TSTP Solution File: SET918+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET918+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 : n011.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 03:06:14 EDT 2022
% Result : Theorem 0.50s 0.68s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 23
% Syntax : Number of formulae : 218 ( 92 unt; 13 typ; 0 def)
% Number of atoms : 1601 ( 767 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 3653 ( 742 ~; 638 |; 46 &;2213 @)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 654 ( 0 ^ 650 !; 4 ?; 654 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY24,type,
sK2_SY24: $i ).
thf(tp_sK3_SY26,type,
sK3_SY26: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_D,type,
sK6_D: $i > $i > $i > $i ).
thf(tp_sK7_D,type,
sK7_D: $i > $i > $i > $i ).
thf(tp_sK8_C,type,
sK8_C: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $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_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_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] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(10,conjecture,
! [A: $i,B: $i,C: $i] :
~ ( ( ( set_intersection2 @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
& ( in @ B @ C )
& ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_zfmisc_1) ).
thf(11,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( ( set_intersection2 @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
& ( in @ B @ C )
& ( A != B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( ( set_intersection2 @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
& ( in @ B @ C )
& ( A != B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,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(18,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(22,plain,
( ( ! [SY24: $i,SY25: $i] :
~ ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ SY24 ) @ SY25 )
= ( singleton @ sK1_A ) )
& ( in @ SY24 @ SY25 )
& ( sK1_A != SY24 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ! [SY26: $i] :
~ ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ SY26 )
= ( singleton @ sK1_A ) )
& ( in @ sK2_SY24 @ SY26 )
& ( sK1_A != sK2_SY24 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( ~ ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
= ( singleton @ sK1_A ) )
& ( in @ sK2_SY24 @ sK3_SY26 )
& ( sK1_A != sK2_SY24 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(25,plain,
( ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
= ( singleton @ sK1_A ) )
& ( in @ sK2_SY24 @ sK3_SY26 )
& ( sK1_A != sK2_SY24 ) )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(26,plain,
( ( ( sK1_A != sK2_SY24 )
& ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
= ( singleton @ sK1_A ) )
& ( in @ sK2_SY24 @ sK3_SY26 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(27,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(28,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(30,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(31,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
= A )
| ( ( sK7_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)],[17]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK8_C @ B @ A )
!= A )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( sK8_C @ B @ A )
= A )
| ( in @ ( sK8_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK8_C @ B @ A )
!= A )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( sK8_C @ B @ A )
= A )
| ( in @ ( sK8_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(38,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
= A )
| ( ( sK7_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)],[31]) ).
thf(39,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(41,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(42,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(43,plain,
( ( ( sK1_A != sK2_SY24 )
& ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
= ( singleton @ sK1_A ) )
& ( in @ sK2_SY24 @ sK3_SY26 ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(44,plain,
( ( ~ ( ~ ( ( sK1_A != sK2_SY24 ) )
| ~ ~ ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
!= ( singleton @ sK1_A ) )
| ~ ( in @ sK2_SY24 @ sK3_SY26 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(46,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(47,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK7_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)],[38]) ).
