TSTP Solution File: SET931+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET931+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 : n019.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 03:06:23 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 222 ( 165 unt; 11 typ; 0 def)
% Number of atoms : 1209 ( 716 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 2419 ( 592 ~; 403 |; 61 &;1349 @)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 550 ( 0 ^ 546 !; 4 ?; 550 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY16,type,
sK3_SY16: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_set_difference,type,
set_difference: $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] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(2,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(3,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).
thf(6,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(8,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ A @ ( unordered_pair @ B @ C ) )
= empty_set )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(9,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ A @ ( unordered_pair @ B @ C ) )
= empty_set )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ A @ ( unordered_pair @ B @ C ) )
= empty_set )
<=> ~ ( ( A != empty_set )
& ( A
!= ( singleton @ B ) )
& ( A
!= ( singleton @ C ) )
& ( A
!= ( unordered_pair @ B @ C ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,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)],[5]) ).
thf(16,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(18,plain,
( ( ! [SY14: $i,SY15: $i] :
( ( ( set_difference @ sK1_A @ ( unordered_pair @ SY14 @ SY15 ) )
= empty_set )
<=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ SY14 ) )
& ( sK1_A
!= ( singleton @ SY15 ) )
& ( sK1_A
!= ( unordered_pair @ SY14 @ SY15 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(19,plain,
( ( ! [SY16: $i] :
( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ SY16 ) )
= empty_set )
<=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY14 ) )
& ( sK1_A
!= ( singleton @ SY16 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ SY16 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= empty_set )
<=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY14 ) )
& ( sK1_A
!= ( singleton @ sK3_SY16 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(21,plain,
( ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= empty_set )
=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY14 ) )
& ( sK1_A
!= ( singleton @ sK3_SY16 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[20]) ).
thf(22,plain,
( ( ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY14 ) )
& ( sK1_A
!= ( singleton @ sK3_SY16 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) )
=> ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[20]) ).
thf(23,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= empty_set )
=> ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY14 ) )
& ( sK1_A
!= ( singleton @ sK3_SY16 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( ~ ( ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY14 ) )
& ( sK1_A
!= ( singleton @ sK3_SY16 ) )
& ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) )
=> ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(25,plain,
( ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= empty_set )
& ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
& ( sK1_A
!= ( singleton @ sK3_SY16 ) )
& ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(26,plain,
( ( ( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
| ( sK1_A
= ( singleton @ sK3_SY16 ) )
| ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY14 ) ) )
& ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(28,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(29,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(30,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(31,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( subset @ A @ ( unordered_pair @ B @ C ) )
| ( A
= ( unordered_pair @ B @ C ) )
| ( A
= ( singleton @ C ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [B: $i,C: $i] :
( ( A
!= ( unordered_pair @ B @ C ) )
| ( subset @ A @ ( unordered_pair @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( A
!= ( singleton @ C ) )
| ( subset @ A @ ( unordered_pair @ B @ C ) ) )
& ( ( A != empty_set )
| ! [B: $i,C: $i] : ( subset @ A @ ( unordered_pair @ B @ C ) ) )
