%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:40:29 AM UTC 2026
% Result : Theorem 0.60s 0.29s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 291 ( 146 unt; 0 typ; 0 def)
% Number of atoms : 1893 ( 682 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 3226 ( 756 ~; 616 |; 15 &;1800 @)
% ( 29 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 645 ( 0 ^; 645 !; 0 ?; 645 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i ).
thf(tp_sK3_SY31,type,
sK3_SY31: $i > $i ).
thf(tp_sK4_SY34,type,
sK4_SY34: $i > $i > $i ).
thf(tp_sK5_SY36,type,
sK5_SY36: $i > $i > $i ).
thf(tp_sK6_SY44,type,
sK6_SY44: $i > $i ).
thf(tp_sK7_SY51,type,
sK7_SY51: $i > $i > $i ).
thf(tp_sK8_SY53,type,
sK8_SY53: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(1,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(2,axiom,
! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
thf(3,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(5,axiom,
! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(6,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(7,axiom,
! [B: $i] :
~ ( member @ B @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
thf(8,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( union @ B @ C ) )
<=> ( ( member @ D @ B )
| ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(9,conjecture,
! [B: $i,C: $i] :
( ( ( union @ B @ C )
= empty_set )
<=> ( ( B = empty_set )
& ( C = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).
thf(10,negated_conjecture,
( ( ! [B: $i,C: $i] :
( ( ( union @ B @ C )
= empty_set )
<=> ( ( B = empty_set )
& ( C = empty_set ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ! [B: $i,C: $i] :
( ( ( union @ B @ C )
= empty_set )
<=> ( ( B = empty_set )
& ( C = empty_set ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( union @ B @ C ) )
<=> ( ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [SY19: $i] :
( ( ( union @ sK1_B @ SY19 )
= empty_set )
<=> ( ( sK1_B = empty_set )
& ( SY19 = empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(21,plain,
( ( ( ( union @ sK1_B @ sK2_SY19 )
= empty_set )
<=> ( ( sK1_B = empty_set )
& ( sK2_SY19 = empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
( ( ( ( union @ sK1_B @ sK2_SY19 )
= empty_set )
=> ( ( sK1_B = empty_set )
& ( sK2_SY19 = empty_set ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[21]) ).
thf(23,plain,
( ( ( ( sK1_B = empty_set )
& ( sK2_SY19 = empty_set ) )
=> ( ( union @ sK1_B @ sK2_SY19 )
= empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[21]) ).
thf(24,plain,
( ( ~ ( ( ( union @ sK1_B @ sK2_SY19 )
= empty_set )
=> ( ( sK1_B = empty_set )
& ( sK2_SY19 = empty_set ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ( ( ( sK1_B = empty_set )
& ( sK2_SY19 = empty_set ) )
=> ( ( union @ sK1_B @ sK2_SY19 )
= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(26,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( union @ B @ C ) )
<=> ( ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(30,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(31,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(32,plain,
( ( ! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(33,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(34,plain,
( ( ~ ( ( ( union @ sK1_B @ sK2_SY19 )
= empty_set )
=> ( ( sK1_B = empty_set )
& ( sK2_SY19 = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(35,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ( ~ ( ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(36,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ! [SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(37,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(38,plain,
( ( ~ ( ( ( union @ sK1_B @ sK2_SY19 )
!= empty_set )
| ~ ( ( sK1_B != empty_set )
| ( sK2_SY19 != empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(40,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( member @ SX1 @ SX0 )
| ( empty @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(41,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(42,plain,
! [SV2: $i] :
( ( ! [SY20: $i] :
( ( union @ SV2 @ SY20 )
= ( union @ SY20 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(43,plain,
! [SV3: $i] :
( ( subset @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(44,plain,
! [SV4: $i] :
( ( ! [SY21: $i,SY22: $i] :
~ ( ~ ( ~ ( member @ SY22 @ ( union @ SV4 @ SY21 ) )
| ( member @ SY22 @ SV4 )
| ( member @ SY22 @ SY21 ) )
| ~ ( ~ ( ( member @ SY22 @ SV4 )
| ( member @ SY22 @ SY21 ) )
| ( member @ SY22 @ ( union @ SV4 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(45,plain,
! [SV5: $i] :
( ( ! [SY23: $i] :
~ ( ~ ( ( SV5 != SY23 )
| ! [SY24: $i] :
~ ( ~ ( ~ ( member @ SY24 @ SV5 )
| ( member @ SY24 @ SY23 ) )
| ~ ( ~ ( member @ SY24 @ SY23 )
| ( member @ SY24 @ SV5 ) ) ) )
| ~ ( ~ ! [SY25: $i] :
~ ( ~ ( ~ ( member @ SY25 @ SV5 )
| ( member @ SY25 @ SY23 ) )
| ~ ( ~ ( member @ SY25 @ SY23 )
| ( member @ SY25 @ SV5 ) ) )
| ( SV5 = SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(46,plain,
! [SV6: $i] :
( ( ! [SY26: $i] :
~ ( ~ ( ( SV6 != SY26 )
| ~ ( ~ ( subset @ SV6 @ SY26 )
| ~ ( subset @ SY26 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV6 @ SY26 )
| ~ ( subset @ SY26 @ SV6 ) )
| ( SV6 = SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(47,plain,
( ( ( ( union @ sK1_B @ sK2_SY19 )
!= empty_set )
| ~ ( ( sK1_B != empty_set )
| ( sK2_SY19 != empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(48,plain,
! [SV7: $i] :
( ( ! [SY27: $i] :
~ ( ~ ( ~ ( subset @ SV7 @ SY27 )
| ! [SY28: $i] :
( ~ ( member @ SY28 @ SV7 )
