%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO607+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:08:52 AM UTC 2026
% Result : Theorem 0.35s 0.38s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 2
% Syntax : Number of formulae : 185 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 3450 (1039 equ; 0 cnn)
% Maximal formula atoms : 13 ( 18 avg)
% Number of connectives : 7356 (2716 ~;1142 |; 45 &;3453 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 3 con; 0-5 aty)
% Number of variables : 1402 ( 0 ^;1342 !; 60 ?;1402 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_g_both,type,
g_both: $i > $i > $o ).
thf(tp_g_false,type,
g_false: $i > $i > $o ).
thf(tp_g_false_only,type,
g_false_only: $i > $i > $o ).
thf(tp_g_true,type,
g_true: $i > $i > $o ).
thf(tp_g_true_only,type,
g_true_only: $i > $i > $o ).
thf(tp_sK10_SX0,type,
sK10_SX0: $i > $i > $i > $i > $i ).
thf(tp_sK11_SY30,type,
sK11_SY30: $i > $i > $i > $i > $i > $i ).
thf(tp_sK12_SY32,type,
sK12_SY32: $i > $i > $i > $i > $i > $i ).
thf(tp_sK13_SX0,type,
sK13_SX0: $i > $i > $i > $i > $i > $i ).
thf(tp_sK14_SX0,type,
sK14_SX0: $i > $i > $i > $i > $i > $i ).
thf(tp_sK1_SY19,type,
sK1_SY19: $i > $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i > $i > $i ).
thf(tp_sK3_SY21,type,
sK3_SY21: $i > $i > $i ).
thf(tp_sK4_SY23,type,
sK4_SY23: $i > $i > $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i > $i > $i > $i ).
thf(tp_sK6_SY28,type,
sK6_SY28: $i > $i > $i > $i ).
thf(tp_sK7_SY25,type,
sK7_SY25: $i > $i > $i > $i > $i ).
thf(tp_sK8_SY27,type,
sK8_SY27: $i > $i > $i > $i > $i ).
thf(tp_sK9_SX0,type,
sK9_SX0: $i > $i > $i > $i > $i ).
thf(1,axiom,
! [X_2: $i,X_1: $i] :
( ( g_true_only @ X_2 @ X_1 )
| ( g_both @ X_2 @ X_1 )
| ( g_false_only @ X_2 @ X_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exhaustion_g) ).
thf(5,conjecture,
( ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
| ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B )
| ( ? [A: $i] :
( ( ( g_both @ a @ A )
| ( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) ) )
& ~ ( g_true_only @ a @ A )
& ~ ! [B: $i] : ( g_true_only @ A @ B ) )
& ~ ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
& ? [A: $i] :
( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) )
& ~ ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nc6) ).
thf(6,negated_conjecture,
( ( ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
| ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B )
| ( ? [A: $i] :
( ( ( g_both @ a @ A )
| ( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) ) )
& ~ ( g_true_only @ a @ A )
& ~ ! [B: $i] : ( g_true_only @ A @ B ) )
& ~ ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
& ? [A: $i] :
( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) )
& ~ ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
| ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B )
| ( ? [A: $i] :
( ( ( g_both @ a @ A )
| ( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) ) )
& ~ ( g_true_only @ a @ A )
& ~ ! [B: $i] : ( g_true_only @ A @ B ) )
& ~ ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
& ? [A: $i] :
( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) )
& ~ ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [X_2: $i,X_1: $i] :
( ( g_true_only @ X_2 @ X_1 )
| ( g_both @ X_2 @ X_1 )
| ( g_false_only @ X_2 @ X_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ~ ( ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
| ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B )
| ( ? [A: $i] :
( ( ( g_both @ a @ A )
| ( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) ) )
& ~ ( g_true_only @ a @ A )
& ~ ! [B: $i] : ( g_true_only @ A @ B ) )
& ~ ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
& ? [A: $i] :
( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) )
& ~ ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X_2: $i,X_1: $i] :
( ( g_true_only @ X_2 @ X_1 )
| ( g_both @ X_2 @ X_1 )
| ( g_false_only @ X_2 @ X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
| ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B )
| ( ? [A: $i] :
( ( ( g_both @ a @ A )
| ( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) ) )
& ~ ( g_true_only @ a @ A )
& ~ ! [B: $i] : ( g_true_only @ A @ B ) )
& ~ ? [A: $i] :
( ( g_false_only @ a @ A )
& ? [B: $i] : ( g_false_only @ A @ B ) )
& ? [A: $i] :
( ? [B: $i] : ( g_both @ A @ B )
& ~ ? [B: $i] : ( g_false_only @ A @ B ) )
& ~ ? [A: $i] :
! [B: $i] : ( g_true_only @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) )
| ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
( ( g_true_only @ SV1 @ SY17 )
| ( g_both @ SV1 @ SY17 )
| ( g_false_only @ SV1 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) )
| ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: $i,SV1: $i] :
( ( ( g_true_only @ SV1 @ SV2 )
| ( g_both @ SV1 @ SV2 )
| ( g_false_only @ SV1 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) )
| ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i,SV1: $i] :
( ( ( ( g_true_only @ SV1 @ SV2 )
| ( g_both @ SV1 @ SV2 ) )
= $true )
| ( ( g_false_only @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: $i,SV1: $i] :
( ( ( g_true_only @ SV1 @ SV2 )
= $true )
| ( ( g_both @ SV1 @ SV2 )
= $true )
| ( ( g_false_only @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ( g_false_only @ a @ SV3 )
| ~ ~ ! [SY18: $i] :
~ ( g_false_only @ SV3 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV4: $i] :
( ( ~ ! [SY19: $i] : ( g_true_only @ SV4 @ SY19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ( ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV3: $i] :
( ( ~ ( ~ ( g_false_only @ a @ SV3 )
| ~ ~ ! [SY18: $i] :
~ ( g_false_only @ SV3 @ SY18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV4: $i] :
( ( ! [SY19: $i] : ( g_true_only @ SV4 @ SY19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV3: $i] :
( ( ~ ( g_false_only @ a @ SV3 )
| ~ ~ ! [SY18: $i] :
~ ( g_false_only @ SV3 @ SY18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV4: $i] :
( ( g_true_only @ SV4 @ ( sK1_SY19 @ SV4 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(34,plain,
( ( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( ~ ( g_false_only @ a @ SV3 ) )
= $true )
| ( ( ~ ~ ! [SY18: $i] :
~ ( g_false_only @ SV3 @ SY18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: $i] :
( ( ( g_false_only @ a @ SV3 )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( g_false_only @ SV3 @ SY18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
( ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
| ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV3: $i] :
( ( ( ~ ! [SY18: $i] :
~ ( g_false_only @ SV3 @ SY18 ) )
= $false )
| ( ( g_false_only @ a @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV3: $i] :
( ( ( ! [SY18: $i] :
~ ( g_false_only @ SV3 @ SY18 ) )
= $true )
| ( ( g_false_only @ a @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(42,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) ) )
= $false )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( g_false_only @ SV3 @ SV5 ) )
= $true )
| ( ( g_false_only @ a @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
( ( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SX0 )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
| ~ ~ ( g_true_only @ a @ SX0 ) )
| ~ ~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
! [SV5: $i,SV3: $i] :
( ( ( g_false_only @ SV3 @ SV5 )
= $false )
| ( ( g_false_only @ a @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( g_both @ a @ SV6 )
| ~ ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) ) )
| ~ ~ ( g_true_only @ a @ SV6 ) )
| ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( g_both @ a @ SV6 )
| ~ ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) ) )
| ~ ~ ( g_true_only @ a @ SV6 ) )
| ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) ) )
= $false )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( ( g_both @ a @ SV6 )
| ~ ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) ) )
| ~ ~ ( g_true_only @ a @ SV6 ) )
| ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(49,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( ( g_both @ a @ SV6 )
| ~ ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) ) )
| ~ ~ ( g_true_only @ a @ SV6 ) ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( ( g_both @ a @ SV6 )
| ~ ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) ) )
| ~ ~ ( g_true_only @ a @ SV6 ) ) )
= $false )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
! [SV6: $i] :
( ( ( ~ ( ( g_both @ a @ SV6 )
| ~ ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) ) )
| ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(52,plain,
! [SV6: $i] :
( ( ( ~ ( ( g_both @ a @ SV6 )
| ~ ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) ) ) )
= $true )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(53,plain,
! [SV6: $i] :
( ( ( ( g_both @ a @ SV6 )
| ~ ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) ) )
= $false )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(54,plain,
