%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 10:42:28 AM UTC 2026
% Result : Theorem 1.30s 0.42s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 213 ( 102 unt; 0 typ; 0 def)
% Number of atoms : 1523 ( 926 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2743 ( 905 ~; 501 |; 33 &;1286 @)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 557 ( 0 ^; 551 !; 6 ?; 557 :)
% 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_SY28,type,
sK2_SY28: $i ).
thf(tp_sK3_SY31,type,
sK3_SY31: $i ).
thf(tp_sK4_SY33,type,
sK4_SY33: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SY41,type,
sK7_SY41: $i > $i ).
thf(tp_sK8_SY58,type,
sK8_SY58: $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
thf(7,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(9,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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,C: $i,D: $i] :
~ ( ( subset @ ( unordered_pair @ A @ B ) @ ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(13,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( subset @ ( unordered_pair @ A @ B ) @ ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( subset @ ( unordered_pair @ A @ B ) @ ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ 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,
( ( ! [SY28: $i,SY29: $i,SY30: $i] :
~ ( ( subset @ ( unordered_pair @ sK1_A @ SY28 ) @ ( unordered_pair @ SY29 @ SY30 ) )
& ( sK1_A != SY29 )
& ( sK1_A != SY30 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(27,plain,
( ( ! [SY31: $i,SY32: $i] :
~ ( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ SY31 @ SY32 ) )
& ( sK1_A != SY31 )
& ( sK1_A != SY32 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
( ( ! [SY33: $i] :
~ ( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ SY33 ) )
& ( sK1_A != sK3_SY31 )
& ( sK1_A != SY33 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( ~ ( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) )
& ( sK1_A != sK3_SY31 )
& ( sK1_A != sK4_SY33 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(30,plain,
( ( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) )
& ( sK1_A != sK3_SY31 )
& ( sK1_A != sK4_SY33 ) )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(36,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ ( unordered_pair @ B @ C ) )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(37,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(38,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(42,plain,
( ( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) )
& ( sK1_A != sK3_SY31 )
& ( sK1_A != sK4_SY33 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(43,plain,
( ( ~ ( ~ ~ ( ~ ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) )
| ~ ( ( sK1_A != sK3_SY31 ) ) )
| ~ ( ( sK1_A != sK4_SY33 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ( SX0
!= ( singleton @ SX1 ) ) ) )
| ~ ( ( SX0
!= ( singleton @ SX2 ) ) ) )
| ~ ( ( SX0
!= ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ( SX0
!= ( singleton @ SX1 ) ) ) )
| ~ ( ( SX0
!= ( singleton @ SX2 ) ) ) )
| ~ ( ( SX0
!= ( unordered_pair @ SX1 @ SX2 ) ) ) )
| ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(46,plain,
( ( ~ ! [SX0: $i] :
~ ( empty @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(47,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(48,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(49,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(50,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( empty @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SX0 @ SX1 )
!= ( unordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 ) ) )
| ~ ( ( SX0 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(52,plain,
! [SV1: $i] :
( ( ! [SY34: $i] :
( ( unordered_pair @ SV1 @ SY34 )
= ( unordered_pair @ SY34 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(53,plain,
! [SV2: $i] :
( ( ! [SY35: $i] : ( subset @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
( ( ~ ~ ( ~ ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) )
| ~ ( ( sK1_A != sK3_SY31 ) ) )
| ~ ( ( sK1_A != sK4_SY33 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(55,plain,
! [SV3: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( ( singleton @ SV3 )
!= ( unordered_pair @ SY36 @ SY37 ) )
| ( SV3 = SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(56,plain,
! [SV4: $i] :
( ( ! [SY38: $i,SY39: $i] :
~ ( ~ ( ~ ( subset @ SV4 @ ( unordered_pair @ SY38 @ SY39 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SY38 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SY39 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SY38 @ SY39 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SY38 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SY39 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SY38 @ SY39 ) ) ) )
| ( subset @ SV4 @ ( unordered_pair @ SY38 @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(57,plain,
( ( ! [SX0: $i] :
~ ( empty @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV5: $i] :
( ( ~ ( ~ ( ( SV5 != empty_set )
| ! [SY40: $i] :
~ ( in @ SY40 @ SV5 ) )
