%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET926^20 : TPTP v9.3.1. Released v8.1.0.
% 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 10:42:35 AM UTC 2026
% Result : Theorem 0.51s 0.31s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 26
% Syntax : Number of formulae : 244 ( 101 unt; 0 typ; 10 def)
% Number of atoms : 2125 ( 535 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 4237 ( 577 ~; 633 |; 15 &;2923 @)
% ( 5 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 8 con; 0-3 aty)
% Number of variables : 503 ( 57 ^; 440 !; 6 ?; 503 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(tp_empty,type,
empty: $i > mworld > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > mworld > $o ).
thf(tp_mactual,type,
mactual: mworld ).
thf(tp_mand,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mbox,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(tp_mdia,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(tp_mequiv,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mexists_di,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mforall_di,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mimplies,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mlocal,type,
mlocal: ( mworld > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(tp_mor,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mrel,type,
mrel: mworld > mworld > $o ).
thf(tp_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(tp_sK1_SY13,type,
sK1_SY13: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] :
( ( eiw_di @ X @ W )
& ( A @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] :
( ( eiw_di @ X @ W )
=> ( A @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(1,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( empty @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(3,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(5,axiom,
mlocal @ ( empty @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(6,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(7,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_substitution_2) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_substitution_1) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_substitution_1) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(11,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_substitution_2) ).
thf(12,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_substitution_1) ).
thf(13,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] :
( mforall_di
@ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(14,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(15,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(19,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(20,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( ! [SY13: $i] :
( ( eiw_di @ SY13 @ mactual )
=> ! [SY14: $i] :
( ( eiw_di @ SY14 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ SY13 ) @ SY14 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY13 ) @ SY14 ) @ ( singleton @ SY13 ) @ mactual ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(22,plain,
( ( ? [SY22: $i] :
( ( eiw_di @ SY22 @ mactual )
& ~ ( empty @ SY22 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(23,plain,
( ( ? [SY27: $i] :
( ( eiw_di @ SY27 @ mactual )
& ( empty @ SY27 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(24,plain,
( ( ! [SY42: $i] :
( ( eiw_di @ SY42 @ mactual )
=> ! [SY43: $i] :
( ( eiw_di @ SY43 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ SY42 ) @ SY43 ) @ empty_set @ mactual )
<=> ( in @ SY42 @ SY43 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(25,plain,
( ( ! [SY60: $i] :
( ( eiw_di @ SY60 @ mactual )
=> ! [SY61: $i] :
( ( eiw_di @ SY61 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ SY60 ) @ SY61 ) @ ( singleton @ SY60 ) @ mactual )
<=> ~ ( in @ SY60 @ SY61 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(26,plain,
( ( empty @ empty_set @ mactual )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(27,plain,
( ( ! [SY78: $i] :
( ( eiw_di @ SY78 @ mactual )
=> ! [SY79: $i] :
( ( eiw_di @ SY79 @ mactual )
=> ( ( in @ SY78 @ SY79 @ mactual )
=> ~ ( in @ SY79 @ SY78 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(28,plain,
( ( ! [SY106: $i] :
( ( eiw_di @ SY106 @ mactual )
=> ! [SY107: $i] :
( ( eiw_di @ SY107 @ mactual )
=> ! [SY108: $i] :
( ( eiw_di @ SY108 @ mactual )
=> ( ( ( qmltpeq @ SY106 @ SY107 @ mactual )
& ( in @ SY108 @ SY106 @ mactual ) )
=> ( in @ SY108 @ SY107 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(29,plain,
( ( ! [SY136: $i] :
( ( eiw_di @ SY136 @ mactual )
=> ! [SY137: $i] :
( ( eiw_di @ SY137 @ mactual )
=> ! [SY138: $i] :
( ( eiw_di @ SY138 @ mactual )
=> ( ( ( qmltpeq @ SY136 @ SY137 @ mactual )
& ( in @ SY136 @ SY138 @ mactual ) )
=> ( in @ SY137 @ SY138 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(30,plain,
( ( ! [SY158: $i] :
( ( eiw_di @ SY158 @ mactual )
=> ! [SY159: $i] :
( ( eiw_di @ SY159 @ mactual )
=> ( ( ( qmltpeq @ SY158 @ SY159 @ mactual )
& ( empty @ SY158 @ mactual ) )
=> ( empty @ SY159 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(31,plain,
( ( ! [SY175: $i] :
( ( eiw_di @ SY175 @ mactual )
=> ! [SY176: $i] :
( ( eiw_di @ SY176 @ mactual )
=> ( ( qmltpeq @ SY175 @ SY176 @ mactual )
=> ( qmltpeq @ ( singleton @ SY175 ) @ ( singleton @ SY176 ) @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(32,plain,
( ( ! [SY200: $i] :
( ( eiw_di @ SY200 @ mactual )
=> ! [SY201: $i] :
( ( eiw_di @ SY201 @ mactual )
=> ! [SY202: $i] :
( ( eiw_di @ SY202 @ mactual )
=> ( ( qmltpeq @ SY200 @ SY201 @ mactual )
=> ( qmltpeq @ ( set_difference @ SY202 @ SY200 ) @ ( set_difference @ SY202 @ SY201 ) @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(33,plain,
( ( ! [SY227: $i] :
( ( eiw_di @ SY227 @ mactual )
=> ! [SY228: $i] :
( ( eiw_di @ SY228 @ mactual )
=> ! [SY229: $i] :
( ( eiw_di @ SY229 @ mactual )
=> ( ( qmltpeq @ SY227 @ SY228 @ mactual )
=> ( qmltpeq @ ( set_difference @ SY227 @ SY229 ) @ ( set_difference @ SY228 @ SY229 ) @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(34,plain,
( ( ! [SY257: $i] :
( ( eiw_di @ SY257 @ mactual )
=> ! [SY258: $i] :
( ( eiw_di @ SY258 @ mactual )
=> ! [SY259: $i] :
( ( eiw_di @ SY259 @ mactual )
=> ( ( ( qmltpeq @ SY257 @ SY258 @ mactual )
& ( qmltpeq @ SY258 @ SY259 @ mactual ) )
=> ( qmltpeq @ SY257 @ SY259 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(35,plain,
( ( ! [SY276: $i] :
( ( eiw_di @ SY276 @ mactual )
=> ! [SY277: $i] :
( ( eiw_di @ SY277 @ mactual )
=> ( ( qmltpeq @ SY276 @ SY277 @ mactual )
=> ( qmltpeq @ SY277 @ SY276 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(36,plain,
( ( ! [SY283: $i] :
( ( eiw_di @ SY283 @ mactual )
=> ( qmltpeq @ SY283 @ SY283 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(37,plain,
( ( ( eiw_di @ sK1_SY13 @ mactual )
=> ! [SY285: $i] :
( ( eiw_di @ SY285 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SY285 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SY285 ) @ ( singleton @ sK1_SY13 ) @ mactual ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(38,plain,
( ( eiw_di @ sK1_SY13 @ mactual )
= $true ),
inference(standard_cnf,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [SY285: $i] :
( ( eiw_di @ SY285 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SY285 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SY285 ) @ ( singleton @ sK1_SY13 ) @ mactual ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[37]) ).