| ( member @ SY28 @ SY27 ) ) )
| ~ ( ~ ! [SY29: $i] :
( ~ ( member @ SY29 @ SV7 )
| ( member @ SY29 @ SY27 ) )
| ( subset @ SV7 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(49,plain,
! [SV8: $i] :
( ( ~ ( ~ ( ~ ( empty @ SV8 )
| ! [SY30: $i] :
~ ( member @ SY30 @ SV8 ) )
| ~ ( ~ ! [SY31: $i] :
~ ( member @ SY31 @ SV8 )
| ( empty @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV9: $i,SV2: $i] :
( ( ( union @ SV2 @ SV9 )
= ( union @ SV9 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY32: $i] :
~ ( ~ ( ~ ( member @ SY32 @ ( union @ SV4 @ SV10 ) )
| ( member @ SY32 @ SV4 )
| ( member @ SY32 @ SV10 ) )
| ~ ( ~ ( ( member @ SY32 @ SV4 )
| ( member @ SY32 @ SV10 ) )
| ( member @ SY32 @ ( union @ SV4 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ( ( SV5 != SV11 )
| ! [SY33: $i] :
~ ( ~ ( ~ ( member @ SY33 @ SV5 )
| ( member @ SY33 @ SV11 ) )
| ~ ( ~ ( member @ SY33 @ SV11 )
| ( member @ SY33 @ SV5 ) ) ) )
| ~ ( ~ ! [SY34: $i] :
~ ( ~ ( ~ ( member @ SY34 @ SV5 )
| ( member @ SY34 @ SV11 ) )
| ~ ( ~ ( member @ SY34 @ SV11 )
| ( member @ SY34 @ SV5 ) ) )
| ( SV5 = SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( ( SV6 != SV12 )
| ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) )
| ( SV6 = SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
( ( ( union @ sK1_B @ sK2_SY19 )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(56,plain,
( ( ~ ( ( sK1_B != empty_set )
| ( sK2_SY19 != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(57,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV7 @ SV13 )
| ! [SY35: $i] :
( ~ ( member @ SY35 @ SV7 )
| ( member @ SY35 @ SV13 ) ) )
| ~ ( ~ ! [SY36: $i] :
( ~ ( member @ SY36 @ SV7 )
| ( member @ SY36 @ SV13 ) )
| ( subset @ SV7 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV8: $i] :
( ( ~ ( ~ ( empty @ SV8 )
| ! [SY30: $i] :
~ ( member @ SY30 @ SV8 ) )
| ~ ( ~ ! [SY31: $i] :
~ ( member @ SY31 @ SV8 )
| ( empty @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
| ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
| ~ ( ~ ( ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
| ( member @ SV14 @ ( union @ SV4 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(60,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ( SV5 != SV11 )
| ! [SY33: $i] :
~ ( ~ ( ~ ( member @ SY33 @ SV5 )
| ( member @ SY33 @ SV11 ) )
| ~ ( ~ ( member @ SY33 @ SV11 )
| ( member @ SY33 @ SV5 ) ) ) )
| ~ ( ~ ! [SY34: $i] :
~ ( ~ ( ~ ( member @ SY34 @ SV5 )
| ( member @ SY34 @ SV11 ) )
| ~ ( ~ ( member @ SY34 @ SV11 )
| ( member @ SY34 @ SV5 ) ) )
| ( SV5 = SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(61,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ( SV6 != SV12 )
| ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) )
| ( SV6 = SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(62,plain,
( ( ( union @ sK1_B @ sK2_SY19 )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(63,plain,
( ( ( sK1_B != empty_set )
| ( sK2_SY19 != empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(64,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ SV13 )
| ! [SY35: $i] :
( ~ ( member @ SY35 @ SV7 )
| ( member @ SY35 @ SV13 ) ) )
| ~ ( ~ ! [SY36: $i] :
( ~ ( member @ SY36 @ SV7 )
| ( member @ SY36 @ SV13 ) )
| ( subset @ SV7 @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV8: $i] :
( ( ~ ( ~ ( empty @ SV8 )
| ! [SY30: $i] :
~ ( member @ SY30 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(66,plain,
! [SV8: $i] :
( ( ~ ( ~ ! [SY31: $i] :
~ ( member @ SY31 @ SV8 )
| ( empty @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(67,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ~ ( ~ ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
| ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
| ~ ( ~ ( ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
| ( member @ SV14 @ ( union @ SV4 @ SV10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ( SV5 != SV11 )
| ! [SY33: $i] :
~ ( ~ ( ~ ( member @ SY33 @ SV5 )
| ( member @ SY33 @ SV11 ) )
| ~ ( ~ ( member @ SY33 @ SV11 )
| ( member @ SY33 @ SV5 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(69,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ! [SY34: $i] :
~ ( ~ ( ~ ( member @ SY34 @ SV5 )
| ( member @ SY34 @ SV11 ) )
| ~ ( ~ ( member @ SY34 @ SV11 )
| ( member @ SY34 @ SV5 ) ) )
| ( SV5 = SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(70,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ( SV6 != SV12 )
| ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(71,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) )
| ( SV6 = SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(72,plain,
( ( ( sK1_B != empty_set )
= $true )
| ( ( sK2_SY19 != empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ SV13 )
| ! [SY35: $i] :
( ~ ( member @ SY35 @ SV7 )
| ( member @ SY35 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(74,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ! [SY36: $i] :
( ~ ( member @ SY36 @ SV7 )
| ( member @ SY36 @ SV13 ) )
| ( subset @ SV7 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(75,plain,
! [SV8: $i] :
( ( ~ ( empty @ SV8 )
| ! [SY30: $i] :
~ ( member @ SY30 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(76,plain,
! [SV8: $i] :
( ( ~ ! [SY31: $i] :
~ ( member @ SY31 @ SV8 )
| ( empty @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(77,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ~ ( ~ ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
| ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(78,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ~ ( ~ ( ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
