%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET002^3 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:38:48 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of formulae : 244 ( 129 unt; 0 typ; 10 def)
% Number of atoms : 1505 ( 361 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 3365 ( 481 ~; 402 |; 14 &;2435 @)
% ( 11 <=>; 22 =>; 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 : 23 ( 20 usr; 4 con; 0-3 aty)
% Number of variables : 623 ( 65 ^; 553 !; 5 ?; 623 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
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_member,type,
member: $i > $i > 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_SY3,type,
sK1_SY3: $i ).
thf(tp_sK2_SY405,type,
sK2_SY405: mworld > mworld ).
thf(tp_sK3_SY413,type,
sK3_SY413: $i > $i > $i ).
thf(tp_sK4_SY417,type,
sK4_SY417: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > mworld > $o ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
thf(1,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mequiv @ ( qmltpeq @ B @ C )
@ ( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(2,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] : ( subset @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(3,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mequiv @ ( subset @ B @ C )
@ ( mforall_di
@ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( qmltpeq @ ( union @ B @ C ) @ ( union @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(5,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(6,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ D @ ( union @ B @ C ) ) @ ( mor @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(7,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( subset @ B @ C ) @ ( qmltpeq @ ( union @ B @ C ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_union) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_2) ).
thf(11,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_1) ).
thf(12,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_substitution_2) ).
thf(13,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_substitution_1) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(15,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(16,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(17,axiom,
! [W: mworld] :
? [V: mworld] : ( mrel @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_serial) ).
thf(18,conjecture,
( mlocal
@ ( mforall_di
@ ^ [B: $i] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
thf(19,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [B: $i] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[18]) ).
thf(20,plain,
( ( ! [SY3: $i] : ( qmltpeq @ ( union @ SY3 @ SY3 ) @ SY3 @ mactual ) )
= $false ),
inference(unfold_def,[status(thm)],[19,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(21,plain,
( ( ! [SY30: $i,SY31: $i] :
( ( qmltpeq @ SY30 @ SY31 @ mactual )
<=> ! [SY32: $i] :
( ( member @ SY32 @ SY30 @ mactual )
<=> ( member @ SY32 @ SY31 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(22,plain,
( ( ! [SY39: $i] : ( subset @ SY39 @ SY39 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(23,plain,
( ( ! [SY66: $i,SY67: $i] :
( ( subset @ SY66 @ SY67 @ mactual )
<=> ! [SY68: $i] :
( ( member @ SY68 @ SY66 @ mactual )
=> ( member @ SY68 @ SY67 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(24,plain,
( ( ! [SY81: $i,SY82: $i] : ( qmltpeq @ ( union @ SY81 @ SY82 ) @ ( union @ SY82 @ SY81 ) @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(25,plain,
( ( ! [SY101: $i,SY102: $i] :
( ( qmltpeq @ SY101 @ SY102 @ mactual )
<=> ( ( subset @ SY101 @ SY102 @ mactual )
& ( subset @ SY102 @ SY101 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(26,plain,
( ( ! [SY129: $i,SY130: $i,SY131: $i] :
( ( member @ SY131 @ ( union @ SY129 @ SY130 ) @ mactual )
<=> ( ( member @ SY131 @ SY129 @ mactual )
| ( member @ SY131 @ SY130 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(27,plain,
( ( ! [SY148: $i,SY149: $i] :
( ( subset @ SY148 @ SY149 @ mactual )