thf(40,plain,
( ( ~ ! [SY285: $i] :
( ( eiw_di @ SY285 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SY285 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SY285 ) @ ( singleton @ sK1_SY13 ) @ mactual ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [SY283: $i] :
( ( eiw_di @ SY283 @ mactual )
=> ( qmltpeq @ SY283 @ SY283 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(42,plain,
( ( ! [SY276: $i] :
( ( eiw_di @ SY276 @ mactual )
=> ! [SY277: $i] :
( ( eiw_di @ SY277 @ mactual )
=> ( ( qmltpeq @ SY276 @ SY277 @ mactual )
=> ( qmltpeq @ SY277 @ SY276 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(43,plain,
( ( ! [SY257: $i] :
( ( eiw_di @ SY257 @ mactual )
=> ! [SY258: $i] :
( ( eiw_di @ SY258 @ mactual )
=> ! [SY259: $i] :
( ( eiw_di @ SY259 @ mactual )
=> ( ( ( qmltpeq @ SY257 @ SY258 @ mactual )
& ( qmltpeq @ SY258 @ SY259 @ mactual ) )
=> ( qmltpeq @ SY257 @ SY259 @ mactual ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(44,plain,
( ( ! [SY227: $i] :
( ( eiw_di @ SY227 @ mactual )
=> ! [SY228: $i] :
( ( eiw_di @ SY228 @ mactual )
=> ! [SY229: $i] :
( ( eiw_di @ SY229 @ mactual )
=> ( ( qmltpeq @ SY227 @ SY228 @ mactual )
=> ( qmltpeq @ ( set_difference @ SY227 @ SY229 ) @ ( set_difference @ SY228 @ SY229 ) @ mactual ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(45,plain,
( ( ! [SY200: $i] :
( ( eiw_di @ SY200 @ mactual )
=> ! [SY201: $i] :
( ( eiw_di @ SY201 @ mactual )
=> ! [SY202: $i] :
( ( eiw_di @ SY202 @ mactual )
=> ( ( qmltpeq @ SY200 @ SY201 @ mactual )
=> ( qmltpeq @ ( set_difference @ SY202 @ SY200 ) @ ( set_difference @ SY202 @ SY201 ) @ mactual ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(46,plain,
( ( ! [SY175: $i] :
( ( eiw_di @ SY175 @ mactual )
=> ! [SY176: $i] :
( ( eiw_di @ SY176 @ mactual )
=> ( ( qmltpeq @ SY175 @ SY176 @ mactual )
=> ( qmltpeq @ ( singleton @ SY175 ) @ ( singleton @ SY176 ) @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(47,plain,
( ( ! [SY158: $i] :
( ( eiw_di @ SY158 @ mactual )
=> ! [SY159: $i] :
( ( eiw_di @ SY159 @ mactual )
=> ( ( ( qmltpeq @ SY158 @ SY159 @ mactual )
& ( empty @ SY158 @ mactual ) )
=> ( empty @ SY159 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(48,plain,
( ( ! [SY136: $i] :
( ( eiw_di @ SY136 @ mactual )
=> ! [SY137: $i] :
( ( eiw_di @ SY137 @ mactual )
=> ! [SY138: $i] :
( ( eiw_di @ SY138 @ mactual )
=> ( ( ( qmltpeq @ SY136 @ SY137 @ mactual )
& ( in @ SY136 @ SY138 @ mactual ) )
=> ( in @ SY137 @ SY138 @ mactual ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(49,plain,
( ( ! [SY106: $i] :
( ( eiw_di @ SY106 @ mactual )
=> ! [SY107: $i] :
( ( eiw_di @ SY107 @ mactual )
=> ! [SY108: $i] :
( ( eiw_di @ SY108 @ mactual )
=> ( ( ( qmltpeq @ SY106 @ SY107 @ mactual )
& ( in @ SY108 @ SY106 @ mactual ) )
=> ( in @ SY108 @ SY107 @ mactual ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(50,plain,
( ( ! [SY78: $i] :
( ( eiw_di @ SY78 @ mactual )
=> ! [SY79: $i] :
( ( eiw_di @ SY79 @ mactual )
=> ( ( in @ SY78 @ SY79 @ mactual )
=> ~ ( in @ SY79 @ SY78 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(51,plain,
( ( empty @ empty_set @ mactual )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(52,plain,
( ( ! [SY60: $i] :
( ( eiw_di @ SY60 @ mactual )
=> ! [SY61: $i] :
( ( eiw_di @ SY61 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ SY60 ) @ SY61 ) @ ( singleton @ SY60 ) @ mactual )
<=> ~ ( in @ SY60 @ SY61 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(53,plain,
( ( ! [SY42: $i] :
( ( eiw_di @ SY42 @ mactual )
=> ! [SY43: $i] :
( ( eiw_di @ SY43 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ SY42 ) @ SY43 ) @ empty_set @ mactual )
<=> ( in @ SY42 @ SY43 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(54,plain,
( ( ? [SY27: $i] :
( ( eiw_di @ SY27 @ mactual )
& ( empty @ SY27 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(55,plain,
( ( ? [SY22: $i] :
( ( eiw_di @ SY22 @ mactual )
& ~ ( empty @ SY22 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(56,plain,
( ( eiw_di @ sK1_SY13 @ mactual )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(57,plain,
( ( ~ ! [SY285: $i] :
( ( eiw_di @ SY285 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SY285 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SY285 ) @ ( singleton @ sK1_SY13 ) @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(58,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( qmltpeq @ SX1 @ SX2 @ mactual ) )
| ( qmltpeq @ SX0 @ SX2 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(59,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(60,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ SX1 @ SX0 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(61,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ( qmltpeq @ SX0 @ SX0 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(62,plain,
( ( ~ ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SX0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SX0 ) @ ( singleton @ sK1_SY13 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(63,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ mactual )
| ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(64,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( empty @ SX0 @ mactual ) )
| ( empty @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(65,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ empty_set @ mactual )
| ( in @ SX0 @ SX1 @ mactual ) )
| ~ ( ~ ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ empty_set @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(66,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ( empty @ SX0 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(67,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ mactual )
| ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ SX2 @ SX0 ) @ ( set_difference @ SX2 @ SX1 ) @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(68,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( in @ SX0 @ SX2 @ mactual ) )
| ( in @ SX1 @ SX2 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(69,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ~ ( empty @ SX0 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(70,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual ) )
| ~ ( ~ ~ ( in @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX0 ) @ SX1 ) @ ( singleton @ SX0 ) @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(71,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( in @ SX2 @ SX0 @ mactual ) )
