).
thf(70,plain,
! [SV3: $i,SV2: $i] :
( ( ( intersect @ SV2 @ SV3 )
= $false )
| ( ( intersect @ SV3 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV4: $i] :
( ( ( member @ ( sK2_C @ SV4 ) @ SV4 )
| ( empty @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(72,plain,
! [SV5: $i] :
( ( ~ ( empty @ SV5 )
| ! [SY15: $i] :
~ ( member @ SY15 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(73,plain,
! [SV6: $i] :
( ( ! [SY16: $i] :
( ! [SY17: $i] :
( ~ ( member @ SY17 @ SV6 )
| ~ ( member @ SY17 @ SY16 ) )
| ( intersect @ SV6 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(74,plain,
! [SV7: $i] :
( ( ! [SY18: $i] :
( ~ ( intersect @ SV7 @ SY18 )
| ~ ( ~ ( member @ ( sK4_D @ SY18 @ SV7 ) @ SV7 )
| ~ ( member @ ( sK4_D @ SY18 @ SV7 ) @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(75,plain,
( ( not_equal @ sK1_B @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV8: $i] :
( ( ! [SY19: $i] :
( ( SV8 = SY19 )
| ( not_equal @ SV8 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV9: $i] :
( ( ! [SY20: $i] :
( ~ ( not_equal @ SV9 @ SY20 )
| ( SV9 != SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV10: $i] :
( ( ! [SY21: $i] :
( ~ ( ~ ( ~ ( member @ ( sK3_D @ SY21 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK3_D @ SY21 @ SV10 ) @ SY21 ) )
| ~ ( ( member @ ( sK3_D @ SY21 @ SV10 ) @ SV10 )
| ( member @ ( sK3_D @ SY21 @ SV10 ) @ SY21 ) ) )
| ( SV10 = SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV11: $i] :
( ( ! [SY22: $i] :
( ( SV11 != SY22 )
| ~ ( ~ ! [SY23: $i] :
( ~ ( member @ SY23 @ SV11 )
| ( member @ SY23 @ SY22 ) )
| ~ ! [SY24: $i] :
( ~ ( member @ SY24 @ SY22 )
| ( member @ SY24 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV4: $i] :
( ( ( member @ ( sK2_C @ SV4 ) @ SV4 )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $true )
| ( ( ! [SY15: $i] :
~ ( member @ SY15 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY25: $i] :
( ~ ( member @ SY25 @ SV6 )
| ~ ( member @ SY25 @ SV12 ) )
| ( intersect @ SV6 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( intersect @ SV7 @ SV13 )
| ~ ( ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV7 )
| ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV14: $i,SV8: $i] :
( ( ( SV8 = SV14 )
| ( not_equal @ SV8 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV15: $i,SV9: $i] :
( ( ~ ( not_equal @ SV9 @ SV15 )
| ( SV9 != SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV10: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) )
| ~ ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) ) )
| ( SV10 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV17: $i,SV11: $i] :
( ( ( SV11 != SV17 )
| ~ ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV11 )
| ( member @ SY26 @ SV17 ) )
| ~ ! [SY27: $i] :
( ~ ( member @ SY27 @ SV17 )
| ( member @ SY27 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $false )
| ( ( ! [SY15: $i] :
~ ( member @ SY15 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV12: $i,SV6: $i] :
( ( ( ! [SY25: $i] :
( ~ ( member @ SY25 @ SV6 )
| ~ ( member @ SY25 @ SV12 ) ) )
= $true )
| ( ( intersect @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( intersect @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV7 )
| ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV14: $i,SV8: $i] :
( ( ( SV8 = SV14 )
= $true )
| ( ( not_equal @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV15: $i,SV9: $i] :
( ( ( ~ ( not_equal @ SV9 @ SV15 ) )
= $true )
| ( ( ( SV9 != SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV10: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) )
| ~ ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) ) ) )
= $true )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV17: $i,SV11: $i] :
( ( ( ( SV11 != SV17 ) )
= $true )
| ( ( ~ ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV11 )
| ( member @ SY26 @ SV17 ) )
| ~ ! [SY27: $i] :
( ~ ( member @ SY27 @ SV17 )
| ( member @ SY27 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ SV5 ) )
= $true )
| ( ( empty @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV12: $i,SV6: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV6 )
| ~ ( member @ SV19 @ SV12 ) )
= $true )
| ( ( intersect @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV13: $i,SV7: $i] :
( ( ( intersect @ SV7 @ SV13 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV7 )
| ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV15: $i,SV9: $i] :
( ( ( not_equal @ SV9 @ SV15 )
= $false )
| ( ( ( SV9 != SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV10: $i,SV16: $i] :
( ( ( ~ ( ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) )
| ~ ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) ) )
= $false )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV17: $i,SV11: $i] :