& ! [B: $i] :
( ( A
!= ( singleton @ B ) )
| ! [C: $i] : ( subset @ A @ ( unordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(33,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(34,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( subset @ A @ ( unordered_pair @ B @ C ) )
| ( A
= ( unordered_pair @ B @ C ) )
| ( A
= ( singleton @ C ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [B: $i,C: $i] :
( ( A
!= ( unordered_pair @ B @ C ) )
| ( subset @ A @ ( unordered_pair @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( A
!= ( singleton @ C ) )
| ( subset @ A @ ( unordered_pair @ B @ C ) ) )
& ( ( A != empty_set )
| ! [B: $i,C: $i] : ( subset @ A @ ( unordered_pair @ B @ C ) ) )
& ! [B: $i] :
( ( A
!= ( singleton @ B ) )
| ! [C: $i] : ( subset @ A @ ( unordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(35,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(36,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= empty_set )
& ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
& ( sK1_A
!= ( singleton @ sK3_SY16 ) )
& ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY14 ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(40,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
!= empty_set )
| ~ ~ ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0
= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0
= ( singleton @ SX2 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX0
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX0
!= ( singleton @ SX2 ) )
| ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i,SX2: $i] : ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ! [SX2: $i] : ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(42,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(43,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
( ( unordered_pair @ SV1 @ SY17 )
= ( unordered_pair @ SY17 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(44,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
( ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
!= empty_set )
| ~ ~ ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY18: $i,SY19: $i] :
( ~ ( subset @ SV3 @ ( unordered_pair @ SY18 @ SY19 ) )
| ( SV3
= ( unordered_pair @ SY18 @ SY19 ) )
| ( SV3
= ( singleton @ SY19 ) )
| ( SV3 = empty_set )
| ( SV3
= ( singleton @ SY18 ) ) )
| ~ ~ ( ~ ! [SY20: $i,SY21: $i] :
( ( SV3
!= ( unordered_pair @ SY20 @ SY21 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY20 @ SY21 ) ) )
| ~ ~ ( ~ ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) )
| ~ ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV4: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV4 )
= ( unordered_pair @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
( ( ~ ~ ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV3: $i] :
( ( ~ ! [SY18: $i,SY19: $i] :
( ~ ( subset @ SV3 @ ( unordered_pair @ SY18 @ SY19 ) )
| ( SV3
= ( unordered_pair @ SY18 @ SY19 ) )
| ( SV3
= ( singleton @ SY19 ) )
| ( SV3 = empty_set )
| ( SV3
= ( singleton @ SY18 ) ) )
| ~ ~ ( ~ ! [SY20: $i,SY21: $i] :
( ( SV3
!= ( unordered_pair @ SY20 @ SY21 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY20 @ SY21 ) ) )
| ~ ~ ( ~ ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) )
| ~ ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(54,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(55,plain,
( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
( ( ~ ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV3: $i] :
( ( ~ ! [SY18: $i,SY19: $i] :
( ~ ( subset @ SV3 @ ( unordered_pair @ SY18 @ SY19 ) )
| ( SV3
= ( unordered_pair @ SY18 @ SY19 ) )
| ( SV3
= ( singleton @ SY19 ) )
| ( SV3 = empty_set )
| ( SV3
= ( singleton @ SY18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(58,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ! [SY20: $i,SY21: $i] :
( ( SV3
!= ( unordered_pair @ SY20 @ SY21 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY20 @ SY21 ) ) )
| ~ ~ ( ~ ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) )
| ~ ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(59,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(61,plain,
( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV3: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( subset @ SV3 @ ( unordered_pair @ SY18 @ SY19 ) )
| ( SV3
= ( unordered_pair @ SY18 @ SY19 ) )
| ( SV3
= ( singleton @ SY19 ) )
| ( SV3 = empty_set )
