TSTP Solution File: SET908+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 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 03:06:08 EDT 2022
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 24
% Syntax : Number of formulae : 179 ( 83 unt; 12 typ; 0 def)
% Number of atoms : 1125 ( 460 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 2419 ( 475 ~; 410 |; 18 &;1500 @)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 466 ( 0 ^ 462 !; 4 ?; 466 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY23,type,
sK2_SY23: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i > $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_C,type,
sK7_C: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(1,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(6,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(8,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(12,conjecture,
! [A: $i,B: $i] :
( ( set_union2 @ ( singleton @ A ) @ B )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(13,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ ( singleton @ A ) @ B )
!= empty_set ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ ( singleton @ A ) @ B )
!= empty_set ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ! [SY23: $i] :
( ( set_union2 @ ( singleton @ sK1_A ) @ SY23 )
!= empty_set ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(27,plain,
( ( ( ( set_union2 @ ( singleton @ sK1_A ) @ sK2_SY23 )
!= empty_set ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
( ( ~ ( ( ( set_union2 @ ( singleton @ sK1_A ) @ sK2_SY23 )
!= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(29,plain,
( ( ( set_union2 @ ( singleton @ sK1_A ) @ sK2_SY23 )
= empty_set )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(30,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(31,plain,
( ( empty @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(35,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK5_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK5_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ( in @ ( sK5_D @ C @ B @ A ) @ A )
| ( in @ ( sK5_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( in @ ( sK6_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK7_C @ B @ A )
!= A )
| ~ ( in @ ( sK7_C @ B @ A ) @ B ) )
& ( ( ( sK7_C @ B @ A )
= A )
| ( in @ ( sK7_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK7_C @ B @ A )
!= A )
| ~ ( in @ ( sK7_C @ B @ A ) @ B ) )
& ( ( ( sK7_C @ B @ A )
= A )
| ( in @ ( sK7_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( in @ ( sK6_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(43,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK5_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK5_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ( in @ ( sK5_D @ C @ B @ A ) @ A )
| ( in @ ( sK5_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(44,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(48,plain,
( ( empty @ sK4_A )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(49,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(50,plain,
( ( ( set_union2 @ ( singleton @ sK1_A ) @ sK2_SY23 )
= empty_set )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(51,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(52,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK6_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(53,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK7_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK7_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(54,plain,
! [SV1: $i] :
( ( ! [SY24: $i] :
( ~ ( in @ SV1 @ SY24 )
| ~ ( in @ SY24 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(55,plain,
! [SV2: $i] :
( ( ! [SY25: $i] :
( ( set_union2 @ SV2 @ SY25 )
= ( set_union2 @ SY25 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
| ! [SY26: $i] :
~ ( empty @ ( set_union2 @ SV3 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(57,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
| ! [SY27: $i] :
~ ( empty @ ( set_union2 @ SY27 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV5: $i] :
( ( ( set_union2 @ SV5 @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(59,plain,
( ( empty @ sK3_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY28: $i,SY29: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY28 ) ) )
| ~ ( ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY28 ) ) )
| ( SY29
= ( set_union2 @ SV6 @ SY28 ) ) )
| ~ ! [SY30: $i,SY31: $i] :
( ( SY31
!= ( set_union2 @ SV6 @ SY30 ) )
| ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ SY31 )
| ( in @ SY32 @ SV6 )
| ( in @ SY32 @ SY30 ) )
| ~ ~ ( ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV6 )
| ( in @ SY33 @ SY31 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY30 )
| ( in @ SX3 @ SY31 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(61,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK6_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(62,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK7_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK7_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV7 )