( ( ( SV11 = SV17 )
= $false )
| ( ( ~ ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV11 )
| ( member @ SY26 @ SV17 ) )
| ~ ! [SY27: $i] :
( ~ ( member @ SY27 @ SV17 )
| ( member @ SY27 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV5: $i,SV18: $i] :
( ( ( member @ SV18 @ SV5 )
= $false )
| ( ( empty @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV12: $i,SV6: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV6 ) )
= $true )
| ( ( ~ ( member @ SV19 @ SV12 ) )
= $true )
| ( ( intersect @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(103,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV7 )
| ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV13 ) )
= $false )
| ( ( intersect @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(104,plain,
! [SV15: $i,SV9: $i] :
( ( ( SV9 = SV15 )
= $false )
| ( ( not_equal @ SV9 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV10: $i,SV16: $i] :
( ( ( ~ ( ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) ) )
= $false )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(106,plain,
! [SV10: $i,SV16: $i] :
( ( ( ~ ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) ) )
= $false )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(107,plain,
! [SV17: $i,SV11: $i] :
( ( ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV11 )
| ( member @ SY26 @ SV17 ) )
| ~ ! [SY27: $i] :
( ~ ( member @ SY27 @ SV17 )
| ( member @ SY27 @ SV11 ) ) )
= $false )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV12: $i,SV6: $i,SV19: $i] :
( ( ( member @ SV19 @ SV6 )
= $false )
| ( ( ~ ( member @ SV19 @ SV12 ) )
= $true )
| ( ( intersect @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV7 ) )
= $false )
| ( ( intersect @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(110,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV13 ) )
= $false )
| ( ( intersect @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(111,plain,
! [SV10: $i,SV16: $i] :
( ( ( ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) )
= $true )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV10: $i,SV16: $i] :
( ( ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
| ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) )
= $true )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(113,plain,
! [SV17: $i,SV11: $i] :
( ( ( ~ ! [SY26: $i] :
( ~ ( member @ SY26 @ SV11 )
| ( member @ SY26 @ SV17 ) ) )
= $false )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(114,plain,
! [SV11: $i,SV17: $i] :
( ( ( ~ ! [SY27: $i] :
( ~ ( member @ SY27 @ SV17 )
| ( member @ SY27 @ SV11 ) ) )
= $false )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(115,plain,
! [SV6: $i,SV12: $i,SV19: $i] :
( ( ( member @ SV19 @ SV12 )
= $false )
| ( ( member @ SV19 @ SV6 )
= $false )
| ( ( intersect @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV7: $i,SV13: $i] :
( ( ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV7 )
= $true )
| ( ( intersect @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(117,plain,
! [SV7: $i,SV13: $i] :
( ( ( member @ ( sK4_D @ SV13 @ SV7 ) @ SV13 )
= $true )
| ( ( intersect @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(118,plain,
! [SV10: $i,SV16: $i] :
( ( ( ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 ) )
= $true )
| ( ( ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) )
= $true )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV10: $i,SV16: $i] :
( ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
= $true )
| ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 )
= $true )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV17: $i,SV11: $i] :
( ( ( ! [SY26: $i] :
( ~ ( member @ SY26 @ SV11 )
| ( member @ SY26 @ SV17 ) ) )
= $true )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(121,plain,
! [SV11: $i,SV17: $i] :
( ( ( ! [SY27: $i] :
( ~ ( member @ SY27 @ SV17 )
| ( member @ SY27 @ SV11 ) ) )
= $true )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(122,plain,
! [SV10: $i,SV16: $i] :
( ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
= $false )
| ( ( ~ ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 ) )
= $true )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV17: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV11 )
| ( member @ SV20 @ SV17 ) )
= $true )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(124,plain,
! [SV11: $i,SV17: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV17 )
| ( member @ SV21 @ SV11 ) )
= $true )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(125,plain,
! [SV10: $i,SV16: $i] :
( ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV16 )
= $false )
| ( ( member @ ( sK3_D @ SV16 @ SV10 ) @ SV10 )
= $false )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(126,plain,