| ( member @ SV14 @ ( union @ SV4 @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(79,plain,
! [SV11: $i,SV5: $i] :
( ( ( SV5 != SV11 )
| ! [SY33: $i] :
~ ( ~ ( ~ ( member @ SY33 @ SV5 )
| ( member @ SY33 @ SV11 ) )
| ~ ( ~ ( member @ SY33 @ SV11 )
| ( member @ SY33 @ SV5 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(80,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ! [SY34: $i] :
~ ( ~ ( ~ ( member @ SY34 @ SV5 )
| ( member @ SY34 @ SV11 ) )
| ~ ( ~ ( member @ SY34 @ SV11 )
| ( member @ SY34 @ SV5 ) ) )
| ( SV5 = SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(81,plain,
! [SV12: $i,SV6: $i] :
( ( ( SV6 != SV12 )
| ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(82,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) )
| ( SV6 = SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(83,plain,
( ( ( sK1_B = empty_set )
= $false )
| ( ( sK2_SY19 != empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(84,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV13 )
| ! [SY35: $i] :
( ~ ( member @ SY35 @ SV7 )
| ( member @ SY35 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(85,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ! [SY36: $i] :
( ~ ( member @ SY36 @ SV7 )
| ( member @ SY36 @ SV13 ) )
| ( subset @ SV7 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(86,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ SV8 ) )
= $true )
| ( ( ! [SY30: $i] :
~ ( member @ SY30 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(87,plain,
! [SV8: $i] :
( ( ( ~ ! [SY31: $i] :
~ ( member @ SY31 @ SV8 ) )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ~ ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
| ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(89,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ~ ( ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
| ( member @ SV14 @ ( union @ SV4 @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(90,plain,
! [SV11: $i,SV5: $i] :
( ( ( SV5 != SV11 )
= $true )
| ( ( ! [SY33: $i] :
~ ( ~ ( ~ ( member @ SY33 @ SV5 )
| ( member @ SY33 @ SV11 ) )
| ~ ( ~ ( member @ SY33 @ SV11 )
| ( member @ SY33 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(91,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ! [SY34: $i] :
~ ( ~ ( ~ ( member @ SY34 @ SV5 )
| ( member @ SY34 @ SV11 ) )
| ~ ( ~ ( member @ SY34 @ SV11 )
| ( member @ SY34 @ SV5 ) ) ) )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(92,plain,
! [SV12: $i,SV6: $i] :
( ( ( SV6 != SV12 )
= $true )
| ( ( ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(93,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) ) )
= $true )
| ( ( SV6 = SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(94,plain,
( ( ( sK2_SY19 = empty_set )
= $false )
| ( ( sK1_B = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(95,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV13 ) )
= $true )
| ( ( ! [SY35: $i] :
( ~ ( member @ SY35 @ SV7 )
| ( member @ SY35 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(96,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ! [SY36: $i] :
( ~ ( member @ SY36 @ SV7 )
| ( member @ SY36 @ SV13 ) ) )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(97,plain,
! [SV8: $i] :
( ( ( empty @ SV8 )
= $false )
| ( ( ! [SY30: $i] :
~ ( member @ SY30 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV8: $i] :
( ( ( ! [SY31: $i] :
~ ( member @ SY31 @ SV8 ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(99,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ ( union @ SV4 @ SV10 ) ) )
= $true )
| ( ( ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(100,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) ) )
= $true )
| ( ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(101,plain,
! [SV11: $i,SV5: $i] :
( ( ( SV5 = SV11 )
= $false )
| ( ( ! [SY33: $i] :
~ ( ~ ( ~ ( member @ SY33 @ SV5 )
| ( member @ SY33 @ SV11 ) )
| ~ ( ~ ( member @ SY33 @ SV11 )
| ( member @ SY33 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(102,plain,
! [SV11: $i,SV5: $i] :
( ( ( ! [SY34: $i] :
~ ( ~ ( ~ ( member @ SY34 @ SV5 )
| ( member @ SY34 @ SV11 ) )
| ~ ( ~ ( member @ SY34 @ SV11 )
| ( member @ SY34 @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(103,plain,
! [SV12: $i,SV6: $i] :
( ( ( SV6 = SV12 )
= $false )
| ( ( ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) ) )
= $false )
| ( ( SV6 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV13: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV13 )
= $false )
| ( ( ! [SY35: $i] :
( ~ ( member @ SY35 @ SV7 )
| ( member @ SY35 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV13: $i,SV7: $i] :
( ( ( ! [SY36: $i] :
( ~ ( member @ SY36 @ SV7 )
| ( member @ SY36 @ SV13 ) ) )
= $false )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(107,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV8 ) )
= $true )
| ( ( empty @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV8: $i] :
( ( ( ~ ( member @ ( sK3_SY31 @ SV8 ) @ SV8 ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(109,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
= $false )
| ( ( ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ( ( member @ SV14 @ SV4 )
| ( member @ SV14 @ SV10 ) )
= $false )
| ( ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( member @ SV16 @ SV5 )
| ( member @ SV16 @ SV11 ) )
| ~ ( ~ ( member @ SV16 @ SV11 )
| ( member @ SV16 @ SV5 ) ) ) )
= $true )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 ) )
| ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[102]) ).