thf(48,plain,
! [SV1: $i] :
( ( ! [SY27: $i] :
( ~ ( in @ SV1 @ SY27 )
| ~ ( in @ SY27 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(49,plain,
! [SV2: $i] :
( ( ! [SY28: $i] :
( ( unordered_pair @ SV2 @ SY28 )
= ( unordered_pair @ SY28 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(50,plain,
! [SV3: $i] :
( ( ! [SY29: $i] :
( ( set_intersection2 @ SV3 @ SY29 )
= ( set_intersection2 @ SY29 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( set_intersection2 @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(52,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(53,plain,
( ( ~ ( ( sK1_A != sK2_SY24 ) )
| ~ ~ ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
!= ( singleton @ sK1_A ) )
| ~ ( in @ sK2_SY24 @ sK3_SY26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY30 )
| ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) )
| ~ ( ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY30 )
| ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) ) ) )
| ( SY31
= ( set_intersection2 @ SV5 @ SY30 ) ) )
| ~ ! [SY32: $i,SY33: $i] :
( ( SY33
!= ( set_intersection2 @ SV5 @ SY32 ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV5 )
| ~ ( in @ SY34 @ SY32 )
| ( in @ SY34 @ SY33 ) )
| ~ ~ ( ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ SY33 )
| ( in @ SY35 @ SV5 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY33 )
| ( in @ SX3 @ SY32 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(55,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY37: $i,SY38: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
!= SY37 ) ) )
| ~ ( ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
= SV6 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
= SY37 ) ) )
| ( SY38
= ( unordered_pair @ SV6 @ SY37 ) ) )
| ~ ! [SY39: $i,SY40: $i] :
( ( SY40
!= ( unordered_pair @ SV6 @ SY39 ) )
| ~ ( ~ ! [SY41: $i] :
( ~ ( in @ SY41 @ SY40 )
| ( SY41 = SV6 )
| ( SY41 = SY39 ) )
| ~ ~ ( ~ ! [SY42: $i] :
( ( SY42 != SV6 )
| ( in @ SY42 @ SY40 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY39 )
| ( in @ SX3 @ SY40 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV7 )
| ~ ( in @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV8: $i,SV2: $i] :
( ( ( unordered_pair @ SV2 @ SV8 )
= ( unordered_pair @ SV8 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV9: $i,SV3: $i] :
( ( ( set_intersection2 @ SV3 @ SV9 )
= ( set_intersection2 @ SV9 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
( ( ~ ( ( sK1_A != sK2_SY24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(61,plain,
( ( ~ ~ ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
!= ( singleton @ sK1_A ) )
| ~ ( in @ sK2_SY24 @ sK3_SY26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(62,plain,
! [SV5: $i] :
( ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY30 )
| ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) )
| ~ ( ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY30 )
| ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) ) ) )
| ( SY31
= ( set_intersection2 @ SV5 @ SY30 ) ) )
| ~ ! [SY32: $i,SY33: $i] :
( ( SY33
!= ( set_intersection2 @ SV5 @ SY32 ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV5 )
| ~ ( in @ SY34 @ SY32 )
| ( in @ SY34 @ SY33 ) )
| ~ ~ ( ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ SY33 )
| ( in @ SY35 @ SV5 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY33 )
| ( in @ SX3 @ SY32 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(63,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(64,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(65,plain,
! [SV6: $i] :
( ( ~ ! [SY37: $i,SY38: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
!= SY37 ) ) )
| ~ ( ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
= SV6 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
= SY37 ) ) )
| ( SY38
= ( unordered_pair @ SV6 @ SY37 ) ) )
| ~ ! [SY39: $i,SY40: $i] :
( ( SY40
!= ( unordered_pair @ SV6 @ SY39 ) )
| ~ ( ~ ! [SY41: $i] :
( ~ ( in @ SY41 @ SY40 )
| ( SY41 = SV6 )
| ( SY41 = SY39 ) )
| ~ ~ ( ~ ! [SY42: $i] :
( ( SY42 != SV6 )
| ( in @ SY42 @ SY40 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY39 )
| ( in @ SX3 @ SY40 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(67,plain,
( ( ( sK1_A != sK2_SY24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(68,plain,
( ( ~ ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
!= ( singleton @ sK1_A ) )
| ~ ( in @ sK2_SY24 @ sK3_SY26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(69,plain,
! [SV5: $i] :
( ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY30 )
| ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) )