| ( SV3
= ( singleton @ SY18 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(63,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY20: $i,SY21: $i] :
( ( SV3
!= ( unordered_pair @ SY20 @ SY21 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY20 @ SY21 ) ) )
| ~ ~ ( ~ ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) )
| ~ ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV5: $i] :
( ( ! [SY28: $i] :
( ( ( set_difference @ SV5 @ SY28 )
!= empty_set )
| ( subset @ SV5 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV6: $i] :
( ( ! [SY29: $i] :
( ~ ( subset @ SV6 @ SY29 )
| ( ( set_difference @ SV6 @ SY29 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(66,plain,
( ( ~ ( ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(67,plain,
( ( ~ ~ ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY30: $i] :
( ~ ( subset @ SV3 @ ( unordered_pair @ SV7 @ SY30 ) )
| ( SV3
= ( unordered_pair @ SV7 @ SY30 ) )
| ( SV3
= ( singleton @ SY30 ) )
| ( SV3 = empty_set )
| ( SV3
= ( singleton @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV3: $i] :
( ( ~ ! [SY20: $i,SY21: $i] :
( ( SV3
!= ( unordered_pair @ SY20 @ SY21 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY20 @ SY21 ) ) )
| ~ ~ ( ~ ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) )
| ~ ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV8: $i,SV5: $i] :
( ( ( ( set_difference @ SV5 @ SV8 )
!= empty_set )
| ( subset @ SV5 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV9: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV9 )
| ( ( set_difference @ SV6 @ SV9 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(72,plain,
( ( ( sK1_A
!= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(73,plain,
( ( ~ ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(74,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ ( unordered_pair @ SV7 @ SV10 ) )
| ( SV3
= ( unordered_pair @ SV7 @ SV10 ) )
| ( SV3
= ( singleton @ SV10 ) )
| ( SV3 = empty_set )
| ( SV3
= ( singleton @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV3: $i] :
( ( ~ ! [SY20: $i,SY21: $i] :
( ( SV3
!= ( unordered_pair @ SY20 @ SY21 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY20 @ SY21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(76,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) )
| ~ ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(77,plain,
! [SV8: $i,SV5: $i] :
( ( ( ( ( set_difference @ SV5 @ SV8 )
!= empty_set ) )
= $true )
| ( ( subset @ SV5 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(78,plain,
! [SV9: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV9 ) )
= $true )
| ( ( ( set_difference @ SV6 @ SV9 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(79,plain,
( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(80,plain,
( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ ( unordered_pair @ SV7 @ SV10 ) ) )
= $true )
| ( ( ( SV3
= ( unordered_pair @ SV7 @ SV10 ) )
| ( SV3
= ( singleton @ SV10 ) )
| ( SV3 = empty_set )
| ( SV3
= ( singleton @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV3: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ( SV3
!= ( unordered_pair @ SY20 @ SY21 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY20 @ SY21 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(83,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) )
| ~ ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(84,plain,
! [SV8: $i,SV5: $i] :
( ( ( ( set_difference @ SV5 @ SV8 )
= empty_set )
= $false )
| ( ( subset @ SV5 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV9: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV9 )
= $false )
| ( ( ( set_difference @ SV6 @ SV9 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(86,plain,
( ( ~ ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(87,plain,
( ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( subset @ SV3 @ ( unordered_pair @ SV7 @ SV10 ) )
= $false )
| ( ( ( SV3
= ( unordered_pair @ SV7 @ SV10 ) )
| ( SV3
= ( singleton @ SV10 ) )
| ( SV3 = empty_set )
| ( SV3
= ( singleton @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV11: $i,SV3: $i] :
( ( ! [SY31: $i] :
( ( SV3
!= ( unordered_pair @ SV11 @ SY31 ) )
| ( subset @ SV3 @ ( unordered_pair @ SV11 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV3: $i] :
( ( ~ ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) )
| ~ ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(91,plain,
( ( ( sK1_A