! [SV6: $i] :
( ( ( g_both @ a @ SV6 )
= $false )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(55,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) ) )
= $false )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV6: $i] :
( ( ( ~ ( g_true_only @ a @ SV6 ) )
= $false )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV6: $i] :
( ( ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 )
| ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) )
= $true )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(58,plain,
! [SV6: $i] :
( ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(59,plain,
! [SV6: $i] :
( ( ( ~ ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 ) )
= $true )
| ( ( ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) )
= $true )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV6: $i] :
( ( ( ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $false )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV6: $i] :
( ( ( ~ ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 ) )
= $false )
| ( ( ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) )
= $true )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV6: $i] :
( ( ( ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(63,plain,
! [SV6: $i] :
( ( ( ! [SY20: $i] :
~ ( g_both @ SV6 @ SY20 ) )
= $true )
| ( ( ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) )
= $true )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(64,plain,
! [SV7: $i,SV6: $i] :
( ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( g_both @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) )
= $true )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV7: $i,SV6: $i] :
( ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV8: $i,SV6: $i] :
( ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( ~ ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) )
= $true )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(68,plain,
! [SV7: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(69,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) )
= $false )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV7: $i,SV6: $i] :
( ( ( ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(72,plain,
! [SV6: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
| ~ ~ ! [SY23: $i] :
~ ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ SY23 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(73,plain,
! [SV8: $i,SV6: $i] :
( ( ( ! [SY21: $i] :
~ ( g_false_only @ SV6 @ SY21 ) )
= $false )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV6: $i,SV7: $i] :
( ( ( ~ ( ~ ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
| ~ ~ ! [SY23: $i] :
~ ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ SY23 ) ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(75,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) ) )
= $false )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(76,plain,
! [SV6: $i,SV7: $i] :
( ( ( ~ ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
| ~ ~ ! [SY23: $i] :
~ ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ SY23 ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(77,plain,
! [SV8: $i,SV6: $i] :
( ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( ~ ~ ( g_true_only @ a @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(78,plain,
! [SV6: $i,SV7: $i] :
( ( ( ~ ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(79,plain,
! [SV6: $i,SV7: $i] :
( ( ( ~ ~ ! [SY23: $i] :
~ ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ SY23 ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(80,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( g_true_only @ a @ SV6 ) )
= $false )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(81,plain,
! [SV6: $i,SV7: $i] :
( ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(82,plain,
! [SV6: $i,SV7: $i] :
( ( ( ~ ! [SY23: $i] :
~ ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ SY23 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(83,plain,
! [SV8: $i,SV6: $i] :
( ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(84,plain,
! [SV7: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV6: $i,SV7: $i] :
( ( ( ! [SY23: $i] :
~ ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ SY23 ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV7: $i,SV6: $i] :
( ( ( ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(88,plain,
! [SV6: $i,SV7: $i] :
( ( ( ~ ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[85]) ).