| ( in @ SX2 @ SX1 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(72,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( in @ SX0 @ SX1 @ mactual )
| ~ ( in @ SX1 @ SX0 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(73,plain,
! [SV1: $i] :
( ( ~ ( eiw_di @ SV1 @ mactual )
| ! [SY286: $i] :
( ~ ( eiw_di @ SY286 @ mactual )
| ! [SY287: $i] :
( ~ ( eiw_di @ SY287 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV1 @ SY286 @ mactual )
| ~ ( qmltpeq @ SY286 @ SY287 @ mactual ) )
| ( qmltpeq @ SV1 @ SY287 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(74,plain,
! [SV2: $i] :
( ( ~ ( eiw_di @ SV2 @ mactual )
| ! [SY288: $i] :
( ~ ( eiw_di @ SY288 @ mactual )
| ~ ( qmltpeq @ SV2 @ SY288 @ mactual )
| ( qmltpeq @ ( singleton @ SV2 ) @ ( singleton @ SY288 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(75,plain,
! [SV3: $i] :
( ( ~ ( eiw_di @ SV3 @ mactual )
| ! [SY289: $i] :
( ~ ( eiw_di @ SY289 @ mactual )
| ~ ( qmltpeq @ SV3 @ SY289 @ mactual )
| ( qmltpeq @ SY289 @ SV3 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(76,plain,
! [SV4: $i] :
( ( ~ ( eiw_di @ SV4 @ mactual )
| ( qmltpeq @ SV4 @ SV4 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(77,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SX0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ SX0 ) @ ( singleton @ sK1_SY13 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(78,plain,
! [SV5: $i] :
( ( ~ ( eiw_di @ SV5 @ mactual )
| ! [SY290: $i] :
( ~ ( eiw_di @ SY290 @ mactual )
| ! [SY291: $i] :
( ~ ( eiw_di @ SY291 @ mactual )
| ~ ( qmltpeq @ SV5 @ SY290 @ mactual )
| ( qmltpeq @ ( set_difference @ SV5 @ SY291 ) @ ( set_difference @ SY290 @ SY291 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(79,plain,
! [SV6: $i] :
( ( ~ ( eiw_di @ SV6 @ mactual )
| ! [SY292: $i] :
( ~ ( eiw_di @ SY292 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV6 @ SY292 @ mactual )
| ~ ( empty @ SV6 @ mactual ) )
| ( empty @ SY292 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV7: $i] :
( ( ~ ( eiw_di @ SV7 @ mactual )
| ! [SY293: $i] :
( ~ ( eiw_di @ SY293 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SY293 ) @ empty_set @ mactual )
| ( in @ SV7 @ SY293 @ mactual ) )
| ~ ( ~ ( in @ SV7 @ SY293 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SY293 ) @ empty_set @ mactual ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ( empty @ SX0 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(82,plain,
! [SV8: $i] :
( ( ~ ( eiw_di @ SV8 @ mactual )
| ! [SY294: $i] :
( ~ ( eiw_di @ SY294 @ mactual )
| ! [SY295: $i] :
( ~ ( eiw_di @ SY295 @ mactual )
| ~ ( qmltpeq @ SV8 @ SY294 @ mactual )
| ( qmltpeq @ ( set_difference @ SY295 @ SV8 ) @ ( set_difference @ SY295 @ SY294 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(83,plain,
! [SV9: $i] :
( ( ~ ( eiw_di @ SV9 @ mactual )
| ! [SY296: $i] :
( ~ ( eiw_di @ SY296 @ mactual )
| ! [SY297: $i] :
( ~ ( eiw_di @ SY297 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV9 @ SY296 @ mactual )
| ~ ( in @ SV9 @ SY297 @ mactual ) )
| ( in @ SY296 @ SY297 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(84,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ~ ( empty @ SX0 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(85,plain,
! [SV10: $i] :
( ( ~ ( eiw_di @ SV10 @ mactual )
| ! [SY298: $i] :
( ~ ( eiw_di @ SY298 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SY298 ) @ ( singleton @ SV10 ) @ mactual )
| ~ ( in @ SV10 @ SY298 @ mactual ) )
| ~ ( ~ ~ ( in @ SV10 @ SY298 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SY298 ) @ ( singleton @ SV10 ) @ mactual ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV11: $i] :
( ( ~ ( eiw_di @ SV11 @ mactual )
| ! [SY299: $i] :
( ~ ( eiw_di @ SY299 @ mactual )
| ! [SY300: $i] :
( ~ ( eiw_di @ SY300 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV11 @ SY299 @ mactual )
| ~ ( in @ SY300 @ SV11 @ mactual ) )
| ( in @ SY300 @ SY299 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV12: $i] :
( ( ~ ( eiw_di @ SV12 @ mactual )
| ! [SY301: $i] :
( ~ ( eiw_di @ SY301 @ mactual )
| ~ ( in @ SV12 @ SY301 @ mactual )
| ~ ( in @ SY301 @ SV12 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV1: $i] :
( ( ( ~ ( eiw_di @ SV1 @ mactual ) )
= $true )
| ( ( ! [SY286: $i] :
( ~ ( eiw_di @ SY286 @ mactual )
| ! [SY287: $i] :
( ~ ( eiw_di @ SY287 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV1 @ SY286 @ mactual )
| ~ ( qmltpeq @ SY286 @ SY287 @ mactual ) )
| ( qmltpeq @ SV1 @ SY287 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV2: $i] :
( ( ( ~ ( eiw_di @ SV2 @ mactual ) )
= $true )
| ( ( ! [SY288: $i] :
( ~ ( eiw_di @ SY288 @ mactual )
| ~ ( qmltpeq @ SV2 @ SY288 @ mactual )
| ( qmltpeq @ ( singleton @ SV2 ) @ ( singleton @ SY288 ) @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(90,plain,
! [SV3: $i] :
( ( ( ~ ( eiw_di @ SV3 @ mactual ) )
= $true )
| ( ( ! [SY289: $i] :
( ~ ( eiw_di @ SY289 @ mactual )
| ~ ( qmltpeq @ SV3 @ SY289 @ mactual )
| ( qmltpeq @ SY289 @ SV3 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(91,plain,
! [SV4: $i] :
( ( ( ~ ( eiw_di @ SV4 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV4 @ SV4 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(92,plain,
( ( ~ ( eiw_di @ sK2_SX0 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ sK2_SX0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ sK2_SX0 ) @ ( singleton @ sK1_SY13 ) @ mactual ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(93,plain,
! [SV5: $i] :
( ( ( ~ ( eiw_di @ SV5 @ mactual ) )
= $true )
| ( ( ! [SY290: $i] :
( ~ ( eiw_di @ SY290 @ mactual )
| ! [SY291: $i] :
( ~ ( eiw_di @ SY291 @ mactual )
| ~ ( qmltpeq @ SV5 @ SY290 @ mactual )
| ( qmltpeq @ ( set_difference @ SV5 @ SY291 ) @ ( set_difference @ SY290 @ SY291 ) @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(94,plain,
! [SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ mactual ) )
= $true )
| ( ( ! [SY292: $i] :
( ~ ( eiw_di @ SY292 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV6 @ SY292 @ mactual )
| ~ ( empty @ SV6 @ mactual ) )
| ( empty @ SY292 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV7: $i] :
( ( ( ~ ( eiw_di @ SV7 @ mactual ) )
= $true )
| ( ( ! [SY293: $i] :
( ~ ( eiw_di @ SY293 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SY293 ) @ empty_set @ mactual )
| ( in @ SV7 @ SY293 @ mactual ) )
| ~ ( ~ ( in @ SV7 @ SY293 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SY293 ) @ empty_set @ mactual ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(96,plain,
( ( ~ ~ ( ~ ( eiw_di @ sK3_SX0 @ mactual )
| ~ ( empty @ sK3_SX0 @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[81]) ).