!= ( singleton @ sK3_SY16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(92,plain,
( ( ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(93,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( SV3
= ( unordered_pair @ SV7 @ SV10 ) )
= $true )
| ( ( ( SV3
= ( singleton @ SV10 ) )
| ( SV3 = empty_set )
| ( SV3
= ( singleton @ SV7 ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV7 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV12: $i,SV11: $i,SV3: $i] :
( ( ( SV3
!= ( unordered_pair @ SV11 @ SV12 ) )
| ( subset @ SV3 @ ( unordered_pair @ SV11 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV3: $i] :
( ( ~ ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(96,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(97,plain,
( ( sK1_A
= ( singleton @ sK3_SY16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(98,plain,
( ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV7: $i,SV10: $i,SV3: $i] :
( ( ( SV3
= ( singleton @ SV10 ) )
= $true )
| ( ( ( SV3 = empty_set )
| ( SV3
= ( singleton @ SV7 ) ) )
= $true )
| ( ( SV3
= ( unordered_pair @ SV7 @ SV10 ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV7 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV12: $i,SV11: $i,SV3: $i] :
( ( ( ( SV3
!= ( unordered_pair @ SV11 @ SV12 ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV11 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV3: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ( SV3
!= ( singleton @ SY23 ) )
| ( subset @ SV3 @ ( unordered_pair @ SY22 @ SY23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(102,plain,
! [SV3: $i] :
( ( ~ ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(103,plain,
( ( ~ ( ( sK1_A != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(104,plain,
( ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(105,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( SV3 = empty_set )
= $true )
| ( ( SV3
= ( singleton @ SV7 ) )
= $true )
| ( ( SV3
= ( singleton @ SV10 ) )
= $true )
| ( ( SV3
= ( unordered_pair @ SV7 @ SV10 ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV7 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV12: $i,SV11: $i,SV3: $i] :
( ( ( SV3
= ( unordered_pair @ SV11 @ SV12 ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV11 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV13: $i,SV3: $i] :
( ( ! [SY32: $i] :
( ( SV3
!= ( singleton @ SY32 ) )
| ( subset @ SV3 @ ( unordered_pair @ SV13 @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV3: $i] :
( ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
| ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(109,plain,
( ( ( sK1_A != empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(110,plain,
( ( ( sK1_A
!= ( singleton @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(111,plain,
! [SV13: $i,SV14: $i,SV3: $i] :
( ( ( SV3
!= ( singleton @ SV14 ) )
| ( subset @ SV3 @ ( unordered_pair @ SV13 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV3: $i] :
( ( ~ ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(113,plain,
! [SV3: $i] :
( ( ~ ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(114,plain,
( ( sK1_A = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(115,plain,
( ( sK1_A
= ( singleton @ sK2_SY14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV13: $i,SV14: $i,SV3: $i] :
( ( ( ( SV3
!= ( singleton @ SV14 ) ) )
= $true )
| ( ( subset @ SV3 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV3: $i] :
( ( ( SV3 != empty_set )
| ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(118,plain,
! [SV3: $i] :
( ( ! [SY26: $i] :
( ( SV3
!= ( singleton @ SY26 ) )
| ! [SY27: $i] : ( subset @ SV3 @ ( unordered_pair @ SY26 @ SY27 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(119,plain,
! [SV13: $i,SV14: $i,SV3: $i] :
( ( ( SV3
= ( singleton @ SV14 ) )
= $false )
| ( ( subset @ SV3 @ ( unordered_pair @ SV13 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(120,plain,
! [SV3: $i] :
( ( ( ( SV3 != empty_set ) )
= $true )
| ( ( ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(121,plain,
! [SV15: $i,SV3: $i] :
( ( ( SV3
!= ( singleton @ SV15 ) )
| ! [SY33: $i] : ( subset @ SV3 @ ( unordered_pair @ SV15 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(122,plain,
! [SV3: $i] :
( ( ( SV3 = empty_set )
= $false )
| ( ( ! [SY24: $i,SY25: $i] : ( subset @ SV3 @ ( unordered_pair @ SY24 @ SY25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(123,plain,