| ~ ( in @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV8: $i,SV2: $i] :
( ( ( set_union2 @ SV2 @ SV8 )
= ( set_union2 @ SV8 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $true )
| ( ( ! [SY26: $i] :
~ ( empty @ ( set_union2 @ SV3 @ SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $true )
| ( ( ! [SY27: $i] :
~ ( empty @ ( set_union2 @ SY27 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV6: $i] :
( ( ~ ! [SY28: $i,SY29: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY28 ) ) )
| ~ ( ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY28 ) ) )
| ( SY29
= ( set_union2 @ SV6 @ SY28 ) ) )
| ~ ! [SY30: $i,SY31: $i] :
( ( SY31
!= ( set_union2 @ SV6 @ SY30 ) )
| ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ SY31 )
| ( in @ SY32 @ SV6 )
| ( in @ SY32 @ SY30 ) )
| ~ ~ ( ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV6 )
| ( in @ SY33 @ SY31 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY30 )
| ( in @ SX3 @ SY31 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(68,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK6_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(70,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK7_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK7_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(71,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(72,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV3 @ SV9 ) ) )
= $true )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV4: $i,SV10: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV10 @ SV4 ) ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV6: $i] :
( ( ~ ! [SY28: $i,SY29: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY28 ) ) )
| ~ ( ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY28 ) ) )
| ( SY29
= ( set_union2 @ SV6 @ SY28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(76,plain,
! [SV6: $i] :
( ( ~ ! [SY30: $i,SY31: $i] :
( ( SY31
!= ( set_union2 @ SV6 @ SY30 ) )
| ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ SY31 )
| ( in @ SY32 @ SV6 )
| ( in @ SY32 @ SY30 ) )
| ~ ~ ( ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV6 )
| ( in @ SY33 @ SY31 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY30 )
| ( in @ SX3 @ SY31 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(77,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK6_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK7_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK7_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK7_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(80,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(81,plain,
! [SV7: $i,SV1: $i] :
( ( ( in @ SV1 @ SV7 )
= $false )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV9: $i,SV3: $i] :
( ( ( empty @ ( set_union2 @ SV3 @ SV9 ) )
= $false )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV4: $i,SV10: $i] :
( ( ( empty @ ( set_union2 @ SV10 @ SV4 ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV6: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ~ ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY28 ) ) )
| ~ ( ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY29 )
| ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SY29 @ SY28 @ SV6 ) @ SY28 ) ) )
| ( SY29
= ( set_union2 @ SV6 @ SY28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV6: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ( SY31
!= ( set_union2 @ SV6 @ SY30 ) )
| ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ SY31 )
| ( in @ SY32 @ SV6 )
| ( in @ SY32 @ SY30 ) )
| ~ ~ ( ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV6 )
| ( in @ SY33 @ SY31 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY30 )
| ( in @ SX3 @ SY31 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(86,plain,
! [SV11: $i] :
( ( ( in @ ( sK6_B @ SV11 ) @ SV11 )
| ( SV11 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV12: $i] :
( ( ( SV12 != empty_set )
| ! [SY35: $i] :
~ ( in @ SY35 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV13: $i] :
( ( ! [SY36: $i] :
( ~ ( ~ ( ( ( sK7_C @ SY36 @ SV13 )
!= SV13 )
| ~ ( in @ ( sK7_C @ SY36 @ SV13 ) @ SY36 ) )
| ~ ( ( ( sK7_C @ SY36 @ SV13 )
= SV13 )
| ( in @ ( sK7_C @ SY36 @ SV13 ) @ SY36 ) ) )
| ( SY36
= ( singleton @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV14: $i] :
( ( ! [SY37: $i] :
( ( SY37
!= ( singleton @ SV14 ) )
| ~ ( ~ ! [SY38: $i] :
( ( SY38 != SV14 )
| ( in @ SY38 @ SY37 ) )
| ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SY37 )
| ( SY39 = SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV6: $i,SV15: $i] :
( ( ! [SY40: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY40 @ SV15 @ SV6 ) @ SY40 )
| ~ ( in @ ( sK5_D @ SY40 @ SV15 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY40 @ SV15 @ SV6 ) @ SY40 )
| ~ ( in @ ( sK5_D @ SY40 @ SV15 @ SV6 ) @ SV15 ) ) )
| ~ ( ( in @ ( sK5_D @ SY40 @ SV15 @ SV6 ) @ SY40 )