thf(113,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) )
= $false )
| ( ( SV6 = SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV12 )
| ~ ( subset @ SV12 @ SV6 ) )
= $true )
| ( ( SV6 = SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(115,plain,
! [SV13: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV7 )
| ( member @ SV17 @ SV13 ) )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK5_SY36 @ SV13 @ SV7 ) @ SV7 )
| ( member @ ( sK5_SY36 @ SV13 @ SV7 ) @ SV13 ) )
= $false )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[106]) ).
thf(117,plain,
! [SV8: $i,SV15: $i] :
( ( ( member @ SV15 @ SV8 )
= $false )
| ( ( empty @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV8: $i] :
( ( ( member @ ( sK3_SY31 @ SV8 ) @ SV8 )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(119,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ( member @ SV14 @ SV4 )
= $true )
| ( ( member @ SV14 @ SV10 )
= $true )
| ( ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV10: $i,SV4: $i,SV14: $i] :
( ( ( member @ SV14 @ SV4 )
= $false )
| ( ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(121,plain,
! [SV4: $i,SV10: $i,SV14: $i] :
( ( ( member @ SV14 @ SV10 )
= $false )
| ( ( member @ SV14 @ ( union @ SV4 @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(122,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( ~ ( member @ SV16 @ SV5 )
| ( member @ SV16 @ SV11 ) )
| ~ ( ~ ( member @ SV16 @ SV11 )
| ( member @ SV16 @ SV5 ) ) )
= $false )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 ) )
| ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(124,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV12 ) )
= $false )
| ( ( SV6 = SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(125,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV6 ) )
= $false )
| ( ( SV6 = SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(126,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ SV6 ) )
= $true )
| ( ( SV6 = SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV13: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV7 ) )
= $true )
| ( ( member @ SV17 @ SV13 )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK5_SY36 @ SV13 @ SV7 ) @ SV7 ) )
= $false )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(129,plain,
! [SV7: $i,SV13: $i] :
( ( ( member @ ( sK5_SY36 @ SV13 @ SV7 ) @ SV13 )
= $false )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(130,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( ~ ( member @ SV16 @ SV5 )
| ( member @ SV16 @ SV11 ) ) )
= $false )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(131,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( ~ ( member @ SV16 @ SV11 )
| ( member @ SV16 @ SV5 ) ) )
= $false )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(132,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV12: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV12 )
= $true )
| ( ( SV6 = SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(134,plain,
! [SV6: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV6 )
= $true )
| ( ( SV6 = SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(135,plain,
! [SV12: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV12 )
= $false )
| ( ( ~ ( subset @ SV12 @ SV6 ) )
= $true )
| ( ( SV6 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV13: $i,SV7: $i,SV17: $i] :
( ( ( member @ SV17 @ SV7 )
= $false )
| ( ( member @ SV17 @ SV13 )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV7: $i,SV13: $i] :
( ( ( member @ ( sK5_SY36 @ SV13 @ SV7 ) @ SV7 )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(138,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV5 )
| ( member @ SV16 @ SV11 ) )
= $true )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(139,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV11 )
| ( member @ SV16 @ SV5 ) )
= $true )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(140,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV6: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV6 )
= $false )
| ( ( subset @ SV6 @ SV12 )
= $false )
| ( ( SV6 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(142,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV5 ) )
= $true )
| ( ( member @ SV16 @ SV11 )
= $true )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV11 ) )
= $true )
| ( ( member @ SV16 @ SV5 )
= $true )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(145,plain,
! [SV5: $i,SV11: $i] :
( ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(146,plain,
! [SV11: $i,SV5: $i,SV16: $i] :
( ( ( member @ SV16 @ SV5 )
= $false )
| ( ( member @ SV16 @ SV11 )
= $true )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(147,plain,
! [SV5: $i,SV11: $i,SV16: $i] :
( ( ( member @ SV16 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV5 )
= $true )
| ( ( SV5 = SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(148,plain,
! [SV5: $i,SV11: $i] :
( ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
= $true )
| ( ( ~ ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) )
= $false )
| ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
= $false )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(150,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
| ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 ) )
= $false )
| ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(151,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
= $false )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(152,plain,
! [SV5: $i,SV11: $i] :
( ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
= $false )
| ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
= $false )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(153,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(154,plain,
! [SV5: $i,SV11: $i] :
( ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
= $false )
| ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(155,plain,
! [SV5: $i,SV11: $i] :
( ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
= $true )
| ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
= $false )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(156,plain,
! [SV5: $i,SV11: $i] :
( ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV11 )
= $true )
| ( ( member @ ( sK4_SY34 @ SV11 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(157,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[43,156,155,154,152,147,146,141,137,136,134,133,129,121,120,119,118,117,94,62,51,50]) ).