thf(89,plain,
! [SV8: $i,SV6: $i] :
( ( ( ! [SY22: $i] : ( g_true_only @ SV6 @ SY22 ) )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(90,plain,
! [SV7: $i,SV6: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ~ ! [SY24: $i] :
~ ( g_both @ SV9 @ SY24 )
| ~ ~ ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV6: $i,SV7: $i] :
( ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(92,plain,
! [SV8: $i,SV10: $i,SV6: $i] :
( ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(93,plain,
! [SV7: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( ~ ~ ! [SY24: $i] :
~ ( g_both @ SV9 @ SY24 )
| ~ ~ ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) ) )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV7: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(96,plain,
! [SV7: $i,SV6: $i,SV9: $i] :
( ( ( ~ ~ ! [SY24: $i] :
~ ( g_both @ SV9 @ SY24 )
| ~ ~ ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(97,plain,
! [SV7: $i,SV6: $i] :
( ( ( ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(98,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(99,plain,
! [SV7: $i,SV6: $i,SV9: $i] :
( ( ( ~ ~ ! [SY24: $i] :
~ ( g_both @ SV9 @ SY24 ) )
= $true )
| ( ( ~ ~ ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(100,plain,
! [SV7: $i,SV6: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ! [SY26: $i] :
~ ( g_both @ SV11 @ SY26 )
| ~ ~ ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(101,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ( ! [SX0: $i] :
~ ~ ( ~ ( g_false_only @ a @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV7: $i,SV6: $i,SV9: $i] :
( ( ( ~ ! [SY24: $i] :
~ ( g_both @ SV9 @ SY24 ) )
= $false )
| ( ( ~ ~ ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(103,plain,
! [SV7: $i,SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ! [SY26: $i] :
~ ( g_both @ SV11 @ SY26 )
| ~ ~ ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) ) )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(104,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
| ~ ~ ! [SY28: $i] :
~ ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ SY28 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(105,plain,
! [SV7: $i,SV6: $i,SV9: $i] :
( ( ( ! [SY24: $i] :
~ ( g_both @ SV9 @ SY24 ) )
= $true )
| ( ( ~ ~ ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(106,plain,
! [SV7: $i,SV6: $i,SV11: $i] :
( ( ( ~ ~ ! [SY26: $i] :
~ ( g_both @ SV11 @ SY26 )
| ~ ~ ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(107,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( ~ ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
| ~ ~ ! [SY28: $i] :
~ ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ SY28 ) ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(108,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV9: $i] :
( ( ( ~ ( g_both @ SV9 @ SV12 ) )
= $true )
| ( ( ~ ~ ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(109,plain,
! [SV7: $i,SV6: $i,SV11: $i] :
( ( ( ~ ~ ! [SY26: $i] :
~ ( g_both @ SV11 @ SY26 ) )
= $true )
| ( ( ~ ~ ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(110,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
| ~ ~ ! [SY28: $i] :
~ ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ SY28 ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(111,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV9: $i] :
( ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( ~ ~ ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(112,plain,
! [SV7: $i,SV6: $i,SV11: $i] :
( ( ( ~ ! [SY26: $i] :
~ ( g_both @ SV11 @ SY26 ) )
= $false )
| ( ( ~ ~ ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(113,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(114,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ~ ! [SY28: $i] :
~ ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ SY28 ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(115,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV9: $i] :
( ( ( ~ ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) )
= $false )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV7: $i,SV6: $i,SV11: $i] :
( ( ( ! [SY26: $i] :
~ ( g_both @ SV11 @ SY26 ) )
= $true )
| ( ( ~ ~ ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(117,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(118,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ! [SY28: $i] :
~ ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ SY28 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(119,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV9: $i] :
( ( ( ~ ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) )
= $true )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(120,plain,
! [SV7: $i,SV6: $i,SV13: $i,SV11: $i] :
( ( ( ~ ( g_both @ SV11 @ SV13 ) )
= $true )
| ( ( ~ ~ ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(121,plain,
! [SV8: $i,SV10: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(122,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( ! [SY28: $i] :
~ ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ SY28 ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV9: $i] :
( ( ( ! [SY25: $i] :
~ ( g_false_only @ SV9 @ SY25 ) )
= $false )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(124,plain,
! [SV7: $i,SV6: $i,SV13: $i,SV11: $i] :
( ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( ~ ~ ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV8: $i,SV10: $i,SV6: $i] :
( ( ( ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(126,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) ) )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[122]) ).