| ~ ( ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY30 )
| ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) ) ) )
| ( SY31
= ( set_intersection2 @ SV5 @ SY30 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(70,plain,
! [SV5: $i] :
( ( ~ ! [SY32: $i,SY33: $i] :
( ( SY33
!= ( set_intersection2 @ SV5 @ SY32 ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV5 )
| ~ ( in @ SY34 @ SY32 )
| ( in @ SY34 @ SY33 ) )
| ~ ~ ( ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ SY33 )
| ( in @ SY35 @ SV5 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY33 )
| ( in @ SX3 @ SY32 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(73,plain,
! [SV6: $i] :
( ( ~ ! [SY37: $i,SY38: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
!= SY37 ) ) )
| ~ ( ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
= SV6 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
= SY37 ) ) )
| ( SY38
= ( unordered_pair @ SV6 @ SY37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(74,plain,
! [SV6: $i] :
( ( ~ ! [SY39: $i,SY40: $i] :
( ( SY40
!= ( unordered_pair @ SV6 @ SY39 ) )
| ~ ( ~ ! [SY41: $i] :
( ~ ( in @ SY41 @ SY40 )
| ( SY41 = SV6 )
| ( SY41 = SY39 ) )
| ~ ~ ( ~ ! [SY42: $i] :
( ( SY42 != SV6 )
| ( in @ SY42 @ SY40 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY39 )
| ( in @ SX3 @ SY40 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
! [SV7: $i,SV1: $i] :
( ( ( in @ SV1 @ SV7 )
= $false )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(76,plain,
( ( sK1_A = sK2_SY24 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(77,plain,
( ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
!= ( singleton @ sK1_A ) )
| ~ ( in @ sK2_SY24 @ sK3_SY26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV5: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY30 )
| ~ ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) )
| ~ ( ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY30 )
| ( in @ ( sK6_D @ SY31 @ SY30 @ SV5 ) @ SY31 ) ) ) )
| ( SY31
= ( set_intersection2 @ SV5 @ SY30 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(79,plain,
! [SV5: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ( SY33
!= ( set_intersection2 @ SV5 @ SY32 ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV5 )
| ~ ( in @ SY34 @ SY32 )
| ( in @ SY34 @ SY33 ) )
| ~ ~ ( ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ SY33 )
| ( in @ SY35 @ SV5 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY33 )
| ( in @ SX3 @ SY32 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(80,plain,
! [SV10: $i] :
( ( ! [SY44: $i] :
( ~ ( ~ ( ( ( sK8_C @ SY44 @ SV10 )
!= SV10 )
| ~ ( in @ ( sK8_C @ SY44 @ SV10 ) @ SY44 ) )
| ~ ( ( ( sK8_C @ SY44 @ SV10 )
= SV10 )
| ( in @ ( sK8_C @ SY44 @ SV10 ) @ SY44 ) ) )
| ( SY44
= ( singleton @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV11: $i] :
( ( ! [SY45: $i] :
( ( SY45
!= ( singleton @ SV11 ) )
| ~ ( ~ ! [SY46: $i] :
( ( SY46 != SV11 )
| ( in @ SY46 @ SY45 ) )
| ~ ! [SY47: $i] :
( ~ ( in @ SY47 @ SY45 )
| ( SY47 = SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV6: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
!= SY37 ) ) )
| ~ ( ( in @ ( sK7_D @ SY38 @ SY37 @ SV6 ) @ SY38 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
= SV6 )
| ( ( sK7_D @ SY38 @ SY37 @ SV6 )
= SY37 ) ) )
| ( SY38
= ( unordered_pair @ SV6 @ SY37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(83,plain,
! [SV6: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ( SY40
!= ( unordered_pair @ SV6 @ SY39 ) )
| ~ ( ~ ! [SY41: $i] :
( ~ ( in @ SY41 @ SY40 )
| ( SY41 = SV6 )
| ( SY41 = SY39 ) )
| ~ ~ ( ~ ! [SY42: $i] :
( ( SY42 != SV6 )
| ( in @ SY42 @ SY40 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY39 )
| ( in @ SX3 @ SY40 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(84,plain,
! [SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(85,plain,
( ( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
!= ( singleton @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(86,plain,
( ( ~ ( in @ sK2_SY24 @ sK3_SY26 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(87,plain,
! [SV5: $i,SV12: $i] :
( ( ! [SY48: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY48 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SY48 @ SV12 @ SV5 ) @ SV12 )
| ~ ( in @ ( sK6_D @ SY48 @ SV12 @ SV5 ) @ SY48 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY48 @ SV12 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SY48 @ SV12 @ SV5 ) @ SY48 ) )
| ~ ( ( in @ ( sK6_D @ SY48 @ SV12 @ SV5 ) @ SV12 )
| ( in @ ( sK6_D @ SY48 @ SV12 @ SV5 ) @ SY48 ) ) ) )
| ( SY48
= ( set_intersection2 @ SV5 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV13: $i,SV5: $i] :