thf(97,plain,
! [SV8: $i] :
( ( ( ~ ( eiw_di @ SV8 @ mactual ) )
= $true )
| ( ( ! [SY294: $i] :
( ~ ( eiw_di @ SY294 @ mactual )
| ! [SY295: $i] :
( ~ ( eiw_di @ SY295 @ mactual )
| ~ ( qmltpeq @ SV8 @ SY294 @ mactual )
| ( qmltpeq @ ( set_difference @ SY295 @ SV8 ) @ ( set_difference @ SY295 @ SY294 ) @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(98,plain,
! [SV9: $i] :
( ( ( ~ ( eiw_di @ SV9 @ mactual ) )
= $true )
| ( ( ! [SY296: $i] :
( ~ ( eiw_di @ SY296 @ mactual )
| ! [SY297: $i] :
( ~ ( eiw_di @ SY297 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV9 @ SY296 @ mactual )
| ~ ( in @ SV9 @ SY297 @ mactual ) )
| ( in @ SY296 @ SY297 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(99,plain,
( ( ~ ~ ( ~ ( eiw_di @ sK4_SX0 @ mactual )
| ~ ~ ( empty @ sK4_SX0 @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(100,plain,
! [SV10: $i] :
( ( ( ~ ( eiw_di @ SV10 @ mactual ) )
= $true )
| ( ( ! [SY298: $i] :
( ~ ( eiw_di @ SY298 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SY298 ) @ ( singleton @ SV10 ) @ mactual )
| ~ ( in @ SV10 @ SY298 @ mactual ) )
| ~ ( ~ ~ ( in @ SV10 @ SY298 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SY298 ) @ ( singleton @ SV10 ) @ mactual ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV11: $i] :
( ( ( ~ ( eiw_di @ SV11 @ mactual ) )
= $true )
| ( ( ! [SY299: $i] :
( ~ ( eiw_di @ SY299 @ mactual )
| ! [SY300: $i] :
( ~ ( eiw_di @ SY300 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV11 @ SY299 @ mactual )
| ~ ( in @ SY300 @ SV11 @ mactual ) )
| ( in @ SY300 @ SY299 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV12: $i] :
( ( ( ~ ( eiw_di @ SV12 @ mactual ) )
= $true )
| ( ( ! [SY301: $i] :
( ~ ( eiw_di @ SY301 @ mactual )
| ~ ( in @ SV12 @ SY301 @ mactual )
| ~ ( in @ SY301 @ SV12 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV1: $i] :
( ( ( eiw_di @ SV1 @ mactual )
= $false )
| ( ( ! [SY286: $i] :
( ~ ( eiw_di @ SY286 @ mactual )
| ! [SY287: $i] :
( ~ ( eiw_di @ SY287 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV1 @ SY286 @ mactual )
| ~ ( qmltpeq @ SY286 @ SY287 @ mactual ) )
| ( qmltpeq @ SV1 @ SY287 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV2: $i] :
( ( ( eiw_di @ SV2 @ mactual )
= $false )
| ( ( ! [SY288: $i] :
( ~ ( eiw_di @ SY288 @ mactual )
| ~ ( qmltpeq @ SV2 @ SY288 @ mactual )
| ( qmltpeq @ ( singleton @ SV2 ) @ ( singleton @ SY288 ) @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV3: $i] :
( ( ( eiw_di @ SV3 @ mactual )
= $false )
| ( ( ! [SY289: $i] :
( ~ ( eiw_di @ SY289 @ mactual )
| ~ ( qmltpeq @ SV3 @ SY289 @ mactual )
| ( qmltpeq @ SY289 @ SV3 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV4: $i] :
( ( ( eiw_di @ SV4 @ mactual )
= $false )
| ( ( qmltpeq @ SV4 @ SV4 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(107,plain,
( ( ~ ( eiw_di @ sK2_SX0 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(108,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ sK2_SX0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ sK2_SX0 ) @ ( singleton @ sK1_SY13 ) @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(109,plain,
! [SV5: $i] :
( ( ( eiw_di @ SV5 @ mactual )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( eiw_di @ SY290 @ mactual )
| ! [SY291: $i] :
( ~ ( eiw_di @ SY291 @ mactual )
| ~ ( qmltpeq @ SV5 @ SY290 @ mactual )
| ( qmltpeq @ ( set_difference @ SV5 @ SY291 ) @ ( set_difference @ SY290 @ SY291 ) @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(110,plain,
! [SV6: $i] :
( ( ( eiw_di @ SV6 @ mactual )
= $false )
| ( ( ! [SY292: $i] :
( ~ ( eiw_di @ SY292 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV6 @ SY292 @ mactual )
| ~ ( empty @ SV6 @ mactual ) )
| ( empty @ SY292 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(111,plain,
! [SV7: $i] :
( ( ( eiw_di @ SV7 @ mactual )
= $false )
| ( ( ! [SY293: $i] :
( ~ ( eiw_di @ SY293 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SY293 ) @ empty_set @ mactual )
| ( in @ SV7 @ SY293 @ mactual ) )
| ~ ( ~ ( in @ SV7 @ SY293 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SY293 ) @ empty_set @ mactual ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(112,plain,
( ( ~ ( ~ ( eiw_di @ sK3_SX0 @ mactual )
| ~ ( empty @ sK3_SX0 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(113,plain,
! [SV8: $i] :
( ( ( eiw_di @ SV8 @ mactual )
= $false )
| ( ( ! [SY294: $i] :
( ~ ( eiw_di @ SY294 @ mactual )
| ! [SY295: $i] :
( ~ ( eiw_di @ SY295 @ mactual )
| ~ ( qmltpeq @ SV8 @ SY294 @ mactual )
| ( qmltpeq @ ( set_difference @ SY295 @ SV8 ) @ ( set_difference @ SY295 @ SY294 ) @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV9: $i] :
( ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( ! [SY296: $i] :
( ~ ( eiw_di @ SY296 @ mactual )
| ! [SY297: $i] :
( ~ ( eiw_di @ SY297 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV9 @ SY296 @ mactual )
| ~ ( in @ SV9 @ SY297 @ mactual ) )
| ( in @ SY296 @ SY297 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(115,plain,
( ( ~ ( ~ ( eiw_di @ sK4_SX0 @ mactual )
| ~ ~ ( empty @ sK4_SX0 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(116,plain,
! [SV10: $i] :
( ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( ! [SY298: $i] :
( ~ ( eiw_di @ SY298 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SY298 ) @ ( singleton @ SV10 ) @ mactual )
| ~ ( in @ SV10 @ SY298 @ mactual ) )
| ~ ( ~ ~ ( in @ SV10 @ SY298 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SY298 ) @ ( singleton @ SV10 ) @ mactual ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(117,plain,
! [SV11: $i] :
( ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( ! [SY299: $i] :
( ~ ( eiw_di @ SY299 @ mactual )
| ! [SY300: $i] :
( ~ ( eiw_di @ SY300 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV11 @ SY299 @ mactual )
| ~ ( in @ SY300 @ SV11 @ mactual ) )
| ( in @ SY300 @ SY299 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(118,plain,
! [SV12: $i] :
( ( ( eiw_di @ SV12 @ mactual )
= $false )
| ( ( ! [SY301: $i] :
( ~ ( eiw_di @ SY301 @ mactual )
| ~ ( in @ SV12 @ SY301 @ mactual )
| ~ ( in @ SY301 @ SV12 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV1: $i,SV13: $i] :
( ( ( ~ ( eiw_di @ SV13 @ mactual )
| ! [SY302: $i] :
( ~ ( eiw_di @ SY302 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SY302 @ mactual ) )
| ( qmltpeq @ SV1 @ SY302 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(120,plain,
! [SV2: $i,SV14: $i] :
( ( ( ~ ( eiw_di @ SV14 @ mactual )
| ~ ( qmltpeq @ SV2 @ SV14 @ mactual )
| ( qmltpeq @ ( singleton @ SV2 ) @ ( singleton @ SV14 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ mactual )