thf(127,plain,
! [SV12: $i,SV6: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( g_false_only @ SV9 @ ( sK7_SY25 @ SV7 @ SV6 @ SV12 @ SV9 ) ) )
= $false )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[123]) ).
thf(128,plain,
! [SV7: $i,SV6: $i,SV13: $i,SV11: $i] :
( ( ( ~ ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) )
= $false )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ! [SY29: $i] :
~ ( g_both @ SV14 @ SY29 )
| ~ ~ ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(131,plain,
! [SV12: $i,SV6: $i,SV7: $i,SV9: $i] :
( ( ( g_false_only @ SV9 @ ( sK7_SY25 @ SV7 @ SV6 @ SV12 @ SV9 ) )
= $true )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(132,plain,
! [SV7: $i,SV6: $i,SV13: $i,SV11: $i] :
( ( ( ~ ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) )
= $true )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(133,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ! [SY29: $i] :
~ ( g_both @ SV14 @ SY29 )
| ~ ~ ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) ) )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(134,plain,
! [SV8: $i,SV10: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(135,plain,
! [SV12: $i,SV9: $i,SV6: $i,SV7: $i] :
( ( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_false_only @ SV9 @ ( sK7_SY25 @ SV7 @ SV6 @ SV12 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV7: $i,SV6: $i,SV13: $i,SV11: $i] :
( ( ( ! [SY27: $i] :
~ ( g_false_only @ SV11 @ SY27 ) )
= $false )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV14: $i] :
( ( ( ~ ~ ! [SY29: $i] :
~ ( g_both @ SV14 @ SY29 )
| ~ ~ ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(138,plain,
! [SV8: $i,SV10: $i,SV6: $i] :
( ( ( ! [SX0: $i] :
~ ~ ( ~ ~ ! [SX1: $i] :
~ ( g_both @ SX0 @ SX1 )
| ~ ~ ~ ! [SX1: $i] :
~ ( g_false_only @ SX0 @ SX1 ) ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(139,plain,
! [SV12: $i,SV9: $i,SV6: $i,SV7: $i] :
( ( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_false_only @ SV9 @ ( sK7_SY25 @ SV7 @ SV6 @ SV12 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(140,plain,
! [SV13: $i,SV6: $i,SV7: $i,SV11: $i] :
( ( ( ~ ( g_false_only @ SV11 @ ( sK8_SY27 @ SV7 @ SV6 @ SV13 @ SV11 ) ) )
= $false )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[136]) ).
thf(141,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV14: $i] :
( ( ( ~ ~ ! [SY29: $i] :
~ ( g_both @ SV14 @ SY29 ) )
= $true )
| ( ( ~ ~ ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(142,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ~ ! [SY31: $i] :
~ ( g_both @ SV15 @ SY31 )
| ~ ~ ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV12: $i,SV9: $i,SV6: $i,SV7: $i] :
( ( ( ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_false_only @ SV9 @ ( sK7_SY25 @ SV7 @ SV6 @ SV12 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV13: $i,SV6: $i,SV7: $i,SV11: $i] :
( ( ( g_false_only @ SV11 @ ( sK8_SY27 @ SV7 @ SV6 @ SV13 @ SV11 ) )
= $true )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(145,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV14: $i] :
( ( ( ~ ! [SY29: $i] :
~ ( g_both @ SV14 @ SY29 ) )
= $false )
| ( ( ~ ~ ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(146,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ! [SY31: $i] :
~ ( g_both @ SV15 @ SY31 )
| ~ ~ ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) ) )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(147,plain,
! [SV7: $i,SV6: $i,SV9: $i,SV12: $i] :
( ( ( ~ ! [SY33: $i] : ( g_true_only @ ( sK9_SX0 @ SV12 @ SV9 @ SV6 @ SV7 ) @ SY33 ) )
= $false )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_false_only @ SV9 @ ( sK7_SY25 @ SV7 @ SV6 @ SV12 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[143]) ).