! [SV17: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV11 ) )
= $true )
| ( ( member @ SV20 @ SV17 )
= $true )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(127,plain,
! [SV11: $i,SV17: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV17 ) )
= $true )
| ( ( member @ SV21 @ SV11 )
= $true )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(128,plain,
! [SV17: $i,SV11: $i,SV20: $i] :
( ( ( member @ SV20 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV17 )
= $true )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(129,plain,
! [SV11: $i,SV17: $i,SV21: $i] :
( ( ( member @ SV21 @ SV17 )
= $false )
| ( ( member @ SV21 @ SV11 )
= $true )
| ( ( SV11 = SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(130,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,129,128,125,119,117,116,115,104,101,91,80,75,70,64]) ).
thf(131,plain,
( ( ! [B: $i,C: $i] :
( ! [D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C ) )
| ( intersect @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( ( member @ ( sK4_D @ C @ B ) @ B )
& ( member @ ( sK4_D @ C @ B ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(132,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(133,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)],[26]) ).
thf(134,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
| ( not_equal @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( not_equal @ B @ C )
| ( B != C ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(135,plain,
( ( ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( intersect @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(136,plain,
( ( ! [B: $i] :
( ( member @ ( sK2_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(137,plain,
( ( ( not_equal @ sK1_B @ empty_set )
& ~ ( intersect @ sK1_B @ sK1_B ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(138,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( not_equal @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( not_equal @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(139,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)],[133]) ).
thf(140,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)],[136]) ).
thf(141,plain,
( ( ~ ( ~ ( not_equal @ sK1_B @ empty_set )
| ~ ~ ( intersect @ sK1_B @ sK1_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(142,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(143,plain,
! [SV22: $i] :
( ( ~ ( member @ SV22 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV23: $i] :
( ( ! [SY28: $i] :
( ~ ( intersect @ SV23 @ SY28 )
| ( intersect @ SY28 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(145,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( not_equal @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( not_equal @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(146,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)],[139]) ).
thf(147,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)],[140]) ).
thf(148,plain,
( ( ~ ( not_equal @ sK1_B @ empty_set )
| ~ ~ ( intersect @ sK1_B @ sK1_B ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(149,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(150,plain,
! [SV22: $i] :
( ( member @ SV22 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(151,plain,
! [SV24: $i,SV23: $i] :
( ( ~ ( intersect @ SV23 @ SV24 )
| ( intersect @ SV24 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(152,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( not_equal @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(153,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( not_equal @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(154,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)],[146]) ).
thf(155,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)],[146]) ).
thf(156,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK2_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(157,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(158,plain,
( ( ~ ( not_equal @ sK1_B @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(159,plain,
( ( ~ ~ ( intersect @ sK1_B @ sK1_B ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(160,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(161,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(162,plain,
! [SV24: $i,SV23: $i] :
( ( ( ~ ( intersect @ SV23 @ SV24 ) )
= $true )
| ( ( intersect @ SV24 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( not_equal @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(164,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( not_equal @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(165,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)],[154]) ).
