%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 10:42:29 AM UTC 2026
% Result : Theorem 199.70s 40.17s
% Output : CNFRefutation 199.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 128 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 1068 ( 575 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 1889 ( 352 ~; 427 |; 0 &;1095 @)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 351 ( 0 ^; 351 !; 0 ?; 351 :)
% 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_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY25,type,
sK2_SY25: $i > $i > $i ).
thf(tp_sK3_SY27,type,
sK3_SY27: $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(5,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_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,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(11,conjecture,
! [A: $i] :
( ( powerset @ ( singleton @ A ) )
= ( unordered_pair @ empty_set @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(12,negated_conjecture,
( ( ! [A: $i] :
( ( powerset @ ( singleton @ A ) )
= ( unordered_pair @ empty_set @ ( singleton @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,plain,
( ( ! [A: $i] :
( ( powerset @ ( singleton @ A ) )
= ( unordered_pair @ empty_set @ ( singleton @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(16,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)],[7]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(19,plain,
( ( ( powerset @ ( singleton @ sK1_A ) )
= ( unordered_pair @ empty_set @ ( singleton @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(20,plain,
( ( ( powerset @ ( singleton @ sK1_A ) )
!= ( unordered_pair @ empty_set @ ( singleton @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(23,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)],[16]) ).
thf(24,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(26,plain,
( ( ( powerset @ ( singleton @ sK1_A ) )
!= ( unordered_pair @ empty_set @ ( singleton @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(28,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)],[23]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( powerset @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(30,plain,
! [SV1: $i] :
( ( ! [SY12: $i] :
( ( unordered_pair @ SV1 @ SY12 )
= ( unordered_pair @ SY12 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(31,plain,
( ( ( powerset @ ( singleton @ sK1_A ) )
= ( unordered_pair @ empty_set @ ( singleton @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV2: $i] :
( ( ! [SY13: $i] :
~ ( ~ ( ~ ( subset @ SV2 @ ( singleton @ SY13 ) )
| ( SV2 = empty_set )
| ( SV2
= ( singleton @ SY13 ) ) )
| ~ ( ~ ( ( SV2 = empty_set )
| ( SV2
= ( singleton @ SY13 ) ) )
| ( subset @ SV2 @ ( singleton @ SY13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV3: $i] :
( ( ! [SY14: $i,SY15: $i] :
~ ( ~ ( ( SY15
!= ( unordered_pair @ SV3 @ SY14 ) )
| ! [SY16: $i] :
~ ( ~ ( ~ ( in @ SY16 @ SY15 )
| ( SY16 = SV3 )
| ( SY16 = SY14 ) )
| ~ ( ~ ( ( SY16 = SV3 )
| ( SY16 = SY14 ) )
| ( in @ SY16 @ SY15 ) ) ) )
| ~ ( ~ ! [SY17: $i] :
~ ( ~ ( ~ ( in @ SY17 @ SY15 )
| ( SY17 = SV3 )
| ( SY17 = SY14 ) )
| ~ ( ~ ( ( SY17 = SV3 )
| ( SY17 = SY14 ) )
| ( in @ SY17 @ SY15 ) ) )
| ( SY15
= ( unordered_pair @ SV3 @ SY14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV4: $i] :
( ( ! [SY18: $i] :
~ ( ~ ( ( SY18
!= ( powerset @ SV4 ) )
| ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SY18 )
| ( subset @ SY19 @ SV4 ) )
| ~ ( ~ ( subset @ SY19 @ SV4 )
| ( in @ SY19 @ SY18 ) ) ) )
| ~ ( ~ ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SY18 )
| ( subset @ SY20 @ SV4 ) )
| ~ ( ~ ( subset @ SY20 @ SV4 )
| ( in @ SY20 @ SY18 ) ) )
| ( SY18
= ( powerset @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV5: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV5 )
= ( unordered_pair @ SV5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV2 @ ( singleton @ SV6 ) )
| ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
| ~ ( ~ ( ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
| ( subset @ SV2 @ ( singleton @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY21: $i] :
~ ( ~ ( ( SY21
!= ( unordered_pair @ SV3 @ SV7 ) )
| ! [SY22: $i] :
~ ( ~ ( ~ ( in @ SY22 @ SY21 )
| ( SY22 = SV3 )
| ( SY22 = SV7 ) )
| ~ ( ~ ( ( SY22 = SV3 )
| ( SY22 = SV7 ) )
| ( in @ SY22 @ SY21 ) ) ) )
| ~ ( ~ ! [SY23: $i] :
~ ( ~ ( ~ ( in @ SY23 @ SY21 )
| ( SY23 = SV3 )
| ( SY23 = SV7 ) )
| ~ ( ~ ( ( SY23 = SV3 )
| ( SY23 = SV7 ) )
| ( in @ SY23 @ SY21 ) ) )
| ( SY21
= ( unordered_pair @ SV3 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( ~ ( ( SV8