| ~ ( qmltpeq @ SV3 @ SV15 @ mactual )
| ( qmltpeq @ SV15 @ SV3 @ mactual ) )
= $true )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(122,plain,
( ( eiw_di @ sK2_SX0 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(123,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ sK2_SX0 ) @ empty_set @ mactual )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(124,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK1_SY13 ) @ sK2_SX0 ) @ ( singleton @ sK1_SY13 ) @ mactual )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(125,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( eiw_di @ SV16 @ mactual )
| ! [SY303: $i] :
( ~ ( eiw_di @ SY303 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV16 @ mactual )
| ( qmltpeq @ ( set_difference @ SV5 @ SY303 ) @ ( set_difference @ SV16 @ SY303 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( eiw_di @ SV17 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV6 @ SV17 @ mactual )
| ~ ( empty @ SV6 @ mactual ) )
| ( empty @ SV17 @ mactual ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( eiw_di @ SV18 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual )
| ( in @ SV7 @ SV18 @ mactual ) )
| ~ ( ~ ( in @ SV7 @ SV18 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(128,plain,
( ( ~ ( eiw_di @ sK3_SX0 @ mactual )
| ~ ( empty @ sK3_SX0 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV8: $i,SV19: $i] :
( ( ( ~ ( eiw_di @ SV19 @ mactual )
| ! [SY304: $i] :
( ~ ( eiw_di @ SY304 @ mactual )
| ~ ( qmltpeq @ SV8 @ SV19 @ mactual )
| ( qmltpeq @ ( set_difference @ SY304 @ SV8 ) @ ( set_difference @ SY304 @ SV19 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV9: $i,SV20: $i] :
( ( ( ~ ( eiw_di @ SV20 @ mactual )
| ! [SY305: $i] :
( ~ ( eiw_di @ SY305 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual )
| ~ ( in @ SV9 @ SY305 @ mactual ) )
| ( in @ SV20 @ SY305 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(131,plain,
( ( ~ ( eiw_di @ sK4_SX0 @ mactual )
| ~ ~ ( empty @ sK4_SX0 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(132,plain,
! [SV10: $i,SV21: $i] :
( ( ( ~ ( eiw_di @ SV21 @ mactual )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
| ~ ( in @ SV10 @ SV21 @ mactual ) )
| ~ ( ~ ~ ( in @ SV10 @ SV21 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(133,plain,
! [SV11: $i,SV22: $i] :
( ( ( ~ ( eiw_di @ SV22 @ mactual )
| ! [SY306: $i] :
( ~ ( eiw_di @ SY306 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual )
| ~ ( in @ SY306 @ SV11 @ mactual ) )
| ( in @ SY306 @ SV22 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(134,plain,
! [SV12: $i,SV23: $i] :
( ( ( ~ ( eiw_di @ SV23 @ mactual )
| ~ ( in @ SV12 @ SV23 @ mactual )
| ~ ( in @ SV23 @ SV12 @ mactual ) )
= $true )
| ( ( eiw_di @ SV12 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV1: $i,SV13: $i] :
( ( ( ~ ( eiw_di @ SV13 @ mactual ) )
= $true )
| ( ( ! [SY302: $i] :
( ~ ( eiw_di @ SY302 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SY302 @ mactual ) )
| ( qmltpeq @ SV1 @ SY302 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV2: $i,SV14: $i] :
( ( ( ~ ( eiw_di @ SV14 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV2 @ SV14 @ mactual )
| ( qmltpeq @ ( singleton @ SV2 ) @ ( singleton @ SV14 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV3 @ SV15 @ mactual )
| ( qmltpeq @ SV15 @ SV3 @ mactual ) )
= $true )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(138,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( eiw_di @ SV16 @ mactual ) )
= $true )
| ( ( ! [SY303: $i] :
( ~ ( eiw_di @ SY303 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV16 @ mactual )
| ( qmltpeq @ ( set_difference @ SV5 @ SY303 ) @ ( set_difference @ SV16 @ SY303 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(139,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( eiw_di @ SV17 @ mactual ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV6 @ SV17 @ mactual )
| ~ ( empty @ SV6 @ mactual ) )
| ( empty @ SV17 @ mactual ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(140,plain,
! [SV7: $i,SV18: $i] :
( ( ( ~ ( eiw_di @ SV18 @ mactual ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual )
| ( in @ SV7 @ SV18 @ mactual ) )
| ~ ( ~ ( in @ SV7 @ SV18 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(141,plain,
( ( ~ ( eiw_di @ sK3_SX0 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(142,plain,
( ( ~ ( empty @ sK3_SX0 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(143,plain,
! [SV8: $i,SV19: $i] :
( ( ( ~ ( eiw_di @ SV19 @ mactual ) )
= $true )
| ( ( ! [SY304: $i] :
( ~ ( eiw_di @ SY304 @ mactual )
| ~ ( qmltpeq @ SV8 @ SV19 @ mactual )
| ( qmltpeq @ ( set_difference @ SY304 @ SV8 ) @ ( set_difference @ SY304 @ SV19 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV9: $i,SV20: $i] :
( ( ( ~ ( eiw_di @ SV20 @ mactual ) )
= $true )
| ( ( ! [SY305: $i] :
( ~ ( eiw_di @ SY305 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual )
| ~ ( in @ SV9 @ SY305 @ mactual ) )
| ( in @ SV20 @ SY305 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(145,plain,
( ( ~ ( eiw_di @ sK4_SX0 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(146,plain,
( ( ~ ~ ( empty @ sK4_SX0 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(147,plain,
! [SV10: $i,SV21: $i] :
( ( ( ~ ( eiw_di @ SV21 @ mactual ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
| ~ ( in @ SV10 @ SV21 @ mactual ) )
| ~ ( ~ ~ ( in @ SV10 @ SV21 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV11: $i,SV22: $i] :
( ( ( ~ ( eiw_di @ SV22 @ mactual ) )
= $true )
| ( ( ! [SY306: $i] :
( ~ ( eiw_di @ SY306 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual )
| ~ ( in @ SY306 @ SV11 @ mactual ) )
| ( in @ SY306 @ SV22 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(149,plain,
! [SV12: $i,SV23: $i] :
( ( ( ~ ( eiw_di @ SV23 @ mactual ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV23 @ mactual )
| ~ ( in @ SV23 @ SV12 @ mactual ) )
= $true )
| ( ( eiw_di @ SV12 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(150,plain,
! [SV1: $i,SV13: $i] :
( ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( ! [SY302: $i] :
( ~ ( eiw_di @ SY302 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SY302 @ mactual ) )
| ( qmltpeq @ SV1 @ SY302 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(151,plain,
! [SV2: $i,SV14: $i] :
( ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV2 @ SV14 @ mactual )
| ( qmltpeq @ ( singleton @ SV2 ) @ ( singleton @ SV14 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(152,plain,
! [SV3: $i,SV15: $i] :