| ( in @ ( sK5_D @ SY40 @ SV15 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SY40 @ SV15 @ SV6 ) @ SV15 ) ) )
| ( SY40
= ( set_union2 @ SV6 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV16: $i,SV6: $i] :
( ( ! [SY41: $i] :
( ( SY41
!= ( set_union2 @ SV6 @ SV16 ) )
| ~ ( ~ ! [SY42: $i] :
( ~ ( in @ SY42 @ SY41 )
| ( in @ SY42 @ SV6 )
| ( in @ SY42 @ SV16 ) )
| ~ ~ ( ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV6 )
| ( in @ SY33 @ SY41 ) )
| ~ ! [SY44: $i] :
( ~ ( in @ SY44 @ SV16 )
| ( in @ SY44 @ SY41 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV11: $i] :
( ( ( in @ ( sK6_B @ SV11 ) @ SV11 )
= $true )
| ( ( SV11 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV12: $i] :
( ( ( ( SV12 != empty_set ) )
= $true )
| ( ( ! [SY35: $i] :
~ ( in @ SY35 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV13: $i,SV17: $i] :
( ( ~ ( ~ ( ( ( sK7_C @ SV17 @ SV13 )
!= SV13 )
| ~ ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) )
| ~ ( ( ( sK7_C @ SV17 @ SV13 )
= SV13 )
| ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) ) )
| ( SV17
= ( singleton @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV14: $i,SV18: $i] :
( ( ( SV18
!= ( singleton @ SV14 ) )
| ~ ( ~ ! [SY45: $i] :
( ( SY45 != SV14 )
| ( in @ SY45 @ SV18 ) )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV18 )
| ( SY46 = SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) )
| ~ ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) )
| ( SV19
= ( set_union2 @ SV6 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV16: $i,SV6: $i,SV20: $i] :
( ( ( SV20
!= ( set_union2 @ SV6 @ SV16 ) )
| ~ ( ~ ! [SY47: $i] :
( ~ ( in @ SY47 @ SV20 )
| ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV16 ) )
| ~ ~ ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV20 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SV16 )
| ( in @ SY49 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV12: $i] :
( ( ( SV12 = empty_set )
= $false )
| ( ( ! [SY35: $i] :
~ ( in @ SY35 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV13: $i,SV17: $i] :
( ( ( ~ ( ~ ( ( ( sK7_C @ SV17 @ SV13 )
!= SV13 )
| ~ ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) )
| ~ ( ( ( sK7_C @ SV17 @ SV13 )
= SV13 )
| ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) ) ) )
= $true )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(101,plain,
! [SV14: $i,SV18: $i] :
( ( ( ( SV18
!= ( singleton @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY45: $i] :
( ( SY45 != SV14 )
| ( in @ SY45 @ SV18 ) )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV18 )
| ( SY46 = SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) )
| ~ ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV16: $i,SV6: $i,SV20: $i] :
( ( ( ( SV20
!= ( set_union2 @ SV6 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY47: $i] :
( ~ ( in @ SY47 @ SV20 )
| ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV16 ) )
| ~ ~ ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV20 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SV16 )
| ( in @ SY49 @ SV20 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV12: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV12 ) )
= $true )
| ( ( SV12 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV13: $i,SV17: $i] :
( ( ( ~ ( ( ( sK7_C @ SV17 @ SV13 )
!= SV13 )
| ~ ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) )
| ~ ( ( ( sK7_C @ SV17 @ SV13 )
= SV13 )
| ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) ) )
= $false )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV14: $i,SV18: $i] :
( ( ( SV18
= ( singleton @ SV14 ) )
= $false )
| ( ( ~ ( ~ ! [SY45: $i] :
( ( SY45 != SV14 )
| ( in @ SY45 @ SV18 ) )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV18 )
| ( SY46 = SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) )
| ~ ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) )
= $false )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV16: $i,SV6: $i,SV20: $i] :
( ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ! [SY47: $i] :
( ~ ( in @ SY47 @ SV20 )
| ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV16 ) )
| ~ ~ ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV20 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SV16 )
| ( in @ SY49 @ SV20 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV12: $i,SV21: $i] :
( ( ( in @ SV21 @ SV12 )
= $false )
| ( ( SV12 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV13: $i,SV17: $i] :
( ( ( ~ ( ( ( sK7_C @ SV17 @ SV13 )
!= SV13 )
| ~ ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) ) )
= $false )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(111,plain,
! [SV13: $i,SV17: $i] :
( ( ( ~ ( ( ( sK7_C @ SV17 @ SV13 )
= SV13 )
| ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) ) )
= $false )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV18: $i,SV14: $i] :
( ( ( ~ ! [SY45: $i] :
( ( SY45 != SV14 )
| ( in @ SY45 @ SV18 ) )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV18 )
| ( SY46 = SV14 ) ) )