| ~ ( ~ ! [SY41: $i] :
~ ( in @ SY41 @ SV5 )
| ( SV5 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(59,plain,
! [SV6: $i] :
( ( ! [SY42: $i,SY43: $i] :
~ ( ~ ( ( SY43
!= ( unordered_pair @ SV6 @ SY42 ) )
| ! [SY44: $i] :
~ ( ~ ( ~ ( in @ SY44 @ SY43 )
| ( SY44 = SV6 )
| ( SY44 = SY42 ) )
| ~ ( ~ ( ( SY44 = SV6 )
| ( SY44 = SY42 ) )
| ( in @ SY44 @ SY43 ) ) ) )
| ~ ( ~ ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SY43 )
| ( SY45 = SV6 )
| ( SY45 = SY42 ) )
| ~ ( ~ ( ( SY45 = SV6 )
| ( SY45 = SY42 ) )
| ( in @ SY45 @ SY43 ) ) )
| ( SY43
= ( unordered_pair @ SV6 @ SY42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV7: $i] :
( ( ! [SY46: $i] :
( ~ ( in @ SV7 @ SY46 )
| ~ ( in @ SY46 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(61,plain,
( ( ! [SX0: $i] :
~ ~ ( empty @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(62,plain,
! [SV8: $i] :
( ( ! [SY47: $i,SY48: $i,SY49: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SV8 @ SY47 )
!= ( unordered_pair @ SY48 @ SY49 ) )
| ~ ( ( SV8 != SY48 ) ) )
| ~ ( ( SV8 != SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(63,plain,
! [SV9: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV9 )
= ( unordered_pair @ SV9 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(65,plain,
( ( ~ ~ ( ~ ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) )
| ~ ( ( sK1_A != sK3_SY31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(66,plain,
( ( ~ ( ( sK1_A != sK4_SY33 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(67,plain,
! [SV11: $i,SV3: $i] :
( ( ! [SY50: $i] :
( ( ( singleton @ SV3 )
!= ( unordered_pair @ SV11 @ SY50 ) )
| ( SV3 = SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(68,plain,
! [SV12: $i,SV4: $i] :
( ( ! [SY51: $i] :
~ ( ~ ( ~ ( subset @ SV4 @ ( unordered_pair @ SV12 @ SY51 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SY51 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SY51 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SY51 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SY51 ) ) ) )
| ( subset @ SV4 @ ( unordered_pair @ SV12 @ SY51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(69,plain,
( ( ~ ( empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(70,plain,
! [SV5: $i] :
( ( ~ ( ( SV5 != empty_set )
| ! [SY40: $i] :
~ ( in @ SY40 @ SV5 ) )
| ~ ( ~ ! [SY41: $i] :
~ ( in @ SY41 @ SV5 )
| ( SV5 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(71,plain,
! [SV13: $i,SV6: $i] :
( ( ! [SY52: $i] :
~ ( ~ ( ( SY52
!= ( unordered_pair @ SV6 @ SV13 ) )
| ! [SY53: $i] :
~ ( ~ ( ~ ( in @ SY53 @ SY52 )
| ( SY53 = SV6 )
| ( SY53 = SV13 ) )
| ~ ( ~ ( ( SY53 = SV6 )
| ( SY53 = SV13 ) )
| ( in @ SY53 @ SY52 ) ) ) )
| ~ ( ~ ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SY52 )
| ( SY54 = SV6 )
| ( SY54 = SV13 ) )
| ~ ( ~ ( ( SY54 = SV6 )
| ( SY54 = SV13 ) )
| ( in @ SY54 @ SY52 ) ) )
| ( SY52
= ( unordered_pair @ SV6 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(72,plain,
! [SV14: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV14 )
| ~ ( in @ SV14 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(73,plain,
( ( ~ ~ ( empty @ sK6_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(74,plain,
! [SV15: $i,SV8: $i] :
( ( ! [SY55: $i,SY56: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SV8 @ SV15 )
!= ( unordered_pair @ SY55 @ SY56 ) )
| ~ ( ( SV8 != SY55 ) ) )
| ~ ( ( SV8 != SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(75,plain,
( ( ~ ( ~ ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) )
| ~ ( ( sK1_A != sK3_SY31 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(76,plain,
( ( sK1_A != sK4_SY33 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(77,plain,
! [SV16: $i,SV11: $i,SV3: $i] :
( ( ( ( singleton @ SV3 )
!= ( unordered_pair @ SV11 @ SV16 ) )
| ( SV3 = SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
| ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(79,plain,
( ( empty @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(80,plain,
! [SV5: $i] :
( ( ~ ( ( SV5 != empty_set )
| ! [SY40: $i] :
~ ( in @ SY40 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(81,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY41: $i] :
~ ( in @ SY41 @ SV5 )
| ( SV5 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(82,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ~ ( ~ ( ( SV18
!= ( unordered_pair @ SV6 @ SV13 ) )
| ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV18 )
| ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ~ ( ~ ( ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ( in @ SY57 @ SV18 ) ) ) )
| ~ ( ~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SV18 )
| ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ~ ( ~ ( ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ( in @ SY58 @ SV18 ) ) )
| ( SV18
= ( unordered_pair @ SV6 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(83,plain,
! [SV14: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV14 ) )
= $true )
| ( ( ~ ( in @ SV14 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(84,plain,
( ( ~ ( empty @ sK6_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(85,plain,