thf(148,plain,
! [SV13: $i,SV11: $i,SV6: $i,SV7: $i] :
( ( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_false_only @ SV11 @ ( sK8_SY27 @ SV7 @ SV6 @ SV13 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(149,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV14: $i] :
( ( ( ! [SY29: $i] :
~ ( g_both @ SV14 @ SY29 ) )
= $true )
| ( ( ~ ~ ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(150,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV15: $i] :
( ( ( ~ ~ ! [SY31: $i] :
~ ( g_both @ SV15 @ SY31 )
| ~ ~ ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(151,plain,
! [SV7: $i,SV6: $i,SV9: $i,SV12: $i] :
( ( ( ! [SY33: $i] : ( g_true_only @ ( sK9_SX0 @ SV12 @ SV9 @ SV6 @ SV7 ) @ SY33 ) )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_false_only @ SV9 @ ( sK7_SY25 @ SV7 @ SV6 @ SV12 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(152,plain,
! [SV13: $i,SV11: $i,SV6: $i,SV7: $i] :
( ( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_false_only @ SV11 @ ( sK8_SY27 @ SV7 @ SV6 @ SV13 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(153,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( g_both @ SV14 @ SV16 ) )
= $true )
| ( ( ~ ~ ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(154,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV15: $i] :
( ( ( ~ ~ ! [SY31: $i] :
~ ( g_both @ SV15 @ SY31 ) )
= $true )
| ( ( ~ ~ ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(155,plain,
! [SV17: $i,SV7: $i,SV6: $i,SV9: $i,SV12: $i] :
( ( ( g_true_only @ ( sK9_SX0 @ SV12 @ SV9 @ SV6 @ SV7 ) @ SV17 )
= $true )
| ( ( g_false_only @ a @ ( sK2_SX0 @ SV7 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV9 @ SV12 )
= $false )
| ( ( g_false_only @ SV9 @ ( sK7_SY25 @ SV7 @ SV6 @ SV12 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(156,plain,
! [SV13: $i,SV11: $i,SV6: $i,SV7: $i] :
( ( ( ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_false_only @ SV11 @ ( sK8_SY27 @ SV7 @ SV6 @ SV13 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(157,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV16: $i,SV14: $i] :
( ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( ~ ~ ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(158,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV15: $i] :
( ( ( ~ ! [SY31: $i] :
~ ( g_both @ SV15 @ SY31 ) )
= $false )
| ( ( ~ ~ ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(159,plain,
! [SV7: $i,SV6: $i,SV11: $i,SV13: $i] :
( ( ( ~ ! [SY34: $i] : ( g_true_only @ ( sK10_SX0 @ SV13 @ SV11 @ SV6 @ SV7 ) @ SY34 ) )
= $false )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_false_only @ SV11 @ ( sK8_SY27 @ SV7 @ SV6 @ SV13 @ SV11 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[156]) ).