=> ( qmltpeq @ ( union @ SY148 @ SY149 ) @ SY149 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(28,plain,
( ( ! [SY176: $i,SY177: $i,SY178: $i] :
( ( ( qmltpeq @ SY176 @ SY177 @ mactual )
& ( subset @ SY178 @ SY176 @ mactual ) )
=> ( subset @ SY178 @ SY177 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(29,plain,
( ( ! [SY206: $i,SY207: $i,SY208: $i] :
( ( ( qmltpeq @ SY206 @ SY207 @ mactual )
& ( subset @ SY206 @ SY208 @ mactual ) )
=> ( subset @ SY207 @ SY208 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(30,plain,
( ( ! [SY236: $i,SY237: $i,SY238: $i] :
( ( ( qmltpeq @ SY236 @ SY237 @ mactual )
& ( member @ SY238 @ SY236 @ mactual ) )
=> ( member @ SY238 @ SY237 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(31,plain,
( ( ! [SY266: $i,SY267: $i,SY268: $i] :
( ( ( qmltpeq @ SY266 @ SY267 @ mactual )
& ( member @ SY266 @ SY268 @ mactual ) )
=> ( member @ SY267 @ SY268 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(32,plain,
( ( ! [SY293: $i,SY294: $i,SY295: $i] :
( ( qmltpeq @ SY293 @ SY294 @ mactual )
=> ( qmltpeq @ ( union @ SY295 @ SY293 ) @ ( union @ SY295 @ SY294 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(33,plain,
( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ( qmltpeq @ SY320 @ SY321 @ mactual )
=> ( qmltpeq @ ( union @ SY320 @ SY322 ) @ ( union @ SY321 @ SY322 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(34,plain,
( ( ! [SY350: $i,SY351: $i,SY352: $i] :
( ( ( qmltpeq @ SY350 @ SY351 @ mactual )
& ( qmltpeq @ SY351 @ SY352 @ mactual ) )
=> ( qmltpeq @ SY350 @ SY352 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(35,plain,
( ( ! [SY369: $i,SY370: $i] :
( ( qmltpeq @ SY369 @ SY370 @ mactual )
=> ( qmltpeq @ SY370 @ SY369 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(36,plain,
( ( ! [SY376: $i] : ( qmltpeq @ SY376 @ SY376 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(37,plain,
( ( ! [W: mworld] :
? [V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(38,plain,
( ( qmltpeq @ ( union @ sK1_SY3 @ sK1_SY3 ) @ sK1_SY3 @ mactual )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(39,plain,
( ( ~ ( qmltpeq @ ( union @ sK1_SY3 @ sK1_SY3 ) @ sK1_SY3 @ mactual ) )
= $true ),
inference(polarity_switch,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [W: mworld] :
? [V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(41,plain,
( ( ! [SY376: $i] : ( qmltpeq @ SY376 @ SY376 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(42,plain,
( ( ! [SY369: $i,SY370: $i] :
( ( qmltpeq @ SY369 @ SY370 @ mactual )
=> ( qmltpeq @ SY370 @ SY369 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(43,plain,
( ( ! [SY350: $i,SY351: $i,SY352: $i] :
( ( ( qmltpeq @ SY350 @ SY351 @ mactual )
& ( qmltpeq @ SY351 @ SY352 @ mactual ) )
=> ( qmltpeq @ SY350 @ SY352 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(44,plain,
( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ( qmltpeq @ SY320 @ SY321 @ mactual )
=> ( qmltpeq @ ( union @ SY320 @ SY322 ) @ ( union @ SY321 @ SY322 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(45,plain,
( ( ! [SY293: $i,SY294: $i,SY295: $i] :
( ( qmltpeq @ SY293 @ SY294 @ mactual )
=> ( qmltpeq @ ( union @ SY295 @ SY293 ) @ ( union @ SY295 @ SY294 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(46,plain,
( ( ! [SY266: $i,SY267: $i,SY268: $i] :
( ( ( qmltpeq @ SY266 @ SY267 @ mactual )
& ( member @ SY266 @ SY268 @ mactual ) )
=> ( member @ SY267 @ SY268 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(47,plain,
( ( ! [SY236: $i,SY237: $i,SY238: $i] :
( ( ( qmltpeq @ SY236 @ SY237 @ mactual )
& ( member @ SY238 @ SY236 @ mactual ) )
=> ( member @ SY238 @ SY237 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(48,plain,
( ( ! [SY206: $i,SY207: $i,SY208: $i] :
( ( ( qmltpeq @ SY206 @ SY207 @ mactual )
& ( subset @ SY206 @ SY208 @ mactual ) )
=> ( subset @ SY207 @ SY208 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(49,plain,
( ( ! [SY176: $i,SY177: $i,SY178: $i] :
( ( ( qmltpeq @ SY176 @ SY177 @ mactual )
& ( subset @ SY178 @ SY176 @ mactual ) )