thf(166,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)],[155]) ).
thf(167,plain,
( ( ! [SX0: $i] :
( ( member @ ( sK2_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(168,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(169,plain,
( ( not_equal @ sK1_B @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(170,plain,
( ( ~ ( intersect @ sK1_B @ sK1_B ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(171,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(173,plain,
! [SV24: $i,SV23: $i] :
( ( ( intersect @ SV23 @ SV24 )
= $false )
| ( ( intersect @ SV24 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(174,plain,
! [SV25: $i] :
( ( ! [SY29: $i] :
( ( SV25 = SY29 )
| ( not_equal @ SV25 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(175,plain,
! [SV26: $i] :
( ( ! [SY30: $i] :
( ~ ( not_equal @ SV26 @ SY30 )
| ( SV26 != SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(176,plain,
! [SV27: $i] :
( ( ! [SY31: $i] :
( ~ ( ~ ( ~ ( member @ ( sK3_D @ SY31 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK3_D @ SY31 @ SV27 ) @ SY31 ) )
| ~ ( ( member @ ( sK3_D @ SY31 @ SV27 ) @ SV27 )
| ( member @ ( sK3_D @ SY31 @ SV27 ) @ SY31 ) ) )
| ( SV27 = SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(177,plain,
! [SV28: $i] :
( ( ! [SY32: $i] :
( ( SV28 != SY32 )
| ~ ( ~ ! [SY33: $i] :
( ~ ( member @ SY33 @ SV28 )
| ( member @ SY33 @ SY32 ) )
| ~ ! [SY34: $i] :
( ~ ( member @ SY34 @ SY32 )
| ( member @ SY34 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(178,plain,
! [SV29: $i] :
( ( ( member @ ( sK2_C @ SV29 ) @ SV29 )
| ( empty @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(179,plain,
! [SV30: $i] :
( ( ~ ( empty @ SV30 )
| ! [SY35: $i] :
~ ( member @ SY35 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(180,plain,
( ( intersect @ sK1_B @ sK1_B )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV31: $i] :
( ( ! [SY36: $i] :
( ! [SY37: $i] :
( ~ ( member @ SY37 @ SV31 )
| ~ ( member @ SY37 @ SY36 ) )
| ( intersect @ SV31 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV32: $i] :
( ( ! [SY38: $i] :
( ~ ( intersect @ SV32 @ SY38 )
| ~ ( ~ ( member @ ( sK4_D @ SY38 @ SV32 ) @ SV32 )
| ~ ( member @ ( sK4_D @ SY38 @ SV32 ) @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV33: $i,SV25: $i] :
( ( ( SV25 = SV33 )
| ( not_equal @ SV25 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(184,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ( not_equal @ SV26 @ SV34 )
| ( SV26 != SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(185,plain,
! [SV27: $i,SV35: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) )
| ~ ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) ) )
| ( SV27 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(186,plain,
! [SV36: $i,SV28: $i] :
( ( ( SV28 != SV36 )
| ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV28 )
| ( member @ SY39 @ SV36 ) )
| ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV36 )
| ( member @ SY40 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV29: $i] :
( ( ( member @ ( sK2_C @ SV29 ) @ SV29 )
= $true )
| ( ( empty @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(188,plain,
! [SV30: $i] :
( ( ( ~ ( empty @ SV30 ) )
= $true )
| ( ( ! [SY35: $i] :
~ ( member @ SY35 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(189,plain,
! [SV37: $i,SV31: $i] :
( ( ! [SY41: $i] :
( ~ ( member @ SY41 @ SV31 )
| ~ ( member @ SY41 @ SV37 ) )
| ( intersect @ SV31 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV38: $i,SV32: $i] :
( ( ~ ( intersect @ SV32 @ SV38 )
| ~ ( ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV32 )
| ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV33: $i,SV25: $i] :
( ( ( SV25 = SV33 )
= $true )
| ( ( not_equal @ SV25 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV34: $i,SV26: $i] :
( ( ( ~ ( not_equal @ SV26 @ SV34 ) )
= $true )
| ( ( ( SV26 != SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV27: $i,SV35: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) )
| ~ ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) ) ) )
= $true )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV36: $i,SV28: $i] :
( ( ( ( SV28 != SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV28 )