thf(158,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( union @ B @ C ) )
<=> ( ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(159,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(160,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(161,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(162,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(163,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(164,plain,
( ( ! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(165,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(166,plain,
( ( ~ ( ( ( sK1_B = empty_set )
& ( sK2_SY19 = empty_set ) )
=> ( ( union @ sK1_B @ sK2_SY19 )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ( ~ ( ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(168,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ! [SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(169,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( member @ SX1 @ SX0 )
| ( empty @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(170,plain,
( ( ~ ( ~ ~ ( ( sK1_B != empty_set )
| ( sK2_SY19 != empty_set ) )
| ( ( union @ sK1_B @ sK2_SY19 )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(171,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(173,plain,
! [SV18: $i] :
( ( ~ ( member @ SV18 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(174,plain,
! [SV19: $i] :
( ( ! [SY37: $i] :
( ( union @ SV19 @ SY37 )
= ( union @ SY37 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV20: $i] :
( ( subset @ SV20 @ SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV21: $i] :
( ( ! [SY38: $i,SY39: $i] :
~ ( ~ ( ~ ( member @ SY39 @ ( union @ SV21 @ SY38 ) )
| ( member @ SY39 @ SV21 )
| ( member @ SY39 @ SY38 ) )
| ~ ( ~ ( ( member @ SY39 @ SV21 )
| ( member @ SY39 @ SY38 ) )
| ( member @ SY39 @ ( union @ SV21 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV22: $i] :
( ( ! [SY40: $i] :
~ ( ~ ( ( SV22 != SY40 )
| ! [SY41: $i] :
~ ( ~ ( ~ ( member @ SY41 @ SV22 )
| ( member @ SY41 @ SY40 ) )
| ~ ( ~ ( member @ SY41 @ SY40 )
| ( member @ SY41 @ SV22 ) ) ) )
| ~ ( ~ ! [SY42: $i] :
~ ( ~ ( ~ ( member @ SY42 @ SV22 )
| ( member @ SY42 @ SY40 ) )
| ~ ( ~ ( member @ SY42 @ SY40 )
| ( member @ SY42 @ SV22 ) ) )
| ( SV22 = SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(178,plain,
! [SV23: $i] :
( ( ~ ( ~ ( ~ ( empty @ SV23 )
| ! [SY43: $i] :
~ ( member @ SY43 @ SV23 ) )
| ~ ( ~ ! [SY44: $i] :
~ ( member @ SY44 @ SV23 )
| ( empty @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(179,plain,
( ( ~ ~ ( ( sK1_B != empty_set )
| ( sK2_SY19 != empty_set ) )
| ( ( union @ sK1_B @ sK2_SY19 )
= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(180,plain,
! [SV24: $i] :
( ( ! [SY45: $i] :
~ ( ~ ( ~ ( subset @ SV24 @ SY45 )
| ! [SY46: $i] :
( ~ ( member @ SY46 @ SV24 )
| ( member @ SY46 @ SY45 ) ) )
| ~ ( ~ ! [SY47: $i] :
( ~ ( member @ SY47 @ SV24 )
| ( member @ SY47 @ SY45 ) )
| ( subset @ SV24 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(181,plain,
! [SV25: $i] :
( ( ! [SY48: $i] :
~ ( ~ ( ( SV25 != SY48 )
| ~ ( ~ ( subset @ SV25 @ SY48 )
| ~ ( subset @ SY48 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV25 @ SY48 )
| ~ ( subset @ SY48 @ SV25 ) )
| ( SV25 = SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(182,plain,
! [SV18: $i] :
( ( member @ SV18 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(183,plain,
! [SV26: $i,SV19: $i] :
( ( ( union @ SV19 @ SV26 )
= ( union @ SV26 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(184,plain,
! [SV27: $i,SV21: $i] :
( ( ! [SY49: $i] :
~ ( ~ ( ~ ( member @ SY49 @ ( union @ SV21 @ SV27 ) )
| ( member @ SY49 @ SV21 )
| ( member @ SY49 @ SV27 ) )
| ~ ( ~ ( ( member @ SY49 @ SV21 )
| ( member @ SY49 @ SV27 ) )
| ( member @ SY49 @ ( union @ SV21 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(185,plain,
! [SV28: $i,SV22: $i] :
( ( ~ ( ~ ( ( SV22 != SV28 )
| ! [SY50: $i] :
~ ( ~ ( ~ ( member @ SY50 @ SV22 )
| ( member @ SY50 @ SV28 ) )
| ~ ( ~ ( member @ SY50 @ SV28 )
| ( member @ SY50 @ SV22 ) ) ) )
| ~ ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( member @ SY51 @ SV22 )
| ( member @ SY51 @ SV28 ) )
| ~ ( ~ ( member @ SY51 @ SV28 )
| ( member @ SY51 @ SV22 ) ) )
| ( SV22 = SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV23: $i] :
( ( ~ ( ~ ( empty @ SV23 )
| ! [SY43: $i] :
~ ( member @ SY43 @ SV23 ) )
| ~ ( ~ ! [SY44: $i] :
~ ( member @ SY44 @ SV23 )
| ( empty @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(187,plain,
( ( ~ ~ ( ( sK1_B != empty_set )
| ( sK2_SY19 != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(188,plain,
( ( ( union @ sK1_B @ sK2_SY19 )
= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(189,plain,
! [SV29: $i,SV24: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV24 @ SV29 )
| ! [SY52: $i] :
( ~ ( member @ SY52 @ SV24 )
| ( member @ SY52 @ SV29 ) ) )
| ~ ( ~ ! [SY53: $i] :
( ~ ( member @ SY53 @ SV24 )
| ( member @ SY53 @ SV29 ) )
| ( subset @ SV24 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(190,plain,
! [SV30: $i,SV25: $i] :
( ( ~ ( ~ ( ( SV25 != SV30 )
| ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) )
| ( SV25 = SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(191,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
| ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
| ~ ( ~ ( ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