! [SV19: $i,SV15: $i,SV8: $i] :
( ( ! [SY59: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SV8 @ SV15 )
!= ( unordered_pair @ SV19 @ SY59 ) )
| ~ ( ( SV8 != SV19 ) ) )
| ~ ( ( SV8 != SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(86,plain,
( ( ~ ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) )
| ~ ( ( sK1_A != sK3_SY31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(87,plain,
( ( sK1_A = sK4_SY33 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV16: $i,SV11: $i,SV3: $i] :
( ( ( ( singleton @ SV3 )
!= ( unordered_pair @ SV11 @ SV16 ) )
= $true )
| ( ( SV3 = SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(89,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ~ ( ~ ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
| ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
| ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(90,plain,
! [SV5: $i] :
( ( ( SV5 != empty_set )
| ! [SY40: $i] :
~ ( in @ SY40 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(91,plain,
! [SV5: $i] :
( ( ~ ! [SY41: $i] :
~ ( in @ SY41 @ SV5 )
| ( SV5 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(92,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ~ ( ( SV18
!= ( unordered_pair @ SV6 @ SV13 ) )
| ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV18 )
| ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ~ ( ~ ( ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ( in @ SY57 @ SV18 ) ) ) )
| ~ ( ~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SV18 )
| ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ~ ( ~ ( ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ( in @ SY58 @ SV18 ) ) )
| ( SV18
= ( unordered_pair @ SV6 @ SV13 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV14: $i,SV7: $i] :
( ( ( in @ SV7 @ SV14 )
= $false )
| ( ( ~ ( in @ SV14 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(94,plain,
( ( empty @ sK6_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(95,plain,
! [SV20: $i,SV19: $i,SV15: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ( ( unordered_pair @ SV8 @ SV15 )
!= ( unordered_pair @ SV19 @ SV20 ) )
| ~ ( ( SV8 != SV19 ) ) )
| ~ ( ( SV8 != SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(96,plain,
( ( ~ ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(97,plain,
( ( ~ ( ( sK1_A != sK3_SY31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(98,plain,
! [SV16: $i,SV11: $i,SV3: $i] :
( ( ( ( singleton @ SV3 )
= ( unordered_pair @ SV11 @ SV16 ) )
= $false )
| ( ( SV3 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ~ ( ~ ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(100,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
| ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(101,plain,
! [SV5: $i] :
( ( ( SV5 != empty_set )
= $true )
| ( ( ! [SY40: $i] :
~ ( in @ SY40 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( ~ ! [SY41: $i] :
~ ( in @ SY41 @ SV5 ) )
= $true )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(103,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ~ ( ( SV18
!= ( unordered_pair @ SV6 @ SV13 ) )
| ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV18 )
| ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ~ ( ~ ( ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ( in @ SY57 @ SV18 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(104,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ~ ( ~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SV18 )
| ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ~ ( ~ ( ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ( in @ SY58 @ SV18 ) ) )
| ( SV18
= ( unordered_pair @ SV6 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(105,plain,
! [SV7: $i,SV14: $i] :
( ( ( in @ SV14 @ SV7 )
= $false )
| ( ( in @ SV7 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV20: $i,SV19: $i,SV15: $i,SV8: $i] :
( ( ~ ( ~ ~ ( ( ( unordered_pair @ SV8 @ SV15 )
!= ( unordered_pair @ SV19 @ SV20 ) )
| ~ ( ( SV8 != SV19 ) ) )
| ~ ( ( SV8 != SV20 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(107,plain,
( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY28 ) @ ( unordered_pair @ sK3_SY31 @ sK4_SY33 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(108,plain,
( ( sK1_A != sK3_SY31 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(109,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ~ ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(110,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
| ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(111,plain,
! [SV5: $i] :
( ( ( SV5 = empty_set )
= $false )
| ( ( ! [SY40: $i] :
~ ( in @ SY40 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV5: $i] :
( ( ( ! [SY41: $i] :
~ ( in @ SY41 @ SV5 ) )
= $false )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(113,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ( SV18
!= ( unordered_pair @ SV6 @ SV13 ) )
| ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV18 )
| ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ~ ( ~ ( ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ( in @ SY57 @ SV18 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(114,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SV18 )
| ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ~ ( ~ ( ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ( in @ SY58 @ SV18 ) ) )
| ( SV18
= ( unordered_pair @ SV6 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(115,plain,
! [SV20: $i,SV19: $i,SV15: $i,SV8: $i] :
( ( ~ ~ ( ( ( unordered_pair @ SV8 @ SV15 )
!= ( unordered_pair @ SV19 @ SV20 ) )
| ~ ( ( SV8 != SV19 ) ) )
| ~ ( ( SV8 != SV20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(116,plain,
( ( sK1_A = sK3_SY31 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(117,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(118,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(119,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV5 ) )
= $true )
| ( ( SV5 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV5: $i] :
( ( ( ~ ( in @ ( sK7_SY41 @ SV5 ) @ SV5 ) )
= $false )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(121,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ( SV18
!= ( unordered_pair @ SV6 @ SV13 ) )
= $true )
| ( ( ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV18 )
| ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ~ ( ~ ( ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ( in @ SY57 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ( ~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SV18 )
| ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ~ ( ~ ( ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ( in @ SY58 @ SV18 ) ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(123,plain,
! [SV20: $i,SV19: $i,SV15: $i,SV8: $i] :
( ( ( ~ ~ ( ( ( unordered_pair @ SV8 @ SV15 )
!= ( unordered_pair @ SV19 @ SV20 ) )
| ~ ( ( SV8 != SV19 ) ) ) )
= $true )
| ( ( ~ ( ( SV8 != SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false )
| ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(125,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV5: $i,SV21: $i] :
( ( ( in @ SV21 @ SV5 )
= $false )
| ( ( SV5 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(127,plain,
! [SV5: $i] :
( ( ( in @ ( sK7_SY41 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(128,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false )
| ( ( ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV18 )
| ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ~ ( ~ ( ( SY57 = SV6 )
| ( SY57 = SV13 ) )
| ( in @ SY57 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ( ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SV18 )
| ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ~ ( ~ ( ( SY58 = SV6 )
| ( SY58 = SV13 ) )
| ( in @ SY58 @ SV18 ) ) ) )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV20: $i,SV19: $i,SV15: $i,SV8: $i] :
( ( ( ~ ( ( ( unordered_pair @ SV8 @ SV15 )
!= ( unordered_pair @ SV19 @ SV20 ) )
| ~ ( ( SV8 != SV19 ) ) ) )
= $false )
| ( ( ~ ( ( SV8 != SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(133,plain,
! [SV13: $i,SV6: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV22 @ SV18 )
| ( SV22 = SV6 )
| ( SV22 = SV13 ) )
| ~ ( ~ ( ( SV22 = SV6 )
| ( SV22 = SV13 ) )
| ( in @ SV22 @ SV18 ) ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ~ ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) ) ) )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(135,plain,
! [SV20: $i,SV19: $i,SV15: $i,SV8: $i] :
( ( ( ( ( unordered_pair @ SV8 @ SV15 )
!= ( unordered_pair @ SV19 @ SV20 ) )
| ~ ( ( SV8 != SV19 ) ) )
= $true )
| ( ( ~ ( ( SV8 != SV20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(136,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(137,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
| ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(138,plain,
! [SV13: $i,SV6: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ SV18 )
| ( SV22 = SV6 )
| ( SV22 = SV13 ) )
| ~ ( ~ ( ( SV22 = SV6 )
| ( SV22 = SV13 ) )
| ( in @ SV22 @ SV18 ) ) )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(139,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ~ ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(140,plain,
! [SV20: $i,SV19: $i,SV15: $i,SV8: $i] :
( ( ( ( unordered_pair @ SV8 @ SV15 )
!= ( unordered_pair @ SV19 @ SV20 ) )
= $true )
| ( ( ~ ( ( SV8 != SV19 ) ) )
= $true )
| ( ( ~ ( ( SV8 != SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(141,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(142,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(143,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(144,plain,
! [SV13: $i,SV6: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ SV18 )
| ( SV22 = SV6 )
| ( SV22 = SV13 ) ) )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(145,plain,
! [SV18: $i,SV13: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( ~ ( ( SV22 = SV6 )
| ( SV22 = SV13 ) )
| ( in @ SV22 @ SV18 ) ) )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(146,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(147,plain,
! [SV20: $i,SV19: $i,SV15: $i,SV8: $i] :
( ( ( ( unordered_pair @ SV8 @ SV15 )