! [SV15: $i,SV3: $i] :
( ( ( ( SV3
!= ( singleton @ SV15 ) ) )
= $true )
| ( ( ! [SY33: $i] : ( subset @ SV3 @ ( unordered_pair @ SV15 @ SY33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(124,plain,
! [SV16: $i,SV3: $i] :
( ( ( ! [SY34: $i] : ( subset @ SV3 @ ( unordered_pair @ SV16 @ SY34 ) ) )
= $true )
| ( ( SV3 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(125,plain,
! [SV15: $i,SV3: $i] :
( ( ( SV3
= ( singleton @ SV15 ) )
= $false )
| ( ( ! [SY33: $i] : ( subset @ SV3 @ ( unordered_pair @ SV15 @ SY33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(126,plain,
! [SV17: $i,SV16: $i,SV3: $i] :
( ( ( subset @ SV3 @ ( unordered_pair @ SV16 @ SV17 ) )
= $true )
| ( ( SV3 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(127,plain,
! [SV18: $i,SV15: $i,SV3: $i] :
( ( ( subset @ SV3 @ ( unordered_pair @ SV15 @ SV18 ) )
= $true )
| ( ( SV3
= ( singleton @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(128,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,127,126,119,115,114,106,105,97,85,84,79,55,49,45,44,35]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(130,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(131,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( subset @ A @ ( unordered_pair @ B @ C ) )
| ( A
= ( unordered_pair @ B @ C ) )
| ( A
= ( singleton @ C ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [B: $i,C: $i] :
( ( A
!= ( unordered_pair @ B @ C ) )
| ( subset @ A @ ( unordered_pair @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( A
!= ( singleton @ C ) )
| ( subset @ A @ ( unordered_pair @ B @ C ) ) )
& ( ( A != empty_set )
| ! [B: $i,C: $i] : ( subset @ A @ ( unordered_pair @ B @ C ) ) )
& ! [B: $i] :
( ( A
!= ( singleton @ B ) )
| ! [C: $i] : ( subset @ A @ ( unordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(132,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(133,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(134,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(136,plain,
( ( ( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
| ( sK1_A
= ( singleton @ sK3_SY16 ) )
| ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY14 ) ) )
& ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(137,plain,
( ( ~ ( ~ ( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
| ( sK1_A
= ( singleton @ sK3_SY16 ) )
| ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY14 ) ) )
| ~ ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(138,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(139,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0
= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0
= ( singleton @ SX2 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX0
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX0
!= ( singleton @ SX2 ) )
| ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i,SX2: $i] : ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ! [SX2: $i] : ( subset @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(140,plain,
! [SV19: $i] :
( ( ! [SY35: $i] :
( ( unordered_pair @ SV19 @ SY35 )
= ( unordered_pair @ SY35 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(141,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV20: $i] :
( ( subset @ SV20 @ SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(143,plain,
( ( ~ ( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
| ( sK1_A
= ( singleton @ sK3_SY16 ) )
| ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY14 ) ) )
| ~ ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
!= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(144,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(145,plain,
! [SV21: $i] :
( ( ~ ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( subset @ SV21 @ ( unordered_pair @ SY36 @ SY37 ) )
| ( SV21
= ( unordered_pair @ SY36 @ SY37 ) )
| ( SV21
= ( singleton @ SY37 ) )
| ( SV21 = empty_set )
| ( SV21
= ( singleton @ SY36 ) ) )
| ~ ~ ( ~ ! [SY38: $i,SY39: $i] :
( ( SV21
!= ( unordered_pair @ SY38 @ SY39 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY38 @ SY39 ) ) )
| ~ ~ ( ~ ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) )
| ~ ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(146,plain,
! [SV22: $i,SV19: $i] :
( ( ( unordered_pair @ SV19 @ SV22 )
= ( unordered_pair @ SV22 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(147,plain,
( ( ~ ( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
| ( sK1_A
= ( singleton @ sK3_SY16 ) )
| ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(148,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
!= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(149,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(150,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(151,plain,
! [SV21: $i] :
( ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( subset @ SV21 @ ( unordered_pair @ SY36 @ SY37 ) )
| ( SV21
= ( unordered_pair @ SY36 @ SY37 ) )
| ( SV21
= ( singleton @ SY37 ) )
| ( SV21 = empty_set )
| ( SV21
= ( singleton @ SY36 ) ) )
| ~ ~ ( ~ ! [SY38: $i,SY39: $i] :
( ( SV21
!= ( unordered_pair @ SY38 @ SY39 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY38 @ SY39 ) ) )
| ~ ~ ( ~ ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) )
| ~ ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(152,plain,
( ( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
| ( sK1_A
= ( singleton @ sK3_SY16 ) )
| ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(153,plain,
( ( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
!= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(154,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(155,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(156,plain,
! [SV21: $i] :
( ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( subset @ SV21 @ ( unordered_pair @ SY36 @ SY37 ) )
| ( SV21
= ( unordered_pair @ SY36 @ SY37 ) )
| ( SV21
= ( singleton @ SY37 ) )
| ( SV21 = empty_set )
| ( SV21
= ( singleton @ SY36 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(157,plain,
! [SV21: $i] :
( ( ~ ~ ( ~ ! [SY38: $i,SY39: $i] :
( ( SV21
!= ( unordered_pair @ SY38 @ SY39 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY38 @ SY39 ) ) )
| ~ ~ ( ~ ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) )
| ~ ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(158,plain,
( ( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= $true )
| ( ( ( sK1_A
= ( singleton @ sK3_SY16 ) )
| ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(159,plain,
( ( ( set_difference @ sK1_A @ ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(160,plain,
! [SV23: $i] :
( ( ! [SY46: $i] :
( ( ( set_difference @ SV23 @ SY46 )
!= empty_set )
| ( subset @ SV23 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(161,plain,
! [SV24: $i] :
( ( ! [SY47: $i] :
( ~ ( subset @ SV24 @ SY47 )
| ( ( set_difference @ SV24 @ SY47 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(162,plain,
! [SV21: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( subset @ SV21 @ ( unordered_pair @ SY36 @ SY37 ) )
| ( SV21
= ( unordered_pair @ SY36 @ SY37 ) )
| ( SV21
= ( singleton @ SY37 ) )
| ( SV21 = empty_set )
| ( SV21
= ( singleton @ SY36 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(163,plain,
! [SV21: $i] :
( ( ~ ( ~ ! [SY38: $i,SY39: $i] :
( ( SV21
!= ( unordered_pair @ SY38 @ SY39 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY38 @ SY39 ) ) )
| ~ ~ ( ~ ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) )
| ~ ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(164,plain,
( ( ( sK1_A
= ( singleton @ sK3_SY16 ) )
= $true )
| ( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY14 ) ) )
= $true )
| ( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(165,plain,
! [SV25: $i,SV23: $i] :
( ( ( ( set_difference @ SV23 @ SV25 )
!= empty_set )
| ( subset @ SV23 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(166,plain,
! [SV26: $i,SV24: $i] :
( ( ~ ( subset @ SV24 @ SV26 )
| ( ( set_difference @ SV24 @ SV26 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(167,plain,
! [SV27: $i,SV21: $i] :
( ( ! [SY48: $i] :
( ~ ( subset @ SV21 @ ( unordered_pair @ SV27 @ SY48 ) )
| ( SV21
= ( unordered_pair @ SV27 @ SY48 ) )
| ( SV21
= ( singleton @ SY48 ) )
| ( SV21 = empty_set )
| ( SV21
= ( singleton @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(168,plain,
! [SV21: $i] :
( ( ~ ! [SY38: $i,SY39: $i] :
( ( SV21
!= ( unordered_pair @ SY38 @ SY39 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY38 @ SY39 ) ) )
| ~ ~ ( ~ ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) )
| ~ ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(169,plain,
( ( ( sK1_A = empty_set )
= $true )
| ( ( sK1_A
= ( singleton @ sK2_SY14 ) )
= $true )
| ( ( sK1_A
= ( singleton @ sK3_SY16 ) )
= $true )
| ( ( sK1_A
= ( unordered_pair @ sK2_SY14 @ sK3_SY16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(170,plain,