=> ( subset @ SY178 @ SY177 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(50,plain,
( ( ! [SY148: $i,SY149: $i] :
( ( subset @ SY148 @ SY149 @ mactual )
=> ( qmltpeq @ ( union @ SY148 @ SY149 ) @ SY149 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(51,plain,
( ( ! [SY129: $i,SY130: $i,SY131: $i] :
( ( member @ SY131 @ ( union @ SY129 @ SY130 ) @ mactual )
<=> ( ( member @ SY131 @ SY129 @ mactual )
| ( member @ SY131 @ SY130 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(52,plain,
( ( ! [SY101: $i,SY102: $i] :
( ( qmltpeq @ SY101 @ SY102 @ mactual )
<=> ( ( subset @ SY101 @ SY102 @ mactual )
& ( subset @ SY102 @ SY101 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(53,plain,
( ( ! [SY81: $i,SY82: $i] : ( qmltpeq @ ( union @ SY81 @ SY82 ) @ ( union @ SY82 @ SY81 ) @ mactual ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(54,plain,
( ( ! [SY66: $i,SY67: $i] :
( ( subset @ SY66 @ SY67 @ mactual )
<=> ! [SY68: $i] :
( ( member @ SY68 @ SY66 @ mactual )
=> ( member @ SY68 @ SY67 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(55,plain,
( ( ! [SY39: $i] : ( subset @ SY39 @ SY39 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(56,plain,
( ( ! [SY30: $i,SY31: $i] :
( ( qmltpeq @ SY30 @ SY31 @ mactual )
<=> ! [SY32: $i] :
( ( member @ SY32 @ SY30 @ mactual )
<=> ( member @ SY32 @ SY31 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(57,plain,
( ( ~ ( qmltpeq @ ( union @ sK1_SY3 @ sK1_SY3 ) @ sK1_SY3 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( 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,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) @ mactual )
| ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) )
| ~ ( ~ ( ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(60,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( member @ SX0 @ SX2 @ mactual ) )
| ( member @ SX1 @ SX2 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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(62,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( union @ SX0 @ SX2 ) @ ( union @ SX1 @ SX2 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(63,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( member @ SX2 @ SX0 @ mactual ) )
| ( member @ SX2 @ SX1 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) )
| ( subset @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( union @ SX2 @ SX0 ) @ ( union @ SX2 @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(66,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX0 @ SX2 @ mactual ) )
| ( subset @ SX1 @ SX2 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) )
| ~ ( ~ ( member @ SX2 @ SX1 @ mactual )
| ( member @ SX2 @ SX0 @ mactual ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) )
| ~ ( ~ ( member @ SX2 @ SX1 @ mactual )
| ( member @ SX2 @ SX0 @ mactual ) ) )
| ( qmltpeq @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual ) )
| ( qmltpeq @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX2 @ SX0 @ mactual ) )
| ( subset @ SX2 @ SX1 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(70,plain,
( ( ! [SX0: mworld] :
~ ! [SX1: mworld] :
~ ( mrel @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[40,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( union @ SX0 @ SX1 ) @ SX1 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(72,plain,
! [SV1: $i] :
( ( qmltpeq @ SV1 @ SV1 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(73,plain,
! [SV2: $i] :
( ( ! [SY380: $i] : ( qmltpeq @ ( union @ SV2 @ SY380 ) @ ( union @ SY380 @ SV2 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(74,plain,
! [SV3: $i] :
( ( subset @ SV3 @ SV3 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(75,plain,
( ( qmltpeq @ ( union @ sK1_SY3 @ sK1_SY3 ) @ sK1_SY3 @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(76,plain,
! [SV4: $i] :
( ( ! [SY381: $i,SY382: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV4 @ SY381 @ mactual )
| ~ ( qmltpeq @ SY381 @ SY382 @ mactual ) )
| ( qmltpeq @ SV4 @ SY382 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(77,plain,