( ( ( eiw_di @ SV15 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV3 @ SV15 @ mactual )
| ( qmltpeq @ SV15 @ SV3 @ mactual ) )
= $true )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(153,plain,
! [SV5: $i,SV16: $i] :
( ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( ! [SY303: $i] :
( ~ ( eiw_di @ SY303 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV16 @ mactual )
| ( qmltpeq @ ( set_difference @ SV5 @ SY303 ) @ ( set_difference @ SV16 @ SY303 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(154,plain,
! [SV6: $i,SV17: $i] :
( ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV6 @ SV17 @ mactual )
| ~ ( empty @ SV6 @ mactual ) )
| ( empty @ SV17 @ mactual ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(155,plain,
! [SV7: $i,SV18: $i] :
( ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual )
| ( in @ SV7 @ SV18 @ mactual ) )
| ~ ( ~ ( in @ SV7 @ SV18 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(156,plain,
( ( eiw_di @ sK3_SX0 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(157,plain,
( ( empty @ sK3_SX0 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(158,plain,
! [SV8: $i,SV19: $i] :
( ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( ! [SY304: $i] :
( ~ ( eiw_di @ SY304 @ mactual )
| ~ ( qmltpeq @ SV8 @ SV19 @ mactual )
| ( qmltpeq @ ( set_difference @ SY304 @ SV8 ) @ ( set_difference @ SY304 @ SV19 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV9: $i,SV20: $i] :
( ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( ! [SY305: $i] :
( ~ ( eiw_di @ SY305 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual )
| ~ ( in @ SV9 @ SY305 @ mactual ) )
| ( in @ SV20 @ SY305 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(160,plain,
( ( eiw_di @ sK4_SX0 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(161,plain,
( ( ~ ( empty @ sK4_SX0 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(162,plain,
! [SV10: $i,SV21: $i] :
( ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
| ~ ( in @ SV10 @ SV21 @ mactual ) )
| ~ ( ~ ~ ( in @ SV10 @ SV21 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV11: $i,SV22: $i] :
( ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( ! [SY306: $i] :
( ~ ( eiw_di @ SY306 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual )
| ~ ( in @ SY306 @ SV11 @ mactual ) )
| ( in @ SY306 @ SV22 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV12: $i,SV23: $i] :
( ( ( eiw_di @ SV23 @ mactual )
= $false )
| ( ( ~ ( in @ SV12 @ SV23 @ mactual )
| ~ ( in @ SV23 @ SV12 @ mactual ) )
= $true )
| ( ( eiw_di @ SV12 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV13: $i,SV1: $i,SV24: $i] :
( ( ( ~ ( eiw_di @ SV24 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SV24 @ mactual ) )
| ( qmltpeq @ SV1 @ SV24 @ mactual ) )
= $true )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV14: $i,SV2: $i] :
( ( ( ~ ( qmltpeq @ SV2 @ SV14 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV2 ) @ ( singleton @ SV14 ) @ mactual )
= $true )
| ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV15: $i,SV3: $i] :
( ( ( ~ ( qmltpeq @ SV3 @ SV15 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV15 @ SV3 @ mactual )
= $true )
| ( ( eiw_di @ SV15 @ mactual )
= $false )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV16: $i,SV5: $i,SV25: $i] :
( ( ( ~ ( eiw_di @ SV25 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV16 @ mactual )
| ( qmltpeq @ ( set_difference @ SV5 @ SV25 ) @ ( set_difference @ SV16 @ SV25 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV6 @ SV17 @ mactual )
| ~ ( empty @ SV6 @ mactual ) ) )
= $true )
| ( ( empty @ SV17 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual )
| ( in @ SV7 @ SV18 @ mactual ) )
| ~ ( ~ ( in @ SV7 @ SV18 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(171,plain,
! [SV19: $i,SV8: $i,SV26: $i] :
( ( ( ~ ( eiw_di @ SV26 @ mactual )
| ~ ( qmltpeq @ SV8 @ SV19 @ mactual )
| ( qmltpeq @ ( set_difference @ SV26 @ SV8 ) @ ( set_difference @ SV26 @ SV19 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV20: $i,SV9: $i,SV27: $i] :
( ( ( ~ ( eiw_di @ SV27 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual )
| ~ ( in @ SV9 @ SV27 @ mactual ) )
| ( in @ SV20 @ SV27 @ mactual ) )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(173,plain,
( ( empty @ sK4_SX0 @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
| ~ ( in @ SV10 @ SV21 @ mactual ) )
| ~ ( ~ ~ ( in @ SV10 @ SV21 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV22: $i,SV11: $i,SV28: $i] :
( ( ( ~ ( eiw_di @ SV28 @ mactual )
| ~ ~ ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual )
| ~ ( in @ SV28 @ SV11 @ mactual ) )
| ( in @ SV28 @ SV22 @ mactual ) )
= $true )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV23: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV23 @ mactual ) )
= $true )
| ( ( ~ ( in @ SV23 @ SV12 @ mactual ) )
= $true )
| ( ( eiw_di @ SV23 @ mactual )
= $false )
| ( ( eiw_di @ SV12 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV13: $i,SV1: $i,SV24: $i] :
( ( ( ~ ( eiw_di @ SV24 @ mactual ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SV24 @ mactual ) )
| ( qmltpeq @ SV1 @ SV24 @ mactual ) )
= $true )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV14: $i,SV2: $i] :
( ( ( qmltpeq @ SV2 @ SV14 @ mactual )
= $false )
| ( ( qmltpeq @ ( singleton @ SV2 ) @ ( singleton @ SV14 ) @ mactual )
= $true )
| ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV15: $i,SV3: $i] :
( ( ( qmltpeq @ SV3 @ SV15 @ mactual )
= $false )
| ( ( qmltpeq @ SV15 @ SV3 @ mactual )
= $true )
| ( ( eiw_di @ SV15 @ mactual )
= $false )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV16: $i,SV5: $i,SV25: $i] :
( ( ( ~ ( eiw_di @ SV25 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV5 @ SV16 @ mactual )
| ( qmltpeq @ ( set_difference @ SV5 @ SV25 ) @ ( set_difference @ SV16 @ SV25 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV6 @ SV17 @ mactual )
| ~ ( empty @ SV6 @ mactual ) ) )
= $false )
| ( ( empty @ SV17 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual )
| ( in @ SV7 @ SV18 @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(183,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV18 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(184,plain,
! [SV19: $i,SV8: $i,SV26: $i] :
( ( ( ~ ( eiw_di @ SV26 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV8 @ SV19 @ mactual )
| ( qmltpeq @ ( set_difference @ SV26 @ SV8 ) @ ( set_difference @ SV26 @ SV19 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(185,plain,
! [SV20: $i,SV9: $i,SV27: $i] :