( ( ! [SY49: $i] :
( ( SY49
!= ( set_intersection2 @ SV5 @ SV13 ) )
| ~ ( ~ ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ~ ( in @ SY50 @ SV13 )
| ( in @ SY50 @ SY49 ) )
| ~ ~ ( ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ SY49 )
| ( in @ SY35 @ SV5 ) )
| ~ ! [SY52: $i] :
( ~ ( in @ SY52 @ SY49 )
| ( in @ SY52 @ SV13 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV10: $i,SV14: $i] :
( ( ~ ( ~ ( ( ( sK8_C @ SV14 @ SV10 )
!= SV10 )
| ~ ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) )
| ~ ( ( ( sK8_C @ SV14 @ SV10 )
= SV10 )
| ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) ) )
| ( SV14
= ( singleton @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV11: $i,SV15: $i] :
( ( ( SV15
!= ( singleton @ SV11 ) )
| ~ ( ~ ! [SY53: $i] :
( ( SY53 != SV11 )
| ( in @ SY53 @ SV15 ) )
| ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV15 )
| ( SY54 = SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV6: $i,SV16: $i] :
( ( ! [SY55: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY55 @ SV16 @ SV6 ) @ SY55 )
| ( ( sK7_D @ SY55 @ SV16 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY55 @ SV16 @ SV6 ) @ SY55 )
| ( ( sK7_D @ SY55 @ SV16 @ SV6 )
!= SV16 ) ) )
| ~ ( ( in @ ( sK7_D @ SY55 @ SV16 @ SV6 ) @ SY55 )
| ( ( sK7_D @ SY55 @ SV16 @ SV6 )
= SV6 )
| ( ( sK7_D @ SY55 @ SV16 @ SV6 )
= SV16 ) ) )
| ( SY55
= ( unordered_pair @ SV6 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV17: $i,SV6: $i] :
( ( ! [SY56: $i] :
( ( SY56
!= ( unordered_pair @ SV6 @ SV17 ) )
| ~ ( ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SY56 )
| ( SY57 = SV6 )
| ( SY57 = SV17 ) )
| ~ ~ ( ~ ! [SY42: $i] :
( ( SY42 != SV6 )
| ( in @ SY42 @ SY56 ) )
| ~ ! [SY59: $i] :
( ( SY59 != SV17 )
| ( in @ SY59 @ SY56 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
( ( ( set_intersection2 @ ( unordered_pair @ sK1_A @ sK2_SY24 ) @ sK3_SY26 )
= ( singleton @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(94,plain,
( ( in @ sK2_SY24 @ sK3_SY26 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(95,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
| ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) ) ) )
| ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV13: $i,SV5: $i,SV19: $i] :
( ( ( SV19
!= ( set_intersection2 @ SV5 @ SV13 ) )
| ~ ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV5 )
| ~ ( in @ SY60 @ SV13 )
| ( in @ SY60 @ SV19 ) )
| ~ ~ ( ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV19 )
| ( in @ SY61 @ SV5 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SV19 )
| ( in @ SY62 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ~ ( ( ( sK8_C @ SV14 @ SV10 )
!= SV10 )
| ~ ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) )
| ~ ( ( ( sK8_C @ SV14 @ SV10 )
= SV10 )
| ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) ) ) )
= $true )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV11: $i,SV15: $i] :
( ( ( ( SV15
!= ( singleton @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY53: $i] :
( ( SY53 != SV11 )
| ( in @ SY53 @ SV15 ) )
| ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV15 )
| ( SY54 = SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) ) )
| ~ ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV6 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV16 ) ) )
| ( SV20
= ( unordered_pair @ SV6 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV17: $i,SV6: $i,SV21: $i] :
( ( ( SV21
!= ( unordered_pair @ SV6 @ SV17 ) )
| ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV21 )
| ( SY63 = SV6 )
| ( SY63 = SV17 ) )
| ~ ~ ( ~ ! [SY64: $i] :
( ( SY64 != SV6 )
| ( in @ SY64 @ SV21 ) )
| ~ ! [SY65: $i] :
( ( SY65 != SV17 )
| ( in @ SY65 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
| ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) ) ) ) )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV13: $i,SV5: $i,SV19: $i] :
( ( ( ( SV19
!= ( set_intersection2 @ SV5 @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV5 )
| ~ ( in @ SY60 @ SV13 )
| ( in @ SY60 @ SV19 ) )
| ~ ~ ( ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV19 )
| ( in @ SY61 @ SV5 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SV19 )
| ( in @ SY62 @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(103,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ( ( sK8_C @ SV14 @ SV10 )
!= SV10 )
| ~ ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) )
| ~ ( ( ( sK8_C @ SV14 @ SV10 )
= SV10 )
| ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) ) )
= $false )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(104,plain,