= ( unordered_pair @ SV19 @ SV20 ) )
= $false )
| ( ( ~ ( ( SV8 != SV19 ) ) )
= $true )
| ( ( ~ ( ( SV8 != SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(148,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(150,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(151,plain,
! [SV13: $i,SV6: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV18 )
| ( SV22 = SV6 )
| ( SV22 = SV13 ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(152,plain,
! [SV18: $i,SV13: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( ( SV22 = SV6 )
| ( SV22 = SV13 ) )
| ( in @ SV22 @ SV18 ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(153,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(154,plain,
! [SV20: $i,SV15: $i,SV19: $i,SV8: $i] :
( ( ( SV8 != SV19 )
= $false )
| ( ( ( unordered_pair @ SV8 @ SV15 )
= ( unordered_pair @ SV19 @ SV20 ) )
= $false )
| ( ( ~ ( ( SV8 != SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(155,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(156,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
| ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4
= ( unordered_pair @ SV12 @ SV17 ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(158,plain,
! [SV13: $i,SV6: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV18 ) )
= $true )
| ( ( ( SV22 = SV6 )
| ( SV22 = SV13 ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(159,plain,
! [SV18: $i,SV13: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( ( SV22 = SV6 )
| ( SV22 = SV13 ) ) )
= $true )
| ( ( in @ SV22 @ SV18 )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(160,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(161,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(162,plain,
! [SV20: $i,SV15: $i,SV19: $i,SV8: $i] :
( ( ( SV8 = SV19 )
= $true )
| ( ( ( unordered_pair @ SV8 @ SV15 )
= ( unordered_pair @ SV19 @ SV20 ) )
= $false )
| ( ( ~ ( ( SV8 != SV20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(163,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(164,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(165,plain,
! [SV12: $i,SV17: $i,SV4: $i] :
( ( ( ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(166,plain,
! [SV13: $i,SV6: $i,SV18: $i,SV22: $i] :
( ( ( in @ SV22 @ SV18 )
= $false )
| ( ( ( SV22 = SV6 )
| ( SV22 = SV13 ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV18: $i,SV13: $i,SV6: $i,SV22: $i] :
( ( ( ( SV22 = SV6 )
| ( SV22 = SV13 ) )
= $false )
| ( ( in @ SV22 @ SV18 )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
= $true )
| ( ( ~ ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(169,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
= $false )
| ( ( ~ ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(170,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 )
= $false )
| ( ( ~ ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(171,plain,
! [SV19: $i,SV15: $i,SV20: $i,SV8: $i] :
( ( ( SV8 != SV20 )
= $false )
| ( ( ( unordered_pair @ SV8 @ SV15 )
= ( unordered_pair @ SV19 @ SV20 ) )
= $false )
| ( ( SV8 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(173,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(174,plain,
! [SV12: $i,SV17: $i,SV4: $i] :
( ( ( SV4
!= ( singleton @ SV17 ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(175,plain,
! [SV18: $i,SV13: $i,SV6: $i,SV22: $i] :
( ( ( SV22 = SV6 )
= $true )
| ( ( SV22 = SV13 )
= $true )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV13: $i,SV18: $i,SV6: $i,SV22: $i] :
( ( ( SV22 = SV6 )
= $false )
| ( ( in @ SV22 @ SV18 )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(177,plain,
! [SV6: $i,SV18: $i,SV13: $i,SV22: $i] :
( ( ( SV22 = SV13 )
= $false )
| ( ( in @ SV22 @ SV18 )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(178,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) )
= $false )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
| ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 ) )
= $false )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV19: $i,SV15: $i,SV20: $i,SV8: $i] :
( ( ( SV8 = SV20 )
= $true )
| ( ( ( unordered_pair @ SV8 @ SV15 )
= ( unordered_pair @ SV19 @ SV20 ) )
= $false )
| ( ( SV8 = SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(182,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(183,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ( SV4 != empty_set ) )
| ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV12: $i,SV17: $i,SV4: $i] :
( ( ( SV4
= ( singleton @ SV17 ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) ) )
= $false )
| ( ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(186,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
= $false )
| ( ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(187,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) ) )
= $false )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(188,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
= $false )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(189,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) ) )
= $false )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(190,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