( ( ( ~ ( eiw_di @ SV27 @ mactual ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual )
| ~ ( in @ SV9 @ SV27 @ mactual ) )
| ( in @ SV20 @ SV27 @ mactual ) )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(186,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
| ~ ( in @ SV10 @ SV21 @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(187,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( in @ SV10 @ SV21 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(188,plain,
! [SV22: $i,SV11: $i,SV28: $i] :
( ( ( ~ ( eiw_di @ SV28 @ mactual ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual )
| ~ ( in @ SV28 @ SV11 @ mactual ) )
| ( in @ SV28 @ SV22 @ mactual ) )
= $true )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(189,plain,
! [SV23: $i,SV12: $i] :
( ( ( in @ SV12 @ SV23 @ mactual )
= $false )
| ( ( ~ ( in @ SV23 @ SV12 @ mactual ) )
= $true )
| ( ( eiw_di @ SV23 @ mactual )
= $false )
| ( ( eiw_di @ SV12 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV13: $i,SV1: $i,SV24: $i] :
( ( ( eiw_di @ SV24 @ mactual )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SV24 @ mactual ) )
| ( qmltpeq @ SV1 @ SV24 @ mactual ) )
= $true )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(191,plain,
! [SV16: $i,SV5: $i,SV25: $i] :
( ( ( eiw_di @ SV25 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV5 @ SV16 @ mactual )
| ( qmltpeq @ ( set_difference @ SV5 @ SV25 ) @ ( set_difference @ SV16 @ SV25 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(192,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV17 @ mactual )
| ~ ( empty @ SV6 @ mactual ) )
= $true )
| ( ( empty @ SV17 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(193,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual )
| ( in @ SV7 @ SV18 @ mactual ) )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(194,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV18 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual ) )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(195,plain,
! [SV19: $i,SV8: $i,SV26: $i] :
( ( ( eiw_di @ SV26 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV8 @ SV19 @ mactual )
| ( qmltpeq @ ( set_difference @ SV26 @ SV8 ) @ ( set_difference @ SV26 @ SV19 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV20: $i,SV9: $i,SV27: $i] :
( ( ( eiw_di @ SV27 @ mactual )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual )
| ~ ( in @ SV9 @ SV27 @ mactual ) )
| ( in @ SV20 @ SV27 @ mactual ) )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(197,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
| ~ ( in @ SV10 @ SV21 @ mactual ) )
= $true )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(198,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ~ ( in @ SV10 @ SV21 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual ) )
= $true )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(199,plain,
! [SV22: $i,SV11: $i,SV28: $i] :
( ( ( eiw_di @ SV28 @ mactual )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual )
| ~ ( in @ SV28 @ SV11 @ mactual ) )
| ( in @ SV28 @ SV22 @ mactual ) )
= $true )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV12: $i,SV23: $i] :
( ( ( in @ SV23 @ SV12 @ mactual )
= $false )
| ( ( in @ SV12 @ SV23 @ mactual )
= $false )
| ( ( eiw_di @ SV23 @ mactual )
= $false )
| ( ( eiw_di @ SV12 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV24: $i,SV13: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SV24 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV1 @ SV24 @ mactual )
= $true )
| ( ( eiw_di @ SV24 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(202,plain,
! [SV25: $i,SV16: $i,SV5: $i] :
( ( ( ~ ( qmltpeq @ SV5 @ SV16 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV5 @ SV25 ) @ ( set_difference @ SV16 @ SV25 ) @ mactual )
= $true )
| ( ( eiw_di @ SV25 @ mactual )
= $false )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(203,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV17 @ mactual ) )
= $true )
| ( ( ~ ( empty @ SV6 @ mactual ) )
= $true )
| ( ( empty @ SV17 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(204,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual ) )
= $true )
| ( ( in @ SV7 @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(205,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV18 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(206,plain,
! [SV26: $i,SV19: $i,SV8: $i] :
( ( ( ~ ( qmltpeq @ SV8 @ SV19 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV26 @ SV8 ) @ ( set_difference @ SV26 @ SV19 ) @ mactual )
= $true )
| ( ( eiw_di @ SV26 @ mactual )
= $false )
| ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(207,plain,
! [SV27: $i,SV20: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual )
| ~ ( in @ SV9 @ SV27 @ mactual ) ) )
= $true )
| ( ( in @ SV20 @ SV27 @ mactual )
= $true )
| ( ( eiw_di @ SV27 @ mactual )
= $false )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(208,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV21 @ mactual ) )
= $true )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(209,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ~ ( in @ SV10 @ SV21 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
= $true )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(210,plain,
! [SV28: $i,SV22: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual )
| ~ ( in @ SV28 @ SV11 @ mactual ) ) )
= $true )
| ( ( in @ SV28 @ SV22 @ mactual )
= $true )
| ( ( eiw_di @ SV28 @ mactual )
= $false )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV24: $i,SV13: $i,SV1: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SV24 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV1 @ SV24 @ mactual )
= $true )
| ( ( eiw_di @ SV24 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(212,plain,
! [SV25: $i,SV16: $i,SV5: $i] :
( ( ( qmltpeq @ SV5 @ SV16 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV5 @ SV25 ) @ ( set_difference @ SV16 @ SV25 ) @ mactual )
= $true )
| ( ( eiw_di @ SV25 @ mactual )
= $false )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(213,plain,
! [SV17: $i,SV6: $i] :
( ( ( qmltpeq @ SV6 @ SV17 @ mactual )
= $false )
| ( ( ~ ( empty @ SV6 @ mactual ) )
= $true )
| ( ( empty @ SV17 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(214,plain,
! [SV18: $i,SV7: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual )
= $false )
| ( ( in @ SV7 @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(215,plain,
! [SV18: $i,SV7: $i] :
( ( ( in @ SV7 @ SV18 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV7 ) @ SV18 ) @ empty_set @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(216,plain,