! [SV5: $i] :
( ( ! [SY383: $i,SY384: $i] :
~ ( ~ ( ~ ( member @ SY384 @ ( union @ SV5 @ SY383 ) @ mactual )
| ( member @ SY384 @ SV5 @ mactual )
| ( member @ SY384 @ SY383 @ mactual ) )
| ~ ( ~ ( ( member @ SY384 @ SV5 @ mactual )
| ( member @ SY384 @ SY383 @ mactual ) )
| ( member @ SY384 @ ( union @ SV5 @ SY383 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(78,plain,
! [SV6: $i] :
( ( ! [SY385: $i,SY386: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV6 @ SY385 @ mactual )
| ~ ( member @ SV6 @ SY386 @ mactual ) )
| ( member @ SY385 @ SY386 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(79,plain,
! [SV7: $i] :
( ( ! [SY387: $i] :
( ~ ( qmltpeq @ SV7 @ SY387 @ mactual )
| ( qmltpeq @ SY387 @ SV7 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(80,plain,
! [SV8: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ( qmltpeq @ SV8 @ SY388 @ mactual )
| ( qmltpeq @ ( union @ SV8 @ SY389 ) @ ( union @ SY388 @ SY389 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(81,plain,
! [SV9: $i] :
( ( ! [SY390: $i,SY391: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV9 @ SY390 @ mactual )
| ~ ( member @ SY391 @ SV9 @ mactual ) )
| ( member @ SY391 @ SY390 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(82,plain,
! [SV10: $i] :
( ( ! [SY392: $i] :
~ ( ~ ( ~ ( subset @ SV10 @ SY392 @ mactual )
| ! [SY393: $i] :
( ~ ( member @ SY393 @ SV10 @ mactual )
| ( member @ SY393 @ SY392 @ mactual ) ) )
| ~ ( ~ ! [SY394: $i] :
( ~ ( member @ SY394 @ SV10 @ mactual )
| ( member @ SY394 @ SY392 @ mactual ) )
| ( subset @ SV10 @ SY392 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(83,plain,
! [SV11: $i] :
( ( ! [SY395: $i,SY396: $i] :
( ~ ( qmltpeq @ SV11 @ SY395 @ mactual )
| ( qmltpeq @ ( union @ SY396 @ SV11 ) @ ( union @ SY396 @ SY395 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(84,plain,
! [SV12: $i] :
( ( ! [SY397: $i,SY398: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV12 @ SY397 @ mactual )
| ~ ( subset @ SV12 @ SY398 @ mactual ) )
| ( subset @ SY397 @ SY398 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(85,plain,
! [SV13: $i] :
( ( ! [SY399: $i] :
~ ( ~ ( ~ ( qmltpeq @ SV13 @ SY399 @ mactual )
| ! [SY400: $i] :
~ ( ~ ( ~ ( member @ SY400 @ SV13 @ mactual )
| ( member @ SY400 @ SY399 @ mactual ) )
| ~ ( ~ ( member @ SY400 @ SY399 @ mactual )
| ( member @ SY400 @ SV13 @ mactual ) ) ) )
| ~ ( ~ ! [SY401: $i] :
~ ( ~ ( ~ ( member @ SY401 @ SV13 @ mactual )
| ( member @ SY401 @ SY399 @ mactual ) )
| ~ ( ~ ( member @ SY401 @ SY399 @ mactual )
| ( member @ SY401 @ SV13 @ mactual ) ) )
| ( qmltpeq @ SV13 @ SY399 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(86,plain,
! [SV14: $i] :
( ( ! [SY402: $i] :
~ ( ~ ( ~ ( qmltpeq @ SV14 @ SY402 @ mactual )
| ~ ( ~ ( subset @ SV14 @ SY402 @ mactual )
| ~ ( subset @ SY402 @ SV14 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SY402 @ mactual )
| ~ ( subset @ SY402 @ SV14 @ mactual ) )
| ( qmltpeq @ SV14 @ SY402 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(87,plain,
! [SV15: $i] :
( ( ! [SY403: $i,SY404: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV15 @ SY403 @ mactual )
| ~ ( subset @ SY404 @ SV15 @ mactual ) )
| ( subset @ SY404 @ SY403 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(88,plain,
! [SV16: mworld] :
( ( ~ ! [SY405: mworld] :
~ ( mrel @ SV16 @ SY405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(89,plain,
! [SV17: $i] :
( ( ! [SY406: $i] :
( ~ ( subset @ SV17 @ SY406 @ mactual )
| ( qmltpeq @ ( union @ SV17 @ SY406 ) @ SY406 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(90,plain,
! [SV18: $i,SV2: $i] :
( ( qmltpeq @ ( union @ SV2 @ SV18 ) @ ( union @ SV18 @ SV2 ) @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(91,plain,
! [SV19: $i,SV4: $i] :
( ( ! [SY407: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV4 @ SV19 @ mactual )
| ~ ( qmltpeq @ SV19 @ SY407 @ mactual ) )
| ( qmltpeq @ SV4 @ SY407 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(92,plain,
! [SV20: $i,SV5: $i] :
( ( ! [SY408: $i] :