! [SV11: $i,SV15: $i] :
( ( ( SV15
= ( singleton @ SV11 ) )
= $false )
| ( ( ~ ( ~ ! [SY53: $i] :
( ( SY53 != SV11 )
| ( in @ SY53 @ SV15 ) )
| ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV15 )
| ( SY54 = SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) ) )
| ~ ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV6 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV16 ) ) ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV17: $i,SV6: $i,SV21: $i] :
( ( ( ( SV21
!= ( unordered_pair @ SV6 @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV21 )
| ( SY63 = SV6 )
| ( SY63 = SV17 ) )
| ~ ~ ( ~ ! [SY64: $i] :
( ( SY64 != SV6 )
| ( in @ SY64 @ SV21 ) )
| ~ ! [SY65: $i] :
( ( SY65 != SV17 )
| ( in @ SY65 @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
| ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) ) ) )
= $false )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV13: $i,SV5: $i,SV19: $i] :
( ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false )
| ( ( ~ ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV5 )
| ~ ( in @ SY60 @ SV13 )
| ( in @ SY60 @ SV19 ) )
| ~ ~ ( ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV19 )
| ( in @ SY61 @ SV5 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SV19 )
| ( in @ SY62 @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ( ( sK8_C @ SV14 @ SV10 )
!= SV10 )
| ~ ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) ) )
= $false )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(110,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ( ( sK8_C @ SV14 @ SV10 )
= SV10 )
| ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) ) )
= $false )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(111,plain,
! [SV15: $i,SV11: $i] :
( ( ( ~ ! [SY53: $i] :
( ( SY53 != SV11 )
| ( in @ SY53 @ SV15 ) )
| ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV15 )
| ( SY54 = SV11 ) ) )
= $false )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) ) )
| ~ ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV6 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV16 ) ) )
= $false )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV17: $i,SV6: $i,SV21: $i] :
( ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false )
| ( ( ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV21 )
| ( SY63 = SV6 )
| ( SY63 = SV17 ) )
| ~ ~ ( ~ ! [SY64: $i] :
( ( SY64 != SV6 )
| ( in @ SY64 @ SV21 ) )
| ~ ! [SY65: $i] :
( ( SY65 != SV17 )
| ( in @ SY65 @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) ) )
= $false )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(115,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
| ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) ) ) )
= $false )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(116,plain,
! [SV19: $i,SV13: $i,SV5: $i] :
( ( ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV5 )
| ~ ( in @ SY60 @ SV13 )
| ( in @ SY60 @ SV19 ) )
| ~ ~ ( ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV19 )
| ( in @ SY61 @ SV5 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SV19 )
| ( in @ SY62 @ SV13 ) ) ) )
= $false )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(117,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( ( sK8_C @ SV14 @ SV10 )
!= SV10 )
| ~ ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(118,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( ( sK8_C @ SV14 @ SV10 )
= SV10 )
| ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(119,plain,
! [SV15: $i,SV11: $i] :
( ( ( ~ ! [SY53: $i] :
( ( SY53 != SV11 )
| ( in @ SY53 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(120,plain,
! [SV11: $i,SV15: $i] :
( ( ( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV15 )
| ( SY54 = SV11 ) ) )
= $false )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(121,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) ) ) )
= $false )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(122,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV6 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV16 ) ) )
= $false )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(123,plain,
! [SV17: $i,SV6: $i,SV21: $i] :
( ( ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV21 )
| ( SY63 = SV6 )
| ( SY63 = SV17 ) )
| ~ ~ ( ~ ! [SY64: $i] :
( ( SY64 != SV6 )
| ( in @ SY64 @ SV21 ) )
| ~ ! [SY65: $i] :
( ( SY65 != SV17 )
| ( in @ SY65 @ SV21 ) ) ) )
= $false )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(125,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
| ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) ) ) )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(126,plain,