! [SV26: $i,SV19: $i,SV8: $i] :
( ( ( qmltpeq @ SV8 @ SV19 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV26 @ SV8 ) @ ( set_difference @ SV26 @ SV19 ) @ mactual )
= $true )
| ( ( eiw_di @ SV26 @ mactual )
= $false )
| ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(217,plain,
! [SV27: $i,SV20: $i,SV9: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual )
| ~ ( in @ SV9 @ SV27 @ mactual ) ) )
= $false )
| ( ( in @ SV20 @ SV27 @ mactual )
= $true )
| ( ( eiw_di @ SV27 @ mactual )
= $false )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(218,plain,
! [SV21: $i,SV10: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
= $false )
| ( ( ~ ( in @ SV10 @ SV21 @ mactual ) )
= $true )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(219,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV21 @ mactual ) )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
= $true )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(220,plain,
! [SV28: $i,SV22: $i,SV11: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual )
| ~ ( in @ SV28 @ SV11 @ mactual ) ) )
= $false )
| ( ( in @ SV28 @ SV22 @ mactual )
= $true )
| ( ( eiw_di @ SV28 @ mactual )
= $false )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(221,plain,
! [SV24: $i,SV13: $i,SV1: $i] :
( ( ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SV24 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV1 @ SV24 @ mactual )
= $true )
| ( ( eiw_di @ SV24 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(222,plain,
! [SV17: $i,SV6: $i] :
( ( ( empty @ SV6 @ mactual )
= $false )
| ( ( qmltpeq @ SV6 @ SV17 @ mactual )
= $false )
| ( ( empty @ SV17 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(223,plain,
! [SV27: $i,SV20: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual )
| ~ ( in @ SV9 @ SV27 @ mactual ) )
= $true )
| ( ( in @ SV20 @ SV27 @ mactual )
= $true )
| ( ( eiw_di @ SV27 @ mactual )
= $false )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(224,plain,
! [SV21: $i,SV10: $i] :
( ( ( in @ SV10 @ SV21 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
= $false )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(225,plain,
! [SV21: $i,SV10: $i] :
( ( ( in @ SV10 @ SV21 @ mactual )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV10 ) @ SV21 ) @ ( singleton @ SV10 ) @ mactual )
= $true )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(226,plain,
! [SV28: $i,SV22: $i,SV11: $i] :
( ( ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual )
| ~ ( in @ SV28 @ SV11 @ mactual ) )
= $true )
| ( ( in @ SV28 @ SV22 @ mactual )
= $true )
| ( ( eiw_di @ SV28 @ mactual )
= $false )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(227,plain,
! [SV24: $i,SV13: $i,SV1: $i] :
( ( ( ~ ( qmltpeq @ SV1 @ SV13 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV13 @ SV24 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV1 @ SV24 @ mactual )
= $true )
| ( ( eiw_di @ SV24 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(228,plain,
! [SV27: $i,SV20: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV20 @ mactual ) )
= $true )
| ( ( ~ ( in @ SV9 @ SV27 @ mactual ) )
= $true )
| ( ( in @ SV20 @ SV27 @ mactual )
= $true )
| ( ( eiw_di @ SV27 @ mactual )
= $false )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(229,plain,
! [SV28: $i,SV22: $i,SV11: $i] :
( ( ( ~ ( qmltpeq @ SV11 @ SV22 @ mactual ) )
= $true )
| ( ( ~ ( in @ SV28 @ SV11 @ mactual ) )
= $true )
| ( ( in @ SV28 @ SV22 @ mactual )
= $true )
| ( ( eiw_di @ SV28 @ mactual )
= $false )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(230,plain,
! [SV24: $i,SV13: $i,SV1: $i] :
( ( ( qmltpeq @ SV1 @ SV13 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV13 @ SV24 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV1 @ SV24 @ mactual )
= $true )
| ( ( eiw_di @ SV24 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(231,plain,
! [SV27: $i,SV20: $i,SV9: $i] :
( ( ( qmltpeq @ SV9 @ SV20 @ mactual )
= $false )
| ( ( ~ ( in @ SV9 @ SV27 @ mactual ) )
= $true )
| ( ( in @ SV20 @ SV27 @ mactual )
= $true )
| ( ( eiw_di @ SV27 @ mactual )
= $false )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(232,plain,
! [SV28: $i,SV22: $i,SV11: $i] :
( ( ( qmltpeq @ SV11 @ SV22 @ mactual )
= $false )
| ( ( ~ ( in @ SV28 @ SV11 @ mactual ) )
= $true )
| ( ( in @ SV28 @ SV22 @ mactual )
= $true )
| ( ( eiw_di @ SV28 @ mactual )
= $false )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(233,plain,
! [SV1: $i,SV24: $i,SV13: $i] :
( ( ( qmltpeq @ SV13 @ SV24 @ mactual )
= $false )
| ( ( qmltpeq @ SV1 @ SV13 @ mactual )
= $false )
| ( ( qmltpeq @ SV1 @ SV24 @ mactual )
= $true )
| ( ( eiw_di @ SV24 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV1 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(234,plain,
! [SV20: $i,SV27: $i,SV9: $i] :
( ( ( in @ SV9 @ SV27 @ mactual )
= $false )
| ( ( qmltpeq @ SV9 @ SV20 @ mactual )
= $false )
| ( ( in @ SV20 @ SV27 @ mactual )
= $true )
| ( ( eiw_di @ SV27 @ mactual )
= $false )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV9 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(235,plain,
! [SV22: $i,SV11: $i,SV28: $i] :
( ( ( in @ SV28 @ SV11 @ mactual )
= $false )
| ( ( qmltpeq @ SV11 @ SV22 @ mactual )
= $false )
| ( ( in @ SV28 @ SV22 @ mactual )
= $true )
| ( ( eiw_di @ SV28 @ mactual )
= $false )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(236,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,235,234,233,225,224,222,216,215,214,212,200,179,178,173,160,157,156,124,123,122,106,56]) ).
thf(237,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET926^20 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:00:16 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.51/0.31
% 0.51/0.31 No.of.Axioms: 15
% 0.51/0.31
% 0.51/0.31 Length.of.Defs: 1663
% 0.51/0.31
% 0.51/0.31 Contains.Choice.Funs: false
% 0.51/0.31 ............
% 0.51/0.31
% 0.51/0.31 ********************************
% 0.51/0.31 * All subproblems solved! *
% 0.51/0.31 ********************************
% 0.51/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:236,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.51/0.31
% 0.51/0.31 %**** Beginning of derivation protocol ****
% 0.51/0.31 % SZS output start CNFRefutation
% See solution above
% 0.51/0.31
% 0.51/0.31 %**** End of derivation protocol ****
% 0.51/0.31 %**** no. of clauses in derivation: 234 ****
% 0.51/0.31 %**** clause counter: 236 ****
% 0.51/0.31
% 0.51/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:236,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------