= $false )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(113,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) ) )
= $false )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(114,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) )
= $false )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(115,plain,
! [SV16: $i,SV6: $i,SV20: $i] :
( ( ( ~ ! [SY47: $i] :
( ~ ( in @ SY47 @ SV20 )
| ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV16 ) )
| ~ ~ ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV20 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SV16 )
| ( in @ SY49 @ SV20 ) ) ) )
= $false )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV13: $i,SV17: $i] :
( ( ( ( ( sK7_C @ SV17 @ SV13 )
!= SV13 )
| ~ ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(117,plain,
! [SV13: $i,SV17: $i] :
( ( ( ( ( sK7_C @ SV17 @ SV13 )
= SV13 )
| ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(118,plain,
! [SV18: $i,SV14: $i] :
( ( ( ~ ! [SY45: $i] :
( ( SY45 != SV14 )
| ( in @ SY45 @ SV18 ) ) )
= $false )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(119,plain,
! [SV14: $i,SV18: $i] :
( ( ( ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV18 )
| ( SY46 = SV14 ) ) )
= $false )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(120,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(121,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(122,plain,
! [SV16: $i,SV6: $i,SV20: $i] :
( ( ( ~ ! [SY47: $i] :
( ~ ( in @ SY47 @ SV20 )
| ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV16 ) ) )
= $false )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(123,plain,
! [SV16: $i,SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV20 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SV16 )
| ( in @ SY49 @ SV20 ) ) ) )
= $false )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(124,plain,
! [SV13: $i,SV17: $i] :
( ( ( ( ( sK7_C @ SV17 @ SV13 )
!= SV13 ) )
= $true )
| ( ( ~ ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(125,plain,
! [SV13: $i,SV17: $i] :
( ( ( ( sK7_C @ SV17 @ SV13 )
= SV13 )
= $true )
| ( ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 )
= $true )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV18: $i,SV14: $i] :
( ( ( ! [SY45: $i] :
( ( SY45 != SV14 )
| ( in @ SY45 @ SV18 ) ) )
= $true )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(127,plain,
! [SV14: $i,SV18: $i] :
( ( ( ! [SY46: $i] :
( ~ ( in @ SY46 @ SV18 )
| ( SY46 = SV14 ) ) )
= $true )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(128,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) )
= $false )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
= $true )
| ( ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 )
| ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(130,plain,
! [SV16: $i,SV6: $i,SV20: $i] :
( ( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ SV20 )
| ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV16 ) ) )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(131,plain,
! [SV16: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV20 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SV16 )
| ( in @ SY49 @ SV20 ) ) ) )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(132,plain,
! [SV13: $i,SV17: $i] :
( ( ( ( sK7_C @ SV17 @ SV13 )
= SV13 )
= $false )
| ( ( ~ ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV18: $i,SV14: $i,SV22: $i] :
( ( ( ( SV22 != SV14 )
| ( in @ SV22 @ SV18 ) )
= $true )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV14: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV18 )
| ( SV23 = SV14 ) )
= $true )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) ) )
= $false )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(136,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) ) )
= $false )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(137,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 )
= $true )
| ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 )
= $true )
| ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV16: $i,SV6: $i,SV20: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV20 )
| ( in @ SV24 @ SV6 )
| ( in @ SV24 @ SV16 ) )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(139,plain,
! [SV16: $i,SV20: $i,SV6: $i] :
( ( ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV20 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SV16 )
| ( in @ SY49 @ SV20 ) ) )
= $false )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(140,plain,
! [SV13: $i,SV17: $i] :
( ( ( in @ ( sK7_C @ SV17 @ SV13 ) @ SV17 )
= $false )
| ( ( ( sK7_C @ SV17 @ SV13 )
= SV13 )
= $false )
| ( ( SV17
= ( singleton @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV18: $i,SV14: $i,SV22: $i] :
( ( ( ( SV22 != SV14 ) )
= $true )
| ( ( in @ SV22 @ SV18 )
= $true )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV14: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV18 ) )
= $true )
| ( ( SV23 = SV14 )
= $true )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(144,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
| ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(145,plain,
! [SV16: $i,SV6: $i,SV20: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV20 ) )
= $true )
| ( ( ( in @ SV24 @ SV6 )
| ( in @ SV24 @ SV16 ) )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(146,plain,
! [SV16: $i,SV20: $i,SV6: $i] :
( ( ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV20 ) ) )
= $false )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(147,plain,
! [SV6: $i,SV20: $i,SV16: $i] :
( ( ( ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SV16 )
| ( in @ SY49 @ SV20 ) ) )
= $false )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(148,plain,
! [SV18: $i,SV14: $i,SV22: $i] :
( ( ( SV22 = SV14 )
= $false )
| ( ( in @ SV22 @ SV18 )
= $true )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV14: $i,SV18: $i,SV23: $i] :
( ( ( in @ SV23 @ SV18 )
= $false )
| ( ( SV23 = SV14 )
= $true )
| ( ( SV18
= ( singleton @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(150,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 ) )
= $true )
| ( ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(151,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 ) )
= $true )
| ( ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(152,plain,
! [SV16: $i,SV6: $i,SV20: $i,SV24: $i] :
( ( ( in @ SV24 @ SV20 )
= $false )
| ( ( ( in @ SV24 @ SV6 )
| ( in @ SV24 @ SV16 ) )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV16: $i,SV20: $i,SV6: $i] :
( ( ( ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV20 ) ) )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(154,plain,
! [SV6: $i,SV20: $i,SV16: $i] :
( ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ SV16 )
| ( in @ SY49 @ SV20 ) ) )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(155,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
= $false )
| ( ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(156,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
= $false )
| ( ( ~ ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 ) )
= $true )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(157,plain,
! [SV20: $i,SV16: $i,SV6: $i,SV24: $i] :
( ( ( in @ SV24 @ SV6 )
= $true )
| ( ( in @ SV24 @ SV16 )
= $true )
| ( ( in @ SV24 @ SV20 )
= $false )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(158,plain,
! [SV16: $i,SV20: $i,SV6: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV6 )
| ( in @ SV25 @ SV20 ) )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(159,plain,
! [SV6: $i,SV20: $i,SV16: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV16 )
| ( in @ SV26 @ SV20 ) )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(160,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV6 )
= $false )
| ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
= $false )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(161,plain,
! [SV6: $i,SV15: $i,SV19: $i] :
( ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV15 )
= $false )
| ( ( in @ ( sK5_D @ SV19 @ SV15 @ SV6 ) @ SV19 )
= $false )
| ( ( SV19
= ( set_union2 @ SV6 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(162,plain,
! [SV16: $i,SV20: $i,SV6: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV6 ) )
= $true )
| ( ( in @ SV25 @ SV20 )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(163,plain,
! [SV6: $i,SV20: $i,SV16: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV16 ) )
= $true )
| ( ( in @ SV26 @ SV20 )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(164,plain,
! [SV16: $i,SV20: $i,SV6: $i,SV25: $i] :
( ( ( in @ SV25 @ SV6 )
= $false )
| ( ( in @ SV25 @ SV20 )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(165,plain,
! [SV6: $i,SV20: $i,SV16: $i,SV26: $i] :
( ( ( in @ SV26 @ SV16 )
= $false )
| ( ( in @ SV26 @ SV20 )
= $true )
| ( ( SV20
= ( set_union2 @ SV6 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(166,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[44,165,164,161,160,157,149,148,140,137,125,109,93,90,83,82,64,59,58,50,48]) ).
thf(167,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % 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 : Sun Jul 10 19:26:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 11
% 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:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:13,loop_count:0,foatp_calls:0,translation:fof_full)............
% 0.18/0.47
% 0.18/0.47 ********************************
% 0.18/0.47 * All subproblems solved! *
% 0.18/0.47 ********************************
% 0.18/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:166,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.48
% 0.18/0.48 %**** Beginning of derivation protocol ****
% 0.18/0.48 % SZS output start CNFRefutation
% See solution above
% 0.18/0.48
% 0.18/0.48 %**** End of derivation protocol ****
% 0.18/0.48 %**** no. of clauses in derivation: 167 ****
% 0.18/0.48 %**** clause counter: 166 ****
% 0.18/0.48
% 0.18/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:166,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------