| ( member @ SV31 @ ( union @ SV21 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(192,plain,
! [SV28: $i,SV22: $i] :
( ( ~ ( ( SV22 != SV28 )
| ! [SY50: $i] :
~ ( ~ ( ~ ( member @ SY50 @ SV22 )
| ( member @ SY50 @ SV28 ) )
| ~ ( ~ ( member @ SY50 @ SV28 )
| ( member @ SY50 @ SV22 ) ) ) )
| ~ ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( member @ SY51 @ SV22 )
| ( member @ SY51 @ SV28 ) )
| ~ ( ~ ( member @ SY51 @ SV28 )
| ( member @ SY51 @ SV22 ) ) )
| ( SV22 = SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(193,plain,
! [SV23: $i] :
( ( ~ ( ~ ( empty @ SV23 )
| ! [SY43: $i] :
~ ( member @ SY43 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(194,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY44: $i] :
~ ( member @ SY44 @ SV23 )
| ( empty @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(195,plain,
( ( ~ ( ( sK1_B != empty_set )
| ( sK2_SY19 != empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(196,plain,
! [SV29: $i,SV24: $i] :
( ( ~ ( ~ ( subset @ SV24 @ SV29 )
| ! [SY52: $i] :
( ~ ( member @ SY52 @ SV24 )
| ( member @ SY52 @ SV29 ) ) )
| ~ ( ~ ! [SY53: $i] :
( ~ ( member @ SY53 @ SV24 )
| ( member @ SY53 @ SV29 ) )
| ( subset @ SV24 @ SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(197,plain,
! [SV30: $i,SV25: $i] :
( ( ~ ( ( SV25 != SV30 )
| ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) )
| ( SV25 = SV30 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(198,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ~ ( ~ ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
| ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
| ~ ( ~ ( ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
| ( member @ SV31 @ ( union @ SV21 @ SV27 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(199,plain,
! [SV28: $i,SV22: $i] :
( ( ~ ( ( SV22 != SV28 )
| ! [SY50: $i] :
~ ( ~ ( ~ ( member @ SY50 @ SV22 )
| ( member @ SY50 @ SV28 ) )
| ~ ( ~ ( member @ SY50 @ SV28 )
| ( member @ SY50 @ SV22 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(200,plain,
! [SV28: $i,SV22: $i] :
( ( ~ ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( member @ SY51 @ SV22 )
| ( member @ SY51 @ SV28 ) )
| ~ ( ~ ( member @ SY51 @ SV28 )
| ( member @ SY51 @ SV22 ) ) )
| ( SV22 = SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(201,plain,
! [SV23: $i] :
( ( ~ ( empty @ SV23 )
| ! [SY43: $i] :
~ ( member @ SY43 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(202,plain,
! [SV23: $i] :
( ( ~ ! [SY44: $i] :
~ ( member @ SY44 @ SV23 )
| ( empty @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(203,plain,
( ( ( sK1_B != empty_set )
| ( sK2_SY19 != empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV29: $i,SV24: $i] :
( ( ~ ( ~ ( subset @ SV24 @ SV29 )
| ! [SY52: $i] :
( ~ ( member @ SY52 @ SV24 )
| ( member @ SY52 @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(205,plain,
! [SV29: $i,SV24: $i] :
( ( ~ ( ~ ! [SY53: $i] :
( ~ ( member @ SY53 @ SV24 )
| ( member @ SY53 @ SV29 ) )
| ( subset @ SV24 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(206,plain,
! [SV30: $i,SV25: $i] :
( ( ~ ( ( SV25 != SV30 )
| ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(207,plain,
! [SV30: $i,SV25: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) )
| ( SV25 = SV30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(208,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ~ ( ~ ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
| ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(209,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ~ ( ~ ( ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
| ( member @ SV31 @ ( union @ SV21 @ SV27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(210,plain,
! [SV28: $i,SV22: $i] :
( ( ( SV22 != SV28 )
| ! [SY50: $i] :
~ ( ~ ( ~ ( member @ SY50 @ SV22 )
| ( member @ SY50 @ SV28 ) )
| ~ ( ~ ( member @ SY50 @ SV28 )
| ( member @ SY50 @ SV22 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(211,plain,
! [SV28: $i,SV22: $i] :
( ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( member @ SY51 @ SV22 )
| ( member @ SY51 @ SV28 ) )
| ~ ( ~ ( member @ SY51 @ SV28 )
| ( member @ SY51 @ SV22 ) ) )
| ( SV22 = SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(212,plain,
! [SV23: $i] :
( ( ( ~ ( empty @ SV23 ) )
= $true )
| ( ( ! [SY43: $i] :
~ ( member @ SY43 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(213,plain,
! [SV23: $i] :
( ( ( ~ ! [SY44: $i] :
~ ( member @ SY44 @ SV23 ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(214,plain,
( ( sK1_B != empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(215,plain,
( ( sK2_SY19 != empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(216,plain,
! [SV29: $i,SV24: $i] :
( ( ~ ( subset @ SV24 @ SV29 )
| ! [SY52: $i] :
( ~ ( member @ SY52 @ SV24 )
| ( member @ SY52 @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(217,plain,
! [SV29: $i,SV24: $i] :
( ( ~ ! [SY53: $i] :
( ~ ( member @ SY53 @ SV24 )
| ( member @ SY53 @ SV29 ) )
| ( subset @ SV24 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(218,plain,
! [SV30: $i,SV25: $i] :
( ( ( SV25 != SV30 )
| ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(219,plain,
! [SV30: $i,SV25: $i] :
( ( ~ ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) )
