TSTP Solution File: SET881+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET881+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 : n007.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 03:05:57 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 121 ( 59 unt; 11 typ; 0 def)
% Number of atoms : 743 ( 410 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1554 ( 324 ~; 281 |; 12 &; 929 @)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 321 ( 0 ^ 317 !; 4 ?; 321 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(4,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(8,conjecture,
! [A: $i,B: $i] :
( ( set_difference @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(9,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
= empty_set ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
= empty_set ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,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)],[5]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(18,plain,
( ( ! [SY14: $i] :
( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ SY14 ) )
= empty_set ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(19,plain,
( ( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ sK2_SY14 ) )
= empty_set )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( ( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ sK2_SY14 ) )
!= empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(21,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(22,plain,
( ( empty @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
!= empty_set )
| ( in @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(24,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ( ( sK5_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ( ( sK5_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ( ( sK5_D @ C @ B @ A )
= A )
| ( ( sK5_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(28,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ( ( sK5_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ( ( sK5_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK5_D @ C @ B @ A ) @ C )
| ( ( sK5_D @ C @ B @ A )
= A )
| ( ( sK5_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(29,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
!= empty_set )
| ( in @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(31,plain,
( ( empty @ sK4_A )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(32,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(33,plain,
( ( ( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ sK2_SY14 ) )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(34,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK5_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK5_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK5_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK5_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(35,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
!= empty_set )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(36,plain,
! [SV1: $i] :
( ( ! [SY15: $i] :
( ~ ( in @ SV1 @ SY15 )
| ~ ( in @ SY15 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
( ( unordered_pair @ SV2 @ SY16 )
= ( unordered_pair @ SY16 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(38,plain,
( ( empty @ sK3_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ sK2_SY14 ) )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY17: $i,SY18: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
!= SY17 ) ) )
| ~ ( ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
= SV3 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
= SY17 ) ) )
| ( SY18
= ( unordered_pair @ SV3 @ SY17 ) ) )
| ~ ! [SY19: $i,SY20: $i] :
( ( SY20
!= ( unordered_pair @ SV3 @ SY19 ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SY20 )
| ( SY21 = SV3 )
| ( SY21 = SY19 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY20 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY19 )
| ( in @ SX3 @ SY20 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
!= empty_set )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV4 )
| ~ ( in @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV5: $i,SV2: $i] :
( ( ( unordered_pair @ SV2 @ SV5 )
= ( unordered_pair @ SV5 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV3: $i] :
( ( ~ ! [SY17: $i,SY18: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
!= SY17 ) ) )
| ~ ( ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
= SV3 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
= SY17 ) ) )
| ( SY18
= ( unordered_pair @ SV3 @ SY17 ) ) )
| ~ ! [SY19: $i,SY20: $i] :
( ( SY20
!= ( unordered_pair @ SV3 @ SY19 ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SY20 )
| ( SY21 = SV3 )
| ( SY21 = SY19 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY20 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY19 )
| ( in @ SX3 @ SY20 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
!= empty_set )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ( in @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV3: $i] :
( ( ~ ! [SY17: $i,SY18: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
!= SY17 ) ) )
| ~ ( ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
= SV3 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
= SY17 ) ) )
| ( SY18
= ( unordered_pair @ SV3 @ SY17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV3: $i] :
( ( ~ ! [SY19: $i,SY20: $i] :
( ( SY20
!= ( unordered_pair @ SV3 @ SY19 ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SY20 )
| ( SY21 = SV3 )
| ( SY21 = SY19 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY20 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY19 )
| ( in @ SX3 @ SY20 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