thf(160,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV16: $i,SV14: $i] :
( ( ( ~ ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) )
= $false )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(161,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV15: $i] :
( ( ( ! [SY31: $i] :
~ ( g_both @ SV15 @ SY31 ) )
= $true )
| ( ( ~ ~ ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(162,plain,
! [SV7: $i,SV6: $i,SV11: $i,SV13: $i] :
( ( ( ! [SY34: $i] : ( g_true_only @ ( sK10_SX0 @ SV13 @ SV11 @ SV6 @ SV7 ) @ SY34 ) )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_false_only @ SV11 @ ( sK8_SY27 @ SV7 @ SV6 @ SV13 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(163,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV16: $i,SV14: $i] :
( ( ( ~ ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) )
= $true )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(164,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV18: $i,SV15: $i] :
( ( ( ~ ( g_both @ SV15 @ SV18 ) )
= $true )
| ( ( ~ ~ ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(165,plain,
! [SV19: $i,SV7: $i,SV6: $i,SV11: $i,SV13: $i] :
( ( ( g_true_only @ ( sK10_SX0 @ SV13 @ SV11 @ SV6 @ SV7 ) @ SV19 )
= $true )
| ( ( g_false_only @ ( sK2_SX0 @ SV7 @ SV6 ) @ ( sK4_SY23 @ SV6 @ SV7 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ a @ SV6 )
= $false )
| ( ( g_true_only @ SV6 @ SV7 )
= $true )
| ( ( g_both @ SV11 @ SV13 )
= $false )
| ( ( g_false_only @ SV11 @ ( sK8_SY27 @ SV7 @ SV6 @ SV13 @ SV11 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(166,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV16: $i,SV14: $i] :
( ( ( ! [SY30: $i] :
~ ( g_false_only @ SV14 @ SY30 ) )
= $false )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(167,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV18: $i,SV15: $i] :
( ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( ~ ~ ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(168,plain,
! [SV16: $i,SV6: $i,SV10: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( g_false_only @ SV14 @ ( sK11_SY30 @ SV8 @ SV10 @ SV6 @ SV16 @ SV14 ) ) )
= $false )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[166]) ).
thf(169,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV18: $i,SV15: $i] :
( ( ( ~ ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) )
= $false )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(170,plain,
! [SV16: $i,SV6: $i,SV10: $i,SV8: $i,SV14: $i] :
( ( ( g_false_only @ SV14 @ ( sK11_SY30 @ SV8 @ SV10 @ SV6 @ SV16 @ SV14 ) )
= $true )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(171,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV18: $i,SV15: $i] :
( ( ( ~ ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) )
= $true )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(172,plain,
! [SV16: $i,SV14: $i,SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_false_only @ SV14 @ ( sK11_SY30 @ SV8 @ SV10 @ SV6 @ SV16 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(173,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV18: $i,SV15: $i] :
( ( ( ! [SY32: $i] :
~ ( g_false_only @ SV15 @ SY32 ) )
= $false )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(174,plain,
! [SV16: $i,SV14: $i,SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_false_only @ SV14 @ ( sK11_SY30 @ SV8 @ SV10 @ SV6 @ SV16 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(175,plain,
! [SV18: $i,SV6: $i,SV10: $i,SV8: $i,SV15: $i] :
( ( ( ~ ( g_false_only @ SV15 @ ( sK12_SY32 @ SV8 @ SV10 @ SV6 @ SV18 @ SV15 ) ) )
= $false )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[173]) ).
thf(176,plain,
! [SV16: $i,SV14: $i,SV6: $i,SV8: $i,SV10: $i] :
( ( ( ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_false_only @ SV14 @ ( sK11_SY30 @ SV8 @ SV10 @ SV6 @ SV16 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(177,plain,
! [SV18: $i,SV6: $i,SV10: $i,SV8: $i,SV15: $i] :
( ( ( g_false_only @ SV15 @ ( sK12_SY32 @ SV8 @ SV10 @ SV6 @ SV18 @ SV15 ) )
= $true )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(178,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV14: $i,SV16: $i] :
( ( ( ~ ! [SY35: $i] : ( g_true_only @ ( sK13_SX0 @ SV16 @ SV14 @ SV6 @ SV8 @ SV10 ) @ SY35 ) )
= $false )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_false_only @ SV14 @ ( sK11_SY30 @ SV8 @ SV10 @ SV6 @ SV16 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[176]) ).