! [SV19: $i,SV13: $i,SV5: $i] :
( ( ( ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV5 )
| ~ ( in @ SY60 @ SV13 )
| ( in @ SY60 @ SV19 ) ) )
= $false )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(127,plain,
! [SV13: $i,SV5: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV19 )
| ( in @ SY61 @ SV5 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SV19 )
| ( in @ SY62 @ SV13 ) ) ) )
= $false )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(128,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( ( sK8_C @ SV14 @ SV10 )
!= SV10 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(129,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( sK8_C @ SV14 @ SV10 )
= SV10 )
= $true )
| ( ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 )
= $true )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(130,plain,
! [SV15: $i,SV11: $i] :
( ( ( ! [SY53: $i] :
( ( SY53 != SV11 )
| ( in @ SY53 @ SV15 ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(131,plain,
! [SV11: $i,SV15: $i] :
( ( ( ! [SY54: $i] :
( ~ ( in @ SY54 @ SV15 )
| ( SY54 = SV11 ) ) )
= $true )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(132,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) ) ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(133,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV6 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV16 ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(134,plain,
! [SV17: $i,SV6: $i,SV21: $i] :
( ( ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV21 )
| ( SY63 = SV6 )
| ( SY63 = SV17 ) ) )
= $false )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(135,plain,
! [SV17: $i,SV21: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ! [SY64: $i] :
( ( SY64 != SV6 )
| ( in @ SY64 @ SV21 ) )
| ~ ! [SY65: $i] :
( ( SY65 != SV17 )
| ( in @ SY65 @ SV21 ) ) ) )
= $false )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(136,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
| ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) ) )
= $false )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV19: $i,SV13: $i,SV5: $i] :
( ( ( ! [SY60: $i] :
( ~ ( in @ SY60 @ SV5 )
| ~ ( in @ SY60 @ SV13 )
| ( in @ SY60 @ SV19 ) ) )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(139,plain,
! [SV13: $i,SV5: $i,SV19: $i] :
( ( ( ~ ( ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV19 )
| ( in @ SY61 @ SV5 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SV19 )
| ( in @ SY62 @ SV13 ) ) ) )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(140,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( sK8_C @ SV14 @ SV10 )
= SV10 )
= $false )
| ( ( ~ ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV15: $i,SV11: $i,SV22: $i] :
( ( ( ( SV22 != SV11 )
| ( in @ SV22 @ SV15 ) )
= $true )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV11: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV15 )
| ( SV23 = SV11 ) )
= $true )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) ) )
= $false )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
= $true )
| ( ( ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV6 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV16 ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(145,plain,
! [SV17: $i,SV6: $i,SV21: $i] :
( ( ( ! [SY63: $i] :
( ~ ( in @ SY63 @ SV21 )
| ( SY63 = SV6 )
| ( SY63 = SV17 ) ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(146,plain,
! [SV17: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( ~ ! [SY64: $i] :
( ( SY64 != SV6 )
| ( in @ SY64 @ SV21 ) )
| ~ ! [SY65: $i] :
( ( SY65 != SV17 )
| ( in @ SY65 @ SV21 ) ) ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(147,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(148,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) ) )
= $false )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(149,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) ) )
= $false )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(150,plain,
! [SV19: $i,SV13: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV5 )
| ~ ( in @ SV24 @ SV13 )
| ( in @ SV24 @ SV19 ) )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(151,plain,
! [SV13: $i,SV5: $i,SV19: $i] :
( ( ( ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV19 )
| ( in @ SY61 @ SV5 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SV19 )
| ( in @ SY62 @ SV13 ) ) )
= $false )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV10: $i,SV14: $i] :
( ( ( in @ ( sK8_C @ SV14 @ SV10 ) @ SV14 )
= $false )
| ( ( ( sK8_C @ SV14 @ SV10 )
= SV10 )
= $false )
| ( ( SV14