= $false )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(191,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ( SV4 != empty_set ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(192,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ( SV4 != empty_set ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(193,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(194,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
= $true )
| ( ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(195,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
= $true )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(196,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
| ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 ) )
= $true )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(197,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4 != empty_set )
= $false )
| ( ( ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(198,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4 != empty_set )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(199,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4
!= ( singleton @ SV12 ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(200,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
= $true )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 )
= $true )
| ( ( in @ ( sK8_SY58 @ SV13 @ SV6 @ SV18 ) @ SV18 )
= $true )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(201,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
= $true )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 )
= $true )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(202,plain,
! [SV18: $i,SV6: $i,SV13: $i] :
( ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV6 )
= $true )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 )
= $true )
| ( ( ( sK8_SY58 @ SV13 @ SV6 @ SV18 )
= SV13 )
= $false )
| ( ( SV18
= ( unordered_pair @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(203,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4 = empty_set )
= $true )
| ( ( ~ ( ( SV4
!= ( singleton @ SV12 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(204,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4 = empty_set )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(205,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4
= ( singleton @ SV12 ) )
= $false )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(206,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4
!= ( singleton @ SV12 ) )
= $false )
| ( ( SV4 = empty_set )
= $true )
| ( ( ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(207,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4
= ( singleton @ SV12 ) )
= $true )
| ( ( SV4 = empty_set )
= $true )
| ( ( ~ ( ( SV4
!= ( singleton @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(208,plain,
! [SV12: $i,SV17: $i,SV4: $i] :
( ( ( SV4
!= ( singleton @ SV17 ) )
= $false )
| ( ( SV4 = empty_set )
= $true )
| ( ( SV4
= ( singleton @ SV12 ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(209,plain,
! [SV12: $i,SV17: $i,SV4: $i] :
( ( ( SV4
= ( singleton @ SV17 ) )
= $true )
| ( ( SV4 = empty_set )
= $true )
| ( ( SV4
= ( singleton @ SV12 ) )
= $true )
| ( ( ~ ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) ) ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(210,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4
!= ( unordered_pair @ SV12 @ SV17 ) )
= $false )
| ( ( SV4
= ( singleton @ SV12 ) )
= $true )
| ( ( SV4 = empty_set )
= $true )
| ( ( SV4
= ( singleton @ SV17 ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(211,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ( SV4
= ( unordered_pair @ SV12 @ SV17 ) )
= $true )
| ( ( SV4
= ( singleton @ SV12 ) )
= $true )
| ( ( SV4 = empty_set )
= $true )
| ( ( SV4
= ( singleton @ SV17 ) )
= $true )
| ( ( subset @ SV4 @ ( unordered_pair @ SV12 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(212,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,211,205,204,202,201,200,190,188,186,184,181,177,176,175,157,127,126,116,107,105,98,94,87,79,64,63]) ).
thf(213,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 14:55:16 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.30/0.42
% 1.30/0.42 No.of.Axioms: 11
% 1.30/0.42
% 1.30/0.42 Length.of.Defs: 0
% 1.30/0.42
% 1.30/0.42 Contains.Choice.Funs: false
% 1.30/0.42 ......
% 1.30/0.42
% 1.30/0.42 ********************************
% 1.30/0.42 * All subproblems solved! *
% 1.30/0.42 ********************************
% 1.30/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:212,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.30/0.42
% 1.30/0.42 %**** Beginning of derivation protocol ****
% 1.30/0.42 % SZS output start CNFRefutation
% See solution above
% 1.30/0.42
% 1.30/0.42 %**** End of derivation protocol ****
% 1.30/0.42 %**** no. of clauses in derivation: 213 ****
% 1.30/0.42 %**** clause counter: 212 ****
% 1.30/0.42
% 1.30/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:212,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------