| ( SV25 = SV30 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(220,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ~ ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
| ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(221,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ~ ( ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
| ( member @ SV31 @ ( union @ SV21 @ SV27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(222,plain,
! [SV28: $i,SV22: $i] :
( ( ( SV22 != SV28 )
= $true )
| ( ( ! [SY50: $i] :
~ ( ~ ( ~ ( member @ SY50 @ SV22 )
| ( member @ SY50 @ SV28 ) )
| ~ ( ~ ( member @ SY50 @ SV28 )
| ( member @ SY50 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(223,plain,
! [SV28: $i,SV22: $i] :
( ( ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( member @ SY51 @ SV22 )
| ( member @ SY51 @ SV28 ) )
| ~ ( ~ ( member @ SY51 @ SV28 )
| ( member @ SY51 @ SV22 ) ) ) )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(224,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $false )
| ( ( ! [SY43: $i] :
~ ( member @ SY43 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(225,plain,
! [SV23: $i] :
( ( ( ! [SY44: $i] :
~ ( member @ SY44 @ SV23 ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(226,plain,
( ( sK1_B = empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(227,plain,
( ( sK2_SY19 = empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(228,plain,
! [SV29: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV29 ) )
= $true )
| ( ( ! [SY52: $i] :
( ~ ( member @ SY52 @ SV24 )
| ( member @ SY52 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(229,plain,
! [SV29: $i,SV24: $i] :
( ( ( ~ ! [SY53: $i] :
( ~ ( member @ SY53 @ SV24 )
| ( member @ SY53 @ SV29 ) ) )
= $true )
| ( ( subset @ SV24 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(230,plain,
! [SV30: $i,SV25: $i] :
( ( ( SV25 != SV30 )
= $true )
| ( ( ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(231,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) ) )
= $true )
| ( ( SV25 = SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(232,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ ( union @ SV21 @ SV27 ) ) )
= $true )
| ( ( ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(233,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ( ~ ( ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) ) )
= $true )
| ( ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(234,plain,
! [SV28: $i,SV22: $i] :
( ( ( SV22 = SV28 )
= $false )
| ( ( ! [SY50: $i] :
~ ( ~ ( ~ ( member @ SY50 @ SV22 )
| ( member @ SY50 @ SV28 ) )
| ~ ( ~ ( member @ SY50 @ SV28 )
| ( member @ SY50 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(235,plain,
! [SV28: $i,SV22: $i] :
( ( ( ! [SY51: $i] :
~ ( ~ ( ~ ( member @ SY51 @ SV22 )
| ( member @ SY51 @ SV28 ) )
| ~ ( ~ ( member @ SY51 @ SV28 )
| ( member @ SY51 @ SV22 ) ) ) )
= $false )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(236,plain,
! [SV23: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV23 ) )
= $true )
| ( ( empty @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(237,plain,
! [SV23: $i] :
( ( ( ~ ( member @ ( sK6_SY44 @ SV23 ) @ SV23 ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[225]) ).
thf(238,plain,
! [SV29: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV29 )
= $false )
| ( ( ! [SY52: $i] :
( ~ ( member @ SY52 @ SV24 )
| ( member @ SY52 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(239,plain,
! [SV29: $i,SV24: $i] :
( ( ( ! [SY53: $i] :
( ~ ( member @ SY53 @ SV24 )
| ( member @ SY53 @ SV29 ) ) )
= $false )
| ( ( subset @ SV24 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(240,plain,
! [SV30: $i,SV25: $i] :
( ( ( SV25 = SV30 )
= $false )
| ( ( ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(241,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) ) )
= $false )
| ( ( SV25 = SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(242,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
= $false )
| ( ( ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(243,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ( ( member @ SV31 @ SV21 )
| ( member @ SV31 @ SV27 ) )
= $false )
| ( ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV28: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( ~ ( ~ ( member @ SV33 @ SV22 )
| ( member @ SV33 @ SV28 ) )
| ~ ( ~ ( member @ SV33 @ SV28 )
| ( member @ SV33 @ SV22 ) ) ) )
= $true )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(245,plain,
! [SV22: $i,SV28: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 ) )
| ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) ) ) )
= $false )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[235]) ).
thf(246,plain,
! [SV23: $i,SV32: $i] :
( ( ( member @ SV32 @ SV23 )
= $false )
| ( ( empty @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(247,plain,
! [SV23: $i] :
( ( ( member @ ( sK6_SY44 @ SV23 ) @ SV23 )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(248,plain,
! [SV29: $i,SV24: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ SV24 )
| ( member @ SV34 @ SV29 ) )
= $true )
| ( ( subset @ SV24 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV24: $i,SV29: $i] :
( ( ( ~ ( member @ ( sK8_SY53 @ SV29 @ SV24 ) @ SV24 )
| ( member @ ( sK8_SY53 @ SV29 @ SV24 ) @ SV29 ) )
= $false )
| ( ( subset @ SV24 @ SV29 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[239]) ).