!= empty_set )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV4: $i,SV1: $i] :
( ( ( in @ SV1 @ SV4 )
= $false )
| ( ( ~ ( in @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV3: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
!= SY17 ) ) )
| ~ ( ( in @ ( sK5_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
= SV3 )
| ( ( sK5_D @ SY18 @ SY17 @ SV3 )
= SY17 ) ) )
| ( SY18
= ( unordered_pair @ SV3 @ SY17 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV3: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ( SY20
!= ( unordered_pair @ SV3 @ SY19 ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SY20 )
| ( SY21 = SV3 )
| ( SY21 = SY19 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY20 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY19 )
| ( in @ SX3 @ SY20 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV6: $i] :
( ( ! [SY24: $i] :
( ( ( set_difference @ ( singleton @ SV6 ) @ SY24 )
!= empty_set )
| ( in @ SV6 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV7: $i] :
( ( ! [SY25: $i] :
( ~ ( in @ SV7 @ SY25 )
| ( ( set_difference @ ( singleton @ SV7 ) @ SY25 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV3: $i,SV8: $i] :
( ( ! [SY26: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SY26 @ SV8 @ SV3 ) @ SY26 )
| ( ( sK5_D @ SY26 @ SV8 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SY26 @ SV8 @ SV3 ) @ SY26 )
| ( ( sK5_D @ SY26 @ SV8 @ SV3 )
!= SV8 ) ) )
| ~ ( ( in @ ( sK5_D @ SY26 @ SV8 @ SV3 ) @ SY26 )
| ( ( sK5_D @ SY26 @ SV8 @ SV3 )
= SV3 )
| ( ( sK5_D @ SY26 @ SV8 @ SV3 )
= SV8 ) ) )
| ( SY26
= ( unordered_pair @ SV3 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY27: $i] :
( ( SY27
!= ( unordered_pair @ SV3 @ SV9 ) )
| ~ ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SY27 )
| ( SY28 = SV3 )
| ( SY28 = SV9 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY27 ) )
| ~ ! [SY30: $i] :
( ( SY30 != SV9 )
| ( in @ SY30 @ SY27 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV10: $i,SV6: $i] :
( ( ( ( set_difference @ ( singleton @ SV6 ) @ SV10 )
!= empty_set )
| ( in @ SV6 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV11: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV11 )
| ( ( set_difference @ ( singleton @ SV7 ) @ SV11 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) ) )
| ~ ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV3 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV8 ) ) )
| ( SV12
= ( unordered_pair @ SV3 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV9: $i,SV3: $i,SV13: $i] :
( ( ( SV13
!= ( unordered_pair @ SV3 @ SV9 ) )
| ~ ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ SV13 )
| ( SY31 = SV3 )
| ( SY31 = SV9 ) )
| ~ ~ ( ~ ! [SY32: $i] :
( ( SY32 != SV3 )
| ( in @ SY32 @ SV13 ) )
| ~ ! [SY33: $i] :
( ( SY33 != SV9 )
| ( in @ SY33 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV10: $i,SV6: $i] :
( ( ( ( ( set_difference @ ( singleton @ SV6 ) @ SV10 )
!= empty_set ) )
= $true )
| ( ( in @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV11: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV11 ) )
= $true )
| ( ( ( set_difference @ ( singleton @ SV7 ) @ SV11 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) ) )
| ~ ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV3 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV8 ) ) ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV9: $i,SV3: $i,SV13: $i] :
( ( ( ( SV13
!= ( unordered_pair @ SV3 @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ SV13 )
| ( SY31 = SV3 )
| ( SY31 = SV9 ) )
| ~ ~ ( ~ ! [SY32: $i] :
( ( SY32 != SV3 )
| ( in @ SY32 @ SV13 ) )
| ~ ! [SY33: $i] :
( ( SY33 != SV9 )
| ( in @ SY33 @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV10: $i,SV6: $i] :
( ( ( ( set_difference @ ( singleton @ SV6 ) @ SV10 )
= empty_set )
= $false )
| ( ( in @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV11: $i,SV7: $i] :
( ( ( in @ SV7 @ SV11 )
= $false )
| ( ( ( set_difference @ ( singleton @ SV7 ) @ SV11 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) ) )
| ~ ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV3 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV8 ) ) )
= $false )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV9: $i,SV3: $i,SV13: $i] :
( ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false )
| ( ( ~ ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ SV13 )
| ( SY31 = SV3 )
| ( SY31 = SV9 ) )
| ~ ~ ( ~ ! [SY32: $i] :
( ( SY32 != SV3 )
| ( in @ SY32 @ SV13 ) )
| ~ ! [SY33: $i] :
( ( SY33 != SV9 )
| ( in @ SY33 @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) ) ) )
= $false )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(73,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV3 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV8 ) ) )
= $false )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV9: $i,SV3: $i,SV13: $i] :
( ( ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ SV13 )
| ( SY31 = SV3 )
| ( SY31 = SV9 ) )
| ~ ~ ( ~ ! [SY32: $i] :
( ( SY32 != SV3 )
| ( in @ SY32 @ SV13 ) )
| ~ ! [SY33: $i] :
( ( SY33 != SV9 )
| ( in @ SY33 @ SV13 ) ) ) )
= $false )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) ) ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV3 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV8 ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(77,plain,
! [SV9: $i,SV3: $i,SV13: $i] :
( ( ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ SV13 )
| ( SY31 = SV3 )
| ( SY31 = SV9 ) ) )
= $false )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(78,plain,
! [SV9: $i,SV13: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ! [SY32: $i] :
( ( SY32 != SV3 )
| ( in @ SY32 @ SV13 ) )
| ~ ! [SY33: $i] :
( ( SY33 != SV9 )
| ( in @ SY33 @ SV13 ) ) ) )