| ( member @ SY39 @ SV36 ) )
| ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV36 )
| ( member @ SY40 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV30: $i] :
( ( ( empty @ SV30 )
= $false )
| ( ( ! [SY35: $i] :
~ ( member @ SY35 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(196,plain,
! [SV37: $i,SV31: $i] :
( ( ( ! [SY41: $i] :
( ~ ( member @ SY41 @ SV31 )
| ~ ( member @ SY41 @ SV37 ) ) )
= $true )
| ( ( intersect @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(197,plain,
! [SV38: $i,SV32: $i] :
( ( ( ~ ( intersect @ SV32 @ SV38 ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV32 )
| ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(198,plain,
! [SV34: $i,SV26: $i] :
( ( ( not_equal @ SV26 @ SV34 )
= $false )
| ( ( ( SV26 != SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(199,plain,
! [SV27: $i,SV35: $i] :
( ( ( ~ ( ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) )
| ~ ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) ) )
= $false )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(200,plain,
! [SV36: $i,SV28: $i] :
( ( ( SV28 = SV36 )
= $false )
| ( ( ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV28 )
| ( member @ SY39 @ SV36 ) )
| ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV36 )
| ( member @ SY40 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(201,plain,
! [SV30: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV30 ) )
= $true )
| ( ( empty @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(202,plain,
! [SV37: $i,SV31: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ SV31 )
| ~ ( member @ SV40 @ SV37 ) )
= $true )
| ( ( intersect @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(203,plain,
! [SV38: $i,SV32: $i] :
( ( ( intersect @ SV32 @ SV38 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV32 )
| ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(204,plain,
! [SV34: $i,SV26: $i] :
( ( ( SV26 = SV34 )
= $false )
| ( ( not_equal @ SV26 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(205,plain,
! [SV27: $i,SV35: $i] :
( ( ( ~ ( ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) ) )
= $false )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(206,plain,
! [SV27: $i,SV35: $i] :
( ( ( ~ ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) ) )
= $false )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(207,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV28 )
| ( member @ SY39 @ SV36 ) )
| ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV36 )
| ( member @ SY40 @ SV28 ) ) )
= $false )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(208,plain,
! [SV30: $i,SV39: $i] :
( ( ( member @ SV39 @ SV30 )
= $false )
| ( ( empty @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(209,plain,
! [SV37: $i,SV31: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ SV31 ) )
= $true )
| ( ( ~ ( member @ SV40 @ SV37 ) )
= $true )
| ( ( intersect @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(210,plain,
! [SV32: $i,SV38: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV32 )
| ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV38 ) )
= $false )
| ( ( intersect @ SV32 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(211,plain,
! [SV27: $i,SV35: $i] :
( ( ( ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) )
= $true )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(212,plain,
! [SV27: $i,SV35: $i] :
( ( ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
| ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) )
= $true )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(213,plain,
! [SV36: $i,SV28: $i] :
( ( ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV28 )
| ( member @ SY39 @ SV36 ) ) )
= $false )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(214,plain,
! [SV28: $i,SV36: $i] :
( ( ( ~ ! [SY40: $i] :
( ~ ( member @ SY40 @ SV36 )
| ( member @ SY40 @ SV28 ) ) )
= $false )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(215,plain,
! [SV37: $i,SV31: $i,SV40: $i] :
( ( ( member @ SV40 @ SV31 )
= $false )
| ( ( ~ ( member @ SV40 @ SV37 ) )
= $true )
| ( ( intersect @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(216,plain,
! [SV32: $i,SV38: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV32 ) )