!= ( powerset @ SV4 ) )
| ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV8 )
| ( subset @ SY24 @ SV4 ) )
| ~ ( ~ ( subset @ SY24 @ SV4 )
| ( in @ SY24 @ SV8 ) ) ) )
| ~ ( ~ ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SV8 )
| ( subset @ SY25 @ SV4 ) )
| ~ ( ~ ( subset @ SY25 @ SV4 )
| ( in @ SY25 @ SV8 ) ) )
| ( SV8
= ( powerset @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ ( singleton @ SV6 ) )
| ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
| ~ ( ~ ( ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
| ( subset @ SV2 @ ( singleton @ SV6 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ~ ( ~ ( ( SV9
!= ( unordered_pair @ SV3 @ SV7 ) )
| ! [SY26: $i] :
~ ( ~ ( ~ ( in @ SY26 @ SV9 )
| ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ~ ( ~ ( ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ( in @ SY26 @ SV9 ) ) ) )
| ~ ( ~ ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SV9 )
| ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ~ ( ~ ( ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ( in @ SY27 @ SV9 ) ) )
| ( SV9
= ( unordered_pair @ SV3 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( ( SV8
!= ( powerset @ SV4 ) )
| ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV8 )
| ( subset @ SY24 @ SV4 ) )
| ~ ( ~ ( subset @ SY24 @ SV4 )
| ( in @ SY24 @ SV8 ) ) ) )
| ~ ( ~ ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SV8 )
| ( subset @ SY25 @ SV4 ) )
| ~ ( ~ ( subset @ SY25 @ SV4 )
| ( in @ SY25 @ SV8 ) ) )
| ( SV8
= ( powerset @ SV4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ ( singleton @ SV6 ) )
| ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( ~ ( ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
| ( subset @ SV2 @ ( singleton @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ~ ( ( SV9
!= ( unordered_pair @ SV3 @ SV7 ) )
| ! [SY26: $i] :
~ ( ~ ( ~ ( in @ SY26 @ SV9 )
| ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ~ ( ~ ( ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ( in @ SY26 @ SV9 ) ) ) )
| ~ ( ~ ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SV9 )
| ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ~ ( ~ ( ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ( in @ SY27 @ SV9 ) ) )
| ( SV9
= ( unordered_pair @ SV3 @ SV7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( ( SV8
!= ( powerset @ SV4 ) )
| ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV8 )
| ( subset @ SY24 @ SV4 ) )
| ~ ( ~ ( subset @ SY24 @ SV4 )
| ( in @ SY24 @ SV8 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( ~ ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SV8 )
| ( subset @ SY25 @ SV4 ) )
| ~ ( ~ ( subset @ SY25 @ SV4 )
| ( in @ SY25 @ SV8 ) ) )
| ( SV8
= ( powerset @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ ( singleton @ SV6 ) )
| ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
| ( subset @ SV2 @ ( singleton @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ~ ( ( SV9
!= ( unordered_pair @ SV3 @ SV7 ) )
| ! [SY26: $i] :
~ ( ~ ( ~ ( in @ SY26 @ SV9 )
| ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ~ ( ~ ( ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ( in @ SY26 @ SV9 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ~ ( ~ ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SV9 )
| ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ~ ( ~ ( ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ( in @ SY27 @ SV9 ) ) )
| ( SV9
= ( unordered_pair @ SV3 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(51,plain,
! [SV4: $i,SV8: $i] :
( ( ( SV8
!= ( powerset @ SV4 ) )
| ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV8 )
| ( subset @ SY24 @ SV4 ) )
| ~ ( ~ ( subset @ SY24 @ SV4 )
| ( in @ SY24 @ SV8 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SV8 )
| ( subset @ SY25 @ SV4 ) )
| ~ ( ~ ( subset @ SY25 @ SV4 )
| ( in @ SY25 @ SV8 ) ) )
| ( SV8
= ( powerset @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ ( singleton @ SV6 ) ) )
= $true )
| ( ( ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) ) )
= $true )
| ( ( subset @ SV2 @ ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ( SV9
!= ( unordered_pair @ SV3 @ SV7 ) )
| ! [SY26: $i] :
~ ( ~ ( ~ ( in @ SY26 @ SV9 )
| ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ~ ( ~ ( ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ( in @ SY26 @ SV9 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(56,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ~ ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SV9 )
| ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ~ ( ~ ( ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ( in @ SY27 @ SV9 ) ) )
| ( SV9
= ( unordered_pair @ SV3 @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(57,plain,
! [SV4: $i,SV8: $i] :
( ( ( SV8
!= ( powerset @ SV4 ) )
= $true )
| ( ( ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV8 )
| ( subset @ SY24 @ SV4 ) )
| ~ ( ~ ( subset @ SY24 @ SV4 )
| ( in @ SY24 @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SV8 )
| ( subset @ SY25 @ SV4 ) )
| ~ ( ~ ( subset @ SY25 @ SV4 )
| ( in @ SY25 @ SV8 ) ) ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV6: $i,SV2: $i] :
( ( ( subset @ SV2 @ ( singleton @ SV6 ) )
= $false )
| ( ( ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV6: $i,SV2: $i] :
( ( ( ( SV2 = empty_set )
| ( SV2
= ( singleton @ SV6 ) ) )
= $false )
| ( ( subset @ SV2 @ ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ( SV9
!= ( unordered_pair @ SV3 @ SV7 ) )
= $true )
| ( ( ! [SY26: $i] :
~ ( ~ ( ~ ( in @ SY26 @ SV9 )
| ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ~ ( ~ ( ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ( in @ SY26 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ( ~ ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SV9 )
| ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ~ ( ~ ( ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ( in @ SY27 @ SV9 ) ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV4: $i,SV8: $i] :
( ( ( SV8
= ( powerset @ SV4 ) )
= $false )
| ( ( ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV8 )
| ( subset @ SY24 @ SV4 ) )
| ~ ( ~ ( subset @ SY24 @ SV4 )
| ( in @ SY24 @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV4: $i,SV8: $i] :
( ( ( ! [SY25: $i] :
~ ( ~ ( ~ ( in @ SY25 @ SV8 )
| ( subset @ SY25 @ SV4 ) )
| ~ ( ~ ( subset @ SY25 @ SV4 )
| ( in @ SY25 @ SV8 ) ) ) )
= $false )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV6: $i,SV2: $i] :
( ( ( SV2 = empty_set )
= $true )
| ( ( SV2
= ( singleton @ SV6 ) )
= $true )
| ( ( subset @ SV2 @ ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV6: $i,SV2: $i] :
( ( ( SV2 = empty_set )
= $false )
| ( ( subset @ SV2 @ ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV6: $i,SV2: $i] :
( ( ( SV2
= ( singleton @ SV6 ) )
= $false )
| ( ( subset @ SV2 @ ( singleton @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(68,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false )
| ( ( ! [SY26: $i] :
~ ( ~ ( ~ ( in @ SY26 @ SV9 )
| ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ~ ( ~ ( ( SY26 = SV3 )
| ( SY26 = SV7 ) )
| ( in @ SY26 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(69,plain,
! [SV7: $i,SV3: $i,SV9: $i] :
( ( ( ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SV9 )
| ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ~ ( ~ ( ( SY27 = SV3 )
| ( SY27 = SV7 ) )
| ( in @ SY27 @ SV9 ) ) ) )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(70,plain,
! [SV4: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV10 @ SV8 )
| ( subset @ SV10 @ SV4 ) )
| ~ ( ~ ( subset @ SV10 @ SV4 )
| ( in @ SV10 @ SV8 ) ) ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(71,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
| ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 ) )
| ~ ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
| ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) ) ) )
= $false )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(72,plain,
! [SV7: $i,SV3: $i,SV9: $i,SV11: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV11 @ SV9 )
| ( SV11 = SV3 )
| ( SV11 = SV7 ) )
| ~ ( ~ ( ( SV11 = SV3 )
| ( SV11 = SV7 ) )
| ( in @ SV11 @ SV9 ) ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ~ ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) ) ) )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(74,plain,
! [SV4: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV8 )
| ( subset @ SV10 @ SV4 ) )
| ~ ( ~ ( subset @ SV10 @ SV4 )
| ( in @ SV10 @ SV8 ) ) )
= $false )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
| ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 ) )
| ~ ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
| ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV7: $i,SV3: $i,SV9: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ SV11 @ SV9 )
| ( SV11 = SV3 )
| ( SV11 = SV7 ) )
| ~ ( ~ ( ( SV11 = SV3 )
| ( SV11 = SV7 ) )
| ( in @ SV11 @ SV9 ) ) )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ~ ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV4: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV8 )