= ( singleton @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV15: $i,SV11: $i,SV22: $i] :
( ( ( ( SV22 != SV11 ) )
= $true )
| ( ( in @ SV22 @ SV15 )
= $true )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(154,plain,
! [SV11: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV15 ) )
= $true )
| ( ( SV23 = SV11 )
= $true )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(155,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) ) )
= $false )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(156,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) ) )
= $false )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(157,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV6 )
= $true )
| ( ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV16 )
= $true )
| ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(158,plain,
! [SV17: $i,SV6: $i,SV21: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV21 )
| ( SV25 = SV6 )
| ( SV25 = SV17 ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(159,plain,
! [SV17: $i,SV21: $i,SV6: $i] :
( ( ( ~ ! [SY64: $i] :
( ( SY64 != SV6 )
| ( in @ SY64 @ SV21 ) )
| ~ ! [SY65: $i] :
( ( SY65 != SV17 )
| ( in @ SY65 @ SV21 ) ) )
= $false )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
= $false )
| ( ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(162,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
| ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(163,plain,
! [SV19: $i,SV13: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV5 )
| ~ ( in @ SV24 @ SV13 ) )
= $true )
| ( ( in @ SV24 @ SV19 )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(164,plain,
! [SV13: $i,SV5: $i,SV19: $i] :
( ( ( ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ SV19 )
| ( in @ SY61 @ SV5 ) ) )
= $false )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(165,plain,
! [SV5: $i,SV13: $i,SV19: $i] :
( ( ( ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SV19 )
| ( in @ SY62 @ SV13 ) ) )
= $false )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(166,plain,
! [SV15: $i,SV11: $i,SV22: $i] :
( ( ( SV22 = SV11 )
= $false )
| ( ( in @ SV22 @ SV15 )
= $true )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV11: $i,SV15: $i,SV23: $i] :
( ( ( in @ SV23 @ SV15 )
= $false )
| ( ( SV23 = SV11 )
= $true )
| ( ( SV15
= ( singleton @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(169,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
| ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(170,plain,
! [SV17: $i,SV6: $i,SV21: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV21 ) )
= $true )
| ( ( ( SV25 = SV6 )
| ( SV25 = SV17 ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(171,plain,
! [SV17: $i,SV21: $i,SV6: $i] :
( ( ( ~ ! [SY64: $i] :
( ( SY64 != SV6 )
| ( in @ SY64 @ SV21 ) ) )
= $false )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(172,plain,
! [SV6: $i,SV21: $i,SV17: $i] :
( ( ( ~ ! [SY65: $i] :
( ( SY65 != SV17 )
| ( in @ SY65 @ SV21 ) ) )
= $false )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(173,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
= $false )
| ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
= $false )
| ( ( ~ ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
= $true )
| ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(176,plain,
! [SV19: $i,SV13: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV24 @ SV13 ) )
= $true )
| ( ( in @ SV24 @ SV19 )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(177,plain,
! [SV13: $i,SV5: $i,SV19: $i] :
( ( ( ! [SY61: $i] :
( ~ ( in @ SY61 @ SV19 )
| ( in @ SY61 @ SV5 ) ) )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(178,plain,
! [SV5: $i,SV13: $i,SV19: $i] :
( ( ( ! [SY62: $i] :
( ~ ( in @ SY62 @ SV19 )
| ( in @ SY62 @ SV13 ) ) )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(179,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 ) )
= $true )
| ( ( ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(180,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 ) )
= $true )
| ( ( ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(181,plain,
! [SV17: $i,SV6: $i,SV21: $i,SV25: $i] :
( ( ( in @ SV25 @ SV21 )
= $false )
| ( ( ( SV25 = SV6 )
| ( SV25 = SV17 ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV17: $i,SV21: $i,SV6: $i] :
( ( ( ! [SY64: $i] :
( ( SY64 != SV6 )
| ( in @ SY64 @ SV21 ) ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(183,plain,
! [SV6: $i,SV21: $i,SV17: $i] :
( ( ( ! [SY65: $i] :
( ( SY65 != SV17 )
| ( in @ SY65 @ SV21 ) ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(184,plain,
! [SV5: $i,SV12: $i,SV18: $i] :
( ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV18 )