= $false )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) ) )
= $false )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
= $true )
| ( ( ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV3 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV8 ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV9: $i,SV3: $i,SV13: $i] :
( ( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ SV13 )
| ( SY31 = SV3 )
| ( SY31 = SV9 ) ) )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(82,plain,
! [SV9: $i,SV13: $i,SV3: $i] :
( ( ( ~ ( ~ ! [SY32: $i] :
( ( SY32 != SV3 )
| ( in @ SY32 @ SV13 ) )
| ~ ! [SY33: $i] :
( ( SY33 != SV9 )
| ( in @ SY33 @ SV13 ) ) ) )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(83,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) ) )
= $false )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(84,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) ) )
= $false )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(85,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV3 )
= $true )
| ( ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV8 )
= $true )
| ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV9: $i,SV3: $i,SV13: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV13 )
| ( SV14 = SV3 )
| ( SV14 = SV9 ) )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV9: $i,SV13: $i,SV3: $i] :
( ( ( ~ ! [SY32: $i] :
( ( SY32 != SV3 )
| ( in @ SY32 @ SV13 ) )
| ~ ! [SY33: $i] :
( ( SY33 != SV9 )
| ( in @ SY33 @ SV13 ) ) )
= $false )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(89,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
| ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(90,plain,
! [SV9: $i,SV3: $i,SV13: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV13 ) )
= $true )
| ( ( ( SV14 = SV3 )
| ( SV14 = SV9 ) )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV9: $i,SV13: $i,SV3: $i] :
( ( ( ~ ! [SY32: $i] :
( ( SY32 != SV3 )
| ( in @ SY32 @ SV13 ) ) )
= $false )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(92,plain,
! [SV3: $i,SV13: $i,SV9: $i] :
( ( ( ~ ! [SY33: $i] :
( ( SY33 != SV9 )
| ( in @ SY33 @ SV13 ) ) )
= $false )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(93,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 ) )
= $true )
| ( ( ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 ) )
= $true )
| ( ( ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV9: $i,SV3: $i,SV13: $i,SV14: $i] :
( ( ( in @ SV14 @ SV13 )
= $false )
| ( ( ( SV14 = SV3 )
| ( SV14 = SV9 ) )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV9: $i,SV13: $i,SV3: $i] :
( ( ( ! [SY32: $i] :
( ( SY32 != SV3 )
| ( in @ SY32 @ SV13 ) ) )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(97,plain,
! [SV3: $i,SV13: $i,SV9: $i] :
( ( ( ! [SY33: $i] :
( ( SY33 != SV9 )
| ( in @ SY33 @ SV13 ) ) )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(98,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
= $false )
| ( ( ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV3 ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
= $false )
| ( ( ( ( sK5_D @ SV12 @ SV8 @ SV3 )
!= SV8 ) )
= $true )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV13: $i,SV9: $i,SV3: $i,SV14: $i] :
( ( ( SV14 = SV3 )
= $true )
| ( ( SV14 = SV9 )
= $true )
| ( ( in @ SV14 @ SV13 )
= $false )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(101,plain,
! [SV9: $i,SV13: $i,SV3: $i,SV15: $i] :
( ( ( ( SV15 != SV3 )
| ( in @ SV15 @ SV13 ) )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV3: $i,SV13: $i,SV9: $i,SV16: $i] :
( ( ( ( SV16 != SV9 )
| ( in @ SV16 @ SV13 ) )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV3 )
= $false )
| ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
= $false )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ( sK5_D @ SV12 @ SV8 @ SV3 )
= SV8 )
= $false )
| ( ( in @ ( sK5_D @ SV12 @ SV8 @ SV3 ) @ SV12 )
= $false )
| ( ( SV12
= ( unordered_pair @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV9: $i,SV13: $i,SV3: $i,SV15: $i] :
( ( ( ( SV15 != SV3 ) )
= $true )
| ( ( in @ SV15 @ SV13 )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV3: $i,SV13: $i,SV9: $i,SV16: $i] :
( ( ( ( SV16 != SV9 ) )
= $true )
| ( ( in @ SV16 @ SV13 )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV9: $i,SV13: $i,SV3: $i,SV15: $i] :
( ( ( SV15 = SV3 )
= $false )
| ( ( in @ SV15 @ SV13 )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(108,plain,
! [SV3: $i,SV13: $i,SV9: $i,SV16: $i] :
( ( ( SV16 = SV9 )
= $false )
| ( ( in @ SV16 @ SV13 )
= $true )
| ( ( SV13
= ( unordered_pair @ SV3 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(109,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,108,107,104,103,100,85,69,68,57,43,39,38,31]) ).
thf(110,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 11:37:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 7
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 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).......
% 0.19/0.44
% 0.19/0.44 ********************************
% 0.19/0.44 * All subproblems solved! *
% 0.19/0.44 ********************************
% 0.19/0.44 % SZS status Theorem for /export/starexec/sandbox2/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:109,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.44
% 0.19/0.44 %**** Beginning of derivation protocol ****
% 0.19/0.44 % SZS output start CNFRefutation
% See solution above
% 0.19/0.44
% 0.19/0.44 %**** End of derivation protocol ****
% 0.19/0.44 %**** no. of clauses in derivation: 110 ****
% 0.19/0.44 %**** clause counter: 109 ****
% 0.19/0.44
% 0.19/0.44 % SZS status Theorem for /export/starexec/sandbox2/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:109,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------