! [SV25: $i,SV23: $i] :
( ( ( ( ( set_difference @ SV23 @ SV25 )
!= empty_set ) )
= $true )
| ( ( subset @ SV23 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(171,plain,
! [SV26: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV26 ) )
= $true )
| ( ( ( set_difference @ SV24 @ SV26 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(172,plain,
! [SV28: $i,SV27: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ ( unordered_pair @ SV27 @ SV28 ) )
| ( SV21
= ( unordered_pair @ SV27 @ SV28 ) )
| ( SV21
= ( singleton @ SV28 ) )
| ( SV21 = empty_set )
| ( SV21
= ( singleton @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(173,plain,
! [SV21: $i] :
( ( ~ ! [SY38: $i,SY39: $i] :
( ( SV21
!= ( unordered_pair @ SY38 @ SY39 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY38 @ SY39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(174,plain,
! [SV21: $i] :
( ( ~ ~ ( ~ ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) )
| ~ ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(175,plain,
! [SV25: $i,SV23: $i] :
( ( ( ( set_difference @ SV23 @ SV25 )
= empty_set )
= $false )
| ( ( subset @ SV23 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(176,plain,
! [SV26: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV26 )
= $false )
| ( ( ( set_difference @ SV24 @ SV26 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(177,plain,
! [SV28: $i,SV27: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ ( unordered_pair @ SV27 @ SV28 ) ) )
= $true )
| ( ( ( SV21
= ( unordered_pair @ SV27 @ SV28 ) )
| ( SV21
= ( singleton @ SV28 ) )
| ( SV21 = empty_set )
| ( SV21
= ( singleton @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(178,plain,
! [SV21: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ( SV21
!= ( unordered_pair @ SY38 @ SY39 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY38 @ SY39 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(179,plain,
! [SV21: $i] :
( ( ~ ( ~ ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) )
| ~ ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(180,plain,
! [SV28: $i,SV27: $i,SV21: $i] :
( ( ( subset @ SV21 @ ( unordered_pair @ SV27 @ SV28 ) )
= $false )
| ( ( ( SV21
= ( unordered_pair @ SV27 @ SV28 ) )
| ( SV21
= ( singleton @ SV28 ) )
| ( SV21 = empty_set )
| ( SV21
= ( singleton @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV29: $i,SV21: $i] :
( ( ! [SY49: $i] :
( ( SV21
!= ( unordered_pair @ SV29 @ SY49 ) )
| ( subset @ SV21 @ ( unordered_pair @ SV29 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(182,plain,
! [SV21: $i] :
( ( ~ ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) )
| ~ ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(183,plain,
! [SV28: $i,SV27: $i,SV21: $i] :
( ( ( SV21
= ( unordered_pair @ SV27 @ SV28 ) )
= $true )
| ( ( ( SV21
= ( singleton @ SV28 ) )
| ( SV21 = empty_set )
| ( SV21
= ( singleton @ SV27 ) ) )
= $true )
| ( ( subset @ SV21 @ ( unordered_pair @ SV27 @ SV28 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(184,plain,
! [SV30: $i,SV29: $i,SV21: $i] :
( ( ( SV21
!= ( unordered_pair @ SV29 @ SV30 ) )
| ( subset @ SV21 @ ( unordered_pair @ SV29 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(185,plain,
! [SV21: $i] :
( ( ~ ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(186,plain,
! [SV21: $i] :
( ( ~ ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(187,plain,
! [SV27: $i,SV28: $i,SV21: $i] :
( ( ( SV21
= ( singleton @ SV28 ) )
= $true )
| ( ( ( SV21 = empty_set )
| ( SV21
= ( singleton @ SV27 ) ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV27 @ SV28 ) )
= $true )
| ( ( subset @ SV21 @ ( unordered_pair @ SV27 @ SV28 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(188,plain,
! [SV30: $i,SV29: $i,SV21: $i] :
( ( ( ( SV21
!= ( unordered_pair @ SV29 @ SV30 ) ) )
= $true )
| ( ( subset @ SV21 @ ( unordered_pair @ SV29 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(189,plain,
! [SV21: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ( SV21
!= ( singleton @ SY41 ) )
| ( subset @ SV21 @ ( unordered_pair @ SY40 @ SY41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(190,plain,
! [SV21: $i] :
( ( ~ ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(191,plain,
! [SV28: $i,SV27: $i,SV21: $i] :
( ( ( SV21 = empty_set )
= $true )
| ( ( SV21
= ( singleton @ SV27 ) )
= $true )
| ( ( SV21
= ( singleton @ SV28 ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV27 @ SV28 ) )
= $true )