~ ( ~ ( ~ ( member @ SY408 @ ( union @ SV5 @ SV20 ) @ mactual )
| ( member @ SY408 @ SV5 @ mactual )
| ( member @ SY408 @ SV20 @ mactual ) )
| ~ ( ~ ( ( member @ SY408 @ SV5 @ mactual )
| ( member @ SY408 @ SV20 @ mactual ) )
| ( member @ SY408 @ ( union @ SV5 @ SV20 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(93,plain,
! [SV21: $i,SV6: $i] :
( ( ! [SY409: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV6 @ SV21 @ mactual )
| ~ ( member @ SV6 @ SY409 @ mactual ) )
| ( member @ SV21 @ SY409 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(94,plain,
! [SV22: $i,SV7: $i] :
( ( ~ ( qmltpeq @ SV7 @ SV22 @ mactual )
| ( qmltpeq @ SV22 @ SV7 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV23: $i,SV8: $i] :
( ( ! [SY410: $i] :
( ~ ( qmltpeq @ SV8 @ SV23 @ mactual )
| ( qmltpeq @ ( union @ SV8 @ SY410 ) @ ( union @ SV23 @ SY410 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV24: $i,SV9: $i] :
( ( ! [SY411: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV24 @ mactual )
| ~ ( member @ SY411 @ SV9 @ mactual ) )
| ( member @ SY411 @ SV24 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
! [SV25: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV10 @ SV25 @ mactual )
| ! [SY412: $i] :
( ~ ( member @ SY412 @ SV10 @ mactual )
| ( member @ SY412 @ SV25 @ mactual ) ) )
| ~ ( ~ ! [SY413: $i] :
( ~ ( member @ SY413 @ SV10 @ mactual )
| ( member @ SY413 @ SV25 @ mactual ) )
| ( subset @ SV10 @ SV25 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(98,plain,
! [SV26: $i,SV11: $i] :
( ( ! [SY414: $i] :
( ~ ( qmltpeq @ SV11 @ SV26 @ mactual )
| ( qmltpeq @ ( union @ SY414 @ SV11 ) @ ( union @ SY414 @ SV26 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV27: $i,SV12: $i] :
( ( ! [SY415: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV12 @ SV27 @ mactual )
| ~ ( subset @ SV12 @ SY415 @ mactual ) )
| ( subset @ SV27 @ SY415 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( qmltpeq @ SV13 @ SV28 @ mactual )
| ! [SY416: $i] :
~ ( ~ ( ~ ( member @ SY416 @ SV13 @ mactual )
| ( member @ SY416 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY416 @ SV28 @ mactual )
| ( member @ SY416 @ SV13 @ mactual ) ) ) )
| ~ ( ~ ! [SY417: $i] :
~ ( ~ ( ~ ( member @ SY417 @ SV13 @ mactual )
| ( member @ SY417 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY417 @ SV28 @ mactual )
| ( member @ SY417 @ SV13 @ mactual ) ) )
| ( qmltpeq @ SV13 @ SV28 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( qmltpeq @ SV14 @ SV29 @ mactual )
| ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) )
| ( qmltpeq @ SV14 @ SV29 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV30: $i,SV15: $i] :
( ( ! [SY418: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV15 @ SV30 @ mactual )
| ~ ( subset @ SY418 @ SV15 @ mactual ) )
| ( subset @ SY418 @ SV30 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV16: mworld] :
( ( ! [SY405: mworld] :
~ ( mrel @ SV16 @ SY405 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV31: $i,SV17: $i] :
( ( ~ ( subset @ SV17 @ SV31 @ mactual )
| ( qmltpeq @ ( union @ SV17 @ SV31 ) @ SV31 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV32: $i,SV19: $i,SV4: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV4 @ SV19 @ mactual )
| ~ ( qmltpeq @ SV19 @ SV32 @ mactual ) )
| ( qmltpeq @ SV4 @ SV32 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ~ ( ~ ( ~ ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
| ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
| ~ ( ~ ( ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
| ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(107,plain,
! [SV34: $i,SV21: $i,SV6: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV6 @ SV21 @ mactual )
| ~ ( member @ SV6 @ SV34 @ mactual ) )
| ( member @ SV21 @ SV34 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV22: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ SV7 @ SV22 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV22 @ SV7 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV35: $i,SV23: $i,SV8: $i] :