= $false )
| ( ( intersect @ SV32 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(217,plain,
! [SV32: $i,SV38: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV38 ) )
= $false )
| ( ( intersect @ SV32 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(218,plain,
! [SV27: $i,SV35: $i] :
( ( ( ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 ) )
= $true )
| ( ( ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) )
= $true )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(219,plain,
! [SV27: $i,SV35: $i] :
( ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
= $true )
| ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 )
= $true )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(220,plain,
! [SV36: $i,SV28: $i] :
( ( ( ! [SY39: $i] :
( ~ ( member @ SY39 @ SV28 )
| ( member @ SY39 @ SV36 ) ) )
= $true )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(221,plain,
! [SV28: $i,SV36: $i] :
( ( ( ! [SY40: $i] :
( ~ ( member @ SY40 @ SV36 )
| ( member @ SY40 @ SV28 ) ) )
= $true )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(222,plain,
! [SV31: $i,SV37: $i,SV40: $i] :
( ( ( member @ SV40 @ SV37 )
= $false )
| ( ( member @ SV40 @ SV31 )
= $false )
| ( ( intersect @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(223,plain,
! [SV32: $i,SV38: $i] :
( ( ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV32 )
= $true )
| ( ( intersect @ SV32 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(224,plain,
! [SV32: $i,SV38: $i] :
( ( ( member @ ( sK4_D @ SV38 @ SV32 ) @ SV38 )
= $true )
| ( ( intersect @ SV32 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(225,plain,
! [SV27: $i,SV35: $i] :
( ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
= $false )
| ( ( ~ ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 ) )
= $true )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(226,plain,
! [SV36: $i,SV28: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ SV28 )
| ( member @ SV41 @ SV36 ) )
= $true )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(227,plain,
! [SV28: $i,SV36: $i,SV42: $i] :
( ( ( ~ ( member @ SV42 @ SV36 )
| ( member @ SV42 @ SV28 ) )
= $true )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(228,plain,
! [SV27: $i,SV35: $i] :
( ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV35 )
= $false )
| ( ( member @ ( sK3_D @ SV35 @ SV27 ) @ SV27 )
= $false )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(229,plain,
! [SV36: $i,SV28: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ SV28 ) )
= $true )
| ( ( member @ SV41 @ SV36 )
= $true )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(230,plain,
! [SV28: $i,SV36: $i,SV42: $i] :
( ( ( ~ ( member @ SV42 @ SV36 ) )
= $true )
| ( ( member @ SV42 @ SV28 )
= $true )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(231,plain,
! [SV36: $i,SV28: $i,SV41: $i] :
( ( ( member @ SV41 @ SV28 )
= $false )
| ( ( member @ SV41 @ SV36 )
= $true )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(232,plain,
! [SV28: $i,SV36: $i,SV42: $i] :
( ( ( member @ SV42 @ SV36 )
= $false )
| ( ( member @ SV42 @ SV28 )
= $true )
| ( ( SV28 = SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(233,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[150,232,231,228,224,223,222,219,208,204,191,187,180,173,169]) ).
thf(234,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[233,130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 02:35:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 6
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full).............
% 0.19/0.45
% 0.19/0.45 ********************************
% 0.19/0.45 * All subproblems solved! *
% 0.19/0.45 ********************************
% 0.19/0.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:233,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.47
% 0.19/0.47 %**** Beginning of derivation protocol ****
% 0.19/0.47 % SZS output start CNFRefutation
% See solution above
% 0.19/0.47
% 0.19/0.47 %**** End of derivation protocol ****
% 0.19/0.47 %**** no. of clauses in derivation: 234 ****
% 0.19/0.47 %**** clause counter: 233 ****
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:233,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------