| ( ( subset @ SV21 @ ( unordered_pair @ SV27 @ SV28 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(192,plain,
! [SV30: $i,SV29: $i,SV21: $i] :
( ( ( SV21
= ( unordered_pair @ SV29 @ SV30 ) )
= $false )
| ( ( subset @ SV21 @ ( unordered_pair @ SV29 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(193,plain,
! [SV31: $i,SV21: $i] :
( ( ! [SY50: $i] :
( ( SV21
!= ( singleton @ SY50 ) )
| ( subset @ SV21 @ ( unordered_pair @ SV31 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(194,plain,
! [SV21: $i] :
( ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
| ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(195,plain,
! [SV31: $i,SV32: $i,SV21: $i] :
( ( ( SV21
!= ( singleton @ SV32 ) )
| ( subset @ SV21 @ ( unordered_pair @ SV31 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(196,plain,
! [SV21: $i] :
( ( ~ ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(197,plain,
! [SV21: $i] :
( ( ~ ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(198,plain,
! [SV31: $i,SV32: $i,SV21: $i] :
( ( ( ( SV21
!= ( singleton @ SV32 ) ) )
= $true )
| ( ( subset @ SV21 @ ( unordered_pair @ SV31 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(199,plain,
! [SV21: $i] :
( ( ( SV21 != empty_set )
| ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(200,plain,
! [SV21: $i] :
( ( ! [SY44: $i] :
( ( SV21
!= ( singleton @ SY44 ) )
| ! [SY45: $i] : ( subset @ SV21 @ ( unordered_pair @ SY44 @ SY45 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(201,plain,
! [SV31: $i,SV32: $i,SV21: $i] :
( ( ( SV21
= ( singleton @ SV32 ) )
= $false )
| ( ( subset @ SV21 @ ( unordered_pair @ SV31 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(202,plain,
! [SV21: $i] :
( ( ( ( SV21 != empty_set ) )
= $true )
| ( ( ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(203,plain,
! [SV33: $i,SV21: $i] :
( ( ( SV21
!= ( singleton @ SV33 ) )
| ! [SY51: $i] : ( subset @ SV21 @ ( unordered_pair @ SV33 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(204,plain,
! [SV21: $i] :
( ( ( SV21 = empty_set )
= $false )
| ( ( ! [SY42: $i,SY43: $i] : ( subset @ SV21 @ ( unordered_pair @ SY42 @ SY43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(205,plain,
! [SV33: $i,SV21: $i] :
( ( ( ( SV21
!= ( singleton @ SV33 ) ) )
= $true )
| ( ( ! [SY51: $i] : ( subset @ SV21 @ ( unordered_pair @ SV33 @ SY51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(206,plain,
! [SV34: $i,SV21: $i] :
( ( ( ! [SY52: $i] : ( subset @ SV21 @ ( unordered_pair @ SV34 @ SY52 ) ) )
= $true )
| ( ( SV21 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(207,plain,
! [SV33: $i,SV21: $i] :
( ( ( SV21
= ( singleton @ SV33 ) )
= $false )
| ( ( ! [SY51: $i] : ( subset @ SV21 @ ( unordered_pair @ SV33 @ SY51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(208,plain,
! [SV35: $i,SV34: $i,SV21: $i] :
( ( ( subset @ SV21 @ ( unordered_pair @ SV34 @ SV35 ) )
= $true )
| ( ( SV21 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(209,plain,
! [SV36: $i,SV33: $i,SV21: $i] :
( ( ( subset @ SV21 @ ( unordered_pair @ SV33 @ SV36 ) )
= $true )
| ( ( SV21
= ( singleton @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(210,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[130,209,208,201,192,191,176,175,169,159,146,142,141,132]) ).
thf(211,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[210,128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET931+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 : n019.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 21:49:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 7
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:7,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:9,loop_count:0,foatp_calls:0,translation:fof_full).............
% 0.19/0.50
% 0.19/0.50 ********************************
% 0.19/0.50 * All subproblems solved! *
% 0.19/0.50 ********************************
% 0.19/0.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:210,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.52
% 0.19/0.52 %**** Beginning of derivation protocol ****
% 0.19/0.52 % SZS output start CNFRefutation
% See solution above
% 0.19/0.52
% 0.19/0.52 %**** End of derivation protocol ****
% 0.19/0.52 %**** no. of clauses in derivation: 211 ****
% 0.19/0.52 %**** clause counter: 210 ****
% 0.19/0.52
% 0.19/0.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:210,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------