= $false )
| ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV5 )
= $false )
| ( ( in @ ( sK6_D @ SV18 @ SV12 @ SV5 ) @ SV12 )
= $false )
| ( ( SV18
= ( set_intersection2 @ SV5 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV19: $i,SV13: $i,SV5: $i,SV24: $i] :
( ( ( in @ SV24 @ SV5 )
= $false )
| ( ( ~ ( in @ SV24 @ SV13 ) )
= $true )
| ( ( in @ SV24 @ SV19 )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(186,plain,
! [SV13: $i,SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV19 )
| ( in @ SV26 @ SV5 ) )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV5: $i,SV13: $i,SV19: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV19 )
| ( in @ SV27 @ SV13 ) )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(188,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
= $false )
| ( ( ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV6 ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(189,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
= $false )
| ( ( ( ( sK7_D @ SV20 @ SV16 @ SV6 )
!= SV16 ) )
= $true )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(190,plain,
! [SV21: $i,SV17: $i,SV6: $i,SV25: $i] :
( ( ( SV25 = SV6 )
= $true )
| ( ( SV25 = SV17 )
= $true )
| ( ( in @ SV25 @ SV21 )
= $false )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(191,plain,
! [SV17: $i,SV21: $i,SV6: $i,SV28: $i] :
( ( ( ( SV28 != SV6 )
| ( in @ SV28 @ SV21 ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(192,plain,
! [SV6: $i,SV21: $i,SV17: $i,SV29: $i] :
( ( ( ( SV29 != SV17 )
| ( in @ SV29 @ SV21 ) )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(193,plain,
! [SV19: $i,SV5: $i,SV13: $i,SV24: $i] :
( ( ( in @ SV24 @ SV13 )
= $false )
| ( ( in @ SV24 @ SV5 )
= $false )
| ( ( in @ SV24 @ SV19 )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV13: $i,SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV19 ) )
= $true )
| ( ( in @ SV26 @ SV5 )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV5: $i,SV13: $i,SV19: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV19 ) )
= $true )
| ( ( in @ SV27 @ SV13 )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV6 )
= $false )
| ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
= $false )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(197,plain,
! [SV6: $i,SV16: $i,SV20: $i] :
( ( ( ( sK7_D @ SV20 @ SV16 @ SV6 )
= SV16 )
= $false )
| ( ( in @ ( sK7_D @ SV20 @ SV16 @ SV6 ) @ SV20 )
= $false )
| ( ( SV20
= ( unordered_pair @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(198,plain,
! [SV17: $i,SV21: $i,SV6: $i,SV28: $i] :
( ( ( ( SV28 != SV6 ) )
= $true )
| ( ( in @ SV28 @ SV21 )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(199,plain,
! [SV6: $i,SV21: $i,SV17: $i,SV29: $i] :
( ( ( ( SV29 != SV17 ) )
= $true )
| ( ( in @ SV29 @ SV21 )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(200,plain,
! [SV13: $i,SV5: $i,SV19: $i,SV26: $i] :
( ( ( in @ SV26 @ SV19 )
= $false )
| ( ( in @ SV26 @ SV5 )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(201,plain,
! [SV5: $i,SV13: $i,SV19: $i,SV27: $i] :
( ( ( in @ SV27 @ SV19 )
= $false )
| ( ( in @ SV27 @ SV13 )
= $true )
| ( ( SV19
= ( set_intersection2 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(202,plain,
! [SV17: $i,SV21: $i,SV6: $i,SV28: $i] :
( ( ( SV28 = SV6 )
= $false )
| ( ( in @ SV28 @ SV21 )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(203,plain,
! [SV6: $i,SV21: $i,SV17: $i,SV29: $i] :
( ( ( SV29 = SV17 )
= $false )
| ( ( in @ SV29 @ SV21 )
= $true )
| ( ( SV21
= ( unordered_pair @ SV6 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(204,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,203,202,201,200,197,196,193,190,184,175,174,167,166,157,152,129,94,93,84,76,59,58,52,51]) ).
thf(205,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 22:59:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 9
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)...............
% 0.50/0.68
% 0.50/0.68 ********************************
% 0.50/0.68 * All subproblems solved! *
% 0.50/0.68 ********************************
% 0.50/0.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:204,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.50/0.70
% 0.50/0.70 %**** Beginning of derivation protocol ****
% 0.50/0.70 % SZS output start CNFRefutation
% See solution above
% 0.50/0.70
% 0.50/0.70 %**** End of derivation protocol ****
% 0.50/0.70 %**** no. of clauses in derivation: 205 ****
% 0.50/0.70 %**** clause counter: 204 ****
% 0.50/0.70
% 0.50/0.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:204,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------