| ( subset @ SV10 @ SV4 ) ) )
= $false )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV8: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( ~ ( subset @ SV10 @ SV4 )
| ( in @ SV10 @ SV8 ) ) )
= $false )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(80,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
| ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
| ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV7: $i,SV3: $i,SV9: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ SV11 @ SV9 )
| ( SV11 = SV3 )
| ( SV11 = SV7 ) ) )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(82,plain,
! [SV9: $i,SV7: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( ~ ( ( SV11 = SV3 )
| ( SV11 = SV7 ) )
| ( in @ SV11 @ SV9 ) ) )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(83,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV4: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV8 )
| ( subset @ SV10 @ SV4 ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(85,plain,
! [SV8: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV4 )
| ( in @ SV10 @ SV8 ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
| ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
| ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV7: $i,SV3: $i,SV9: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV9 )
| ( SV11 = SV3 )
| ( SV11 = SV7 ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(88,plain,
! [SV9: $i,SV7: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( ( SV11 = SV3 )
| ( SV11 = SV7 ) )
| ( in @ SV11 @ SV9 ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(89,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV4: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV8 ) )
= $true )
| ( ( subset @ SV10 @ SV4 )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV8: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV4 ) )
= $true )
| ( ( in @ SV10 @ SV8 )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
| ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(93,plain,
! [SV8: $i,SV4: $i] :
( ( ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
| ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(94,plain,
! [SV7: $i,SV3: $i,SV9: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV9 ) )
= $true )
| ( ( ( SV11 = SV3 )
| ( SV11 = SV7 ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV9: $i,SV7: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( ( SV11 = SV3 )
| ( SV11 = SV7 ) ) )
= $true )
| ( ( in @ SV11 @ SV9 )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(97,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(98,plain,
! [SV4: $i,SV8: $i,SV10: $i] :
( ( ( in @ SV10 @ SV8 )
= $false )
| ( ( subset @ SV10 @ SV4 )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV8: $i,SV4: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV4 )
= $false )
| ( ( in @ SV10 @ SV8 )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV8: $i,SV4: $i] :
( ( ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
| ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(101,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
| ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) )
= $false )
| ( ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
= $false )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV7: $i,SV3: $i,SV9: $i,SV11: $i] :
( ( ( in @ SV11 @ SV9 )
= $false )
| ( ( ( SV11 = SV3 )
| ( SV11 = SV7 ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV9: $i,SV7: $i,SV3: $i,SV11: $i] :
( ( ( ( SV11 = SV3 )
| ( SV11 = SV7 ) )
= $false )
| ( ( in @ SV11 @ SV9 )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( ~ ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(105,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(106,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(107,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
| ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 ) )
= $false )
| ( ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 ) )
= $false )
| ( ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
= $false )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(109,plain,
! [SV8: $i,SV4: $i] :
( ( ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
= $false )
| ( ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
= $false )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(110,plain,
! [SV9: $i,SV7: $i,SV3: $i,SV11: $i] :
( ( ( SV11 = SV3 )
= $true )
| ( ( SV11 = SV7 )
= $true )
| ( ( in @ SV11 @ SV9 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV7: $i,SV9: $i,SV3: $i,SV11: $i] :