thf(250,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) )
= $false )
| ( ( SV25 = SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(251,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV30 )
| ~ ( subset @ SV30 @ SV25 ) )
= $true )
| ( ( SV25 = SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(252,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ( member @ SV31 @ SV21 )
= $true )
| ( ( member @ SV31 @ SV27 )
= $true )
| ( ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(253,plain,
! [SV27: $i,SV21: $i,SV31: $i] :
( ( ( member @ SV31 @ SV21 )
= $false )
| ( ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(254,plain,
! [SV21: $i,SV27: $i,SV31: $i] :
( ( ( member @ SV31 @ SV27 )
= $false )
| ( ( member @ SV31 @ ( union @ SV21 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(255,plain,
! [SV28: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( ~ ( member @ SV33 @ SV22 )
| ( member @ SV33 @ SV28 ) )
| ~ ( ~ ( member @ SV33 @ SV28 )
| ( member @ SV33 @ SV22 ) ) )
= $false )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(256,plain,
! [SV22: $i,SV28: $i] :
( ( ( ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 ) )
| ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(257,plain,
! [SV29: $i,SV24: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ SV24 ) )
= $true )
| ( ( member @ SV34 @ SV29 )
= $true )
| ( ( subset @ SV24 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(258,plain,
! [SV24: $i,SV29: $i] :
( ( ( ~ ( member @ ( sK8_SY53 @ SV29 @ SV24 ) @ SV24 ) )
= $false )
| ( ( subset @ SV24 @ SV29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(259,plain,
! [SV24: $i,SV29: $i] :
( ( ( member @ ( sK8_SY53 @ SV29 @ SV24 ) @ SV29 )
= $false )
| ( ( subset @ SV24 @ SV29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(260,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV30 ) )
= $false )
| ( ( SV25 = SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(261,plain,
! [SV25: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV25 ) )
= $false )
| ( ( SV25 = SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(262,plain,
! [SV30: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV30 ) )
= $true )
| ( ( ~ ( subset @ SV30 @ SV25 ) )
= $true )
| ( ( SV25 = SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(263,plain,
! [SV28: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( ~ ( member @ SV33 @ SV22 )
| ( member @ SV33 @ SV28 ) ) )
= $false )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(264,plain,
! [SV22: $i,SV28: $i,SV33: $i] :
( ( ( ~ ( ~ ( member @ SV33 @ SV28 )
| ( member @ SV33 @ SV22 ) ) )
= $false )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(265,plain,
! [SV22: $i,SV28: $i] :
( ( ( ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(266,plain,
! [SV29: $i,SV24: $i,SV34: $i] :
( ( ( member @ SV34 @ SV24 )
= $false )
| ( ( member @ SV34 @ SV29 )
= $true )
| ( ( subset @ SV24 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(267,plain,
! [SV24: $i,SV29: $i] :
( ( ( member @ ( sK8_SY53 @ SV29 @ SV24 ) @ SV24 )
= $true )
| ( ( subset @ SV24 @ SV29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(268,plain,
! [SV30: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV30 )
= $true )
| ( ( SV25 = SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(269,plain,
! [SV25: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV25 )
= $true )
| ( ( SV25 = SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(270,plain,
! [SV30: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV30 )
= $false )
| ( ( ~ ( subset @ SV30 @ SV25 ) )
= $true )
| ( ( SV25 = SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(271,plain,
! [SV28: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV22 )
| ( member @ SV33 @ SV28 ) )
= $true )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(272,plain,
! [SV22: $i,SV28: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV28 )
| ( member @ SV33 @ SV22 ) )
= $true )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(273,plain,
! [SV22: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(274,plain,
! [SV25: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV25 )
= $false )
| ( ( subset @ SV25 @ SV30 )
= $false )
| ( ( SV25 = SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(275,plain,
! [SV28: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV22 ) )
= $true )
| ( ( member @ SV33 @ SV28 )
= $true )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(276,plain,
! [SV22: $i,SV28: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV28 ) )
= $true )
| ( ( member @ SV33 @ SV22 )
= $true )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(277,plain,
! [SV22: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(278,plain,
! [SV22: $i,SV28: $i] :
( ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(279,plain,
! [SV28: $i,SV22: $i,SV33: $i] :
( ( ( member @ SV33 @ SV22 )
= $false )
| ( ( member @ SV33 @ SV28 )
= $true )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(280,plain,
! [SV22: $i,SV28: $i,SV33: $i] :
( ( ( member @ SV33 @ SV28 )
= $false )
| ( ( member @ SV33 @ SV22 )
= $true )
| ( ( SV22 = SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(281,plain,
! [SV22: $i,SV28: $i] :
( ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
= $true )
| ( ( ~ ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(282,plain,
! [SV22: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) )
= $false )
| ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
= $false )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(283,plain,
! [SV22: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
| ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 ) )
= $false )
| ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(284,plain,
! [SV22: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 ) )
= $false )
| ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
= $false )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(285,plain,
! [SV22: $i,SV28: $i] :
( ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
= $false )
| ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
= $false )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(286,plain,
! [SV22: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 ) )
= $false )
| ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(287,plain,
! [SV22: $i,SV28: $i] :
( ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
= $false )
| ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(288,plain,
! [SV22: $i,SV28: $i] :
( ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
= $true )
| ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
= $false )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(289,plain,
! [SV22: $i,SV28: $i] :
( ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV28 )
= $true )
| ( ( member @ ( sK7_SY51 @ SV28 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22 = SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(290,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[175,289,288,287,285,280,279,274,269,268,267,266,259,254,253,252,247,246,227,226,188,183,182]) ).
thf(291,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[290,157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.15 % Computer : n020.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Oct 6 14:47:51 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.29
% 0.60/0.29 No.of.Axioms: 8
% 0.60/0.29
% 0.60/0.29 Length.of.Defs: 0
% 0.60/0.29
% 0.60/0.29 Contains.Choice.Funs: false
% 0.60/0.29 .......
% 0.60/0.29
% 0.60/0.29 ********************************
% 0.60/0.29 * All subproblems solved! *
% 0.60/0.29 ********************************
% 0.60/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:290,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.60/0.29
% 0.60/0.29 %**** Beginning of derivation protocol ****
% 0.60/0.29 % SZS output start CNFRefutation
% See solution above
% 0.60/0.29
% 0.60/0.29 %**** End of derivation protocol ****
% 0.60/0.29 %**** no. of clauses in derivation: 291 ****
% 0.60/0.29 %**** clause counter: 290 ****
% 0.60/0.29
% 0.60/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:290,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------