thf(179,plain,
! [SV18: $i,SV15: $i,SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_false_only @ SV15 @ ( sK12_SY32 @ SV8 @ SV10 @ SV6 @ SV18 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(180,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV14: $i,SV16: $i] :
( ( ( ! [SY35: $i] : ( g_true_only @ ( sK13_SX0 @ SV16 @ SV14 @ SV6 @ SV8 @ SV10 ) @ SY35 ) )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_false_only @ SV14 @ ( sK11_SY30 @ SV8 @ SV10 @ SV6 @ SV16 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(181,plain,
! [SV18: $i,SV15: $i,SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_false_only @ SV15 @ ( sK12_SY32 @ SV8 @ SV10 @ SV6 @ SV18 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(182,plain,
! [SV20: $i,SV10: $i,SV8: $i,SV6: $i,SV14: $i,SV16: $i] :
( ( ( g_true_only @ ( sK13_SX0 @ SV16 @ SV14 @ SV6 @ SV8 @ SV10 ) @ SV20 )
= $true )
| ( ( g_false_only @ a @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV14 @ SV16 )
= $false )
| ( ( g_false_only @ SV14 @ ( sK11_SY30 @ SV8 @ SV10 @ SV6 @ SV16 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(183,plain,
! [SV18: $i,SV15: $i,SV6: $i,SV8: $i,SV10: $i] :
( ( ( ! [SX0: $i] :
~ ! [SX1: $i] : ( g_true_only @ SX0 @ SX1 ) )
= $false )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_false_only @ SV15 @ ( sK12_SY32 @ SV8 @ SV10 @ SV6 @ SV18 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(184,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV15: $i,SV18: $i] :
( ( ( ~ ! [SY36: $i] : ( g_true_only @ ( sK14_SX0 @ SV18 @ SV15 @ SV6 @ SV8 @ SV10 ) @ SY36 ) )
= $false )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_false_only @ SV15 @ ( sK12_SY32 @ SV8 @ SV10 @ SV6 @ SV18 @ SV15 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[183]) ).
thf(185,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV15: $i,SV18: $i] :
( ( ( ! [SY36: $i] : ( g_true_only @ ( sK14_SX0 @ SV18 @ SV15 @ SV6 @ SV8 @ SV10 ) @ SY36 ) )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_false_only @ SV15 @ ( sK12_SY32 @ SV8 @ SV10 @ SV6 @ SV18 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(186,plain,
! [SV21: $i,SV10: $i,SV8: $i,SV6: $i,SV15: $i,SV18: $i] :
( ( ( g_true_only @ ( sK14_SX0 @ SV18 @ SV15 @ SV6 @ SV8 @ SV10 ) @ SV21 )
= $true )
| ( ( g_false_only @ ( sK5_SX0 @ SV10 @ SV8 @ SV6 ) @ ( sK6_SY28 @ SV6 @ SV8 @ SV10 ) )
= $true )
| ( ( g_true_only @ a @ SV6 )
= $true )
| ( ( g_both @ SV6 @ SV8 )
= $false )
| ( ( g_false_only @ SV6 @ ( sK3_SY21 @ SV8 @ SV6 ) )
= $true )
| ( ( g_true_only @ SV6 @ SV10 )
= $true )
| ( ( g_both @ SV15 @ SV18 )
= $false )
| ( ( g_false_only @ SV15 @ ( sK12_SY32 @ SV8 @ SV10 @ SV6 @ SV18 @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(187,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,186,182,165,155,45,33]) ).
thf(188,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO607+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 17:46:32 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.38
% 0.35/0.38 No.of.Axioms: 1
% 0.35/0.38
% 0.35/0.38 Length.of.Defs: 0
% 0.35/0.38
% 0.35/0.38 Contains.Choice.Funs: false
% 0.35/0.38 ......
% 0.35/0.38
% 0.35/0.38 ********************************
% 0.35/0.38 * All subproblems solved! *
% 0.35/0.38 ********************************
% 0.35/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:187,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.35/0.38
% 0.35/0.38 %**** Beginning of derivation protocol ****
% 0.35/0.38 % SZS output start CNFRefutation
% See solution above
% 0.35/0.38
% 0.35/0.38 %**** End of derivation protocol ****
% 0.35/0.38 %**** no. of clauses in derivation: 185 ****
% 0.35/0.38 %**** clause counter: 187 ****
% 0.35/0.38
% 0.35/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:187,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------