( ( ( SV11 = SV3 )
= $false )
| ( ( in @ SV11 @ SV9 )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(112,plain,
! [SV3: $i,SV9: $i,SV7: $i,SV11: $i] :
( ( ( SV11 = SV7 )
= $false )
| ( ( in @ SV11 @ SV9 )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(113,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) )
= $false )
| ( ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) )
= $false )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
| ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 ) )
= $false )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 ) )
= $false )
| ( ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(117,plain,
! [SV8: $i,SV4: $i] :
( ( ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
= $false )
| ( ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(118,plain,
! [SV8: $i,SV4: $i] :
( ( ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
= $true )
| ( ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
= $false )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(119,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) ) )
= $false )
| ( ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(120,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
= $false )
| ( ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(121,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) ) )
= $false )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(122,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
= $false )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(123,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) ) )
= $false )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(124,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
= $false )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(125,plain,
! [SV8: $i,SV4: $i] :
( ( ( subset @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV4 )
= $true )
| ( ( in @ ( sK2_SY25 @ SV4 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( powerset @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(126,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
= $true )
| ( ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(127,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
= $true )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(128,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
| ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 ) )
= $true )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(129,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
= $true )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 )
= $true )
| ( ( in @ ( sK3_SY27 @ SV7 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(130,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
= $true )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 )
= $true )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(131,plain,
! [SV9: $i,SV3: $i,SV7: $i] :
( ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV3 )
= $true )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 )
= $true )
| ( ( ( sK3_SY27 @ SV7 @ SV3 @ SV9 )
= SV7 )
= $false )
| ( ( SV9
= ( unordered_pair @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(132,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,131,130,129,125,124,122,120,118,117,112,111,110,109,99,98,67,66,65,35,31]) ).
thf(133,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n014.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:55:26 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 199.70/40.17
% 199.70/40.17 No.of.Axioms: 5
% 199.70/40.17
% 199.70/40.17 Length.of.Defs: 0
% 199.70/40.17
% 199.70/40.17 Contains.Choice.Funs: false
% 199.70/40.17 ...
% 199.70/40.17
% 199.70/40.17 ********************************
% 199.70/40.17 * All subproblems solved! *
% 199.70/40.17 ********************************
% 199.70/40.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,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:132,loop_count:0,foatp_calls:1,translation:fof_full)
% 199.70/40.17
% 199.70/40.17 %**** Beginning of derivation protocol ****
% 199.70/40.17 % SZS output start CNFRefutation
% See solution above
% 199.70/40.17
% 199.70/40.17 %**** End of derivation protocol ****
% 199.70/40.17 %**** no. of clauses in derivation: 128 ****
% 199.70/40.17 %**** clause counter: 132 ****
% 199.70/40.17
% 199.70/40.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,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:132,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------