( ( ~ ( qmltpeq @ SV8 @ SV23 @ mactual )
| ( qmltpeq @ ( union @ SV8 @ SV35 ) @ ( union @ SV23 @ SV35 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV36: $i,SV24: $i,SV9: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV24 @ mactual )
| ~ ( member @ SV36 @ SV9 @ mactual ) )
| ( member @ SV36 @ SV24 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(111,plain,
! [SV25: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ SV25 @ mactual )
| ! [SY412: $i] :
( ~ ( member @ SY412 @ SV10 @ mactual )
| ( member @ SY412 @ SV25 @ mactual ) ) )
| ~ ( ~ ! [SY413: $i] :
( ~ ( member @ SY413 @ SV10 @ mactual )
| ( member @ SY413 @ SV25 @ mactual ) )
| ( subset @ SV10 @ SV25 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(112,plain,
! [SV37: $i,SV26: $i,SV11: $i] :
( ( ~ ( qmltpeq @ SV11 @ SV26 @ mactual )
| ( qmltpeq @ ( union @ SV37 @ SV11 ) @ ( union @ SV37 @ SV26 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(113,plain,
! [SV38: $i,SV27: $i,SV12: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV12 @ SV27 @ mactual )
| ~ ( subset @ SV12 @ SV38 @ mactual ) )
| ( subset @ SV27 @ SV38 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(114,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( ~ ( qmltpeq @ SV13 @ SV28 @ mactual )
| ! [SY416: $i] :
~ ( ~ ( ~ ( member @ SY416 @ SV13 @ mactual )
| ( member @ SY416 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY416 @ SV28 @ mactual )
| ( member @ SY416 @ SV13 @ mactual ) ) ) )
| ~ ( ~ ! [SY417: $i] :
~ ( ~ ( ~ ( member @ SY417 @ SV13 @ mactual )
| ( member @ SY417 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY417 @ SV28 @ mactual )
| ( member @ SY417 @ SV13 @ mactual ) ) )
| ( qmltpeq @ SV13 @ SV28 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(115,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( ~ ( qmltpeq @ SV14 @ SV29 @ mactual )
| ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) )
| ( qmltpeq @ SV14 @ SV29 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(116,plain,
! [SV39: $i,SV30: $i,SV15: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV15 @ SV30 @ mactual )
| ~ ( subset @ SV39 @ SV15 @ mactual ) )
| ( subset @ SV39 @ SV30 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(117,plain,
! [SV16: mworld] :
( ( ~ ( mrel @ SV16 @ ( sK2_SY405 @ SV16 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[103]) ).
thf(118,plain,
! [SV31: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV31 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( union @ SV17 @ SV31 ) @ SV31 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(119,plain,
! [SV32: $i,SV19: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV4 @ SV19 @ mactual )
| ~ ( qmltpeq @ SV19 @ SV32 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV4 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(120,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ~ ( ~ ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
| ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
| ~ ( ~ ( ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
| ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(121,plain,
! [SV34: $i,SV21: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV6 @ SV21 @ mactual )
| ~ ( member @ SV6 @ SV34 @ mactual ) ) )
= $true )
| ( ( member @ SV21 @ SV34 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(122,plain,
! [SV22: $i,SV7: $i] :
( ( ( qmltpeq @ SV7 @ SV22 @ mactual )
= $false )
| ( ( qmltpeq @ SV22 @ SV7 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV35: $i,SV23: $i,SV8: $i] :
( ( ( ~ ( qmltpeq @ SV8 @ SV23 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( union @ SV8 @ SV35 ) @ ( union @ SV23 @ SV35 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV36: $i,SV24: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV24 @ mactual )
| ~ ( member @ SV36 @ SV9 @ mactual ) ) )
= $true )
| ( ( member @ SV36 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV25: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ SV25 @ mactual )
| ! [SY412: $i] :
( ~ ( member @ SY412 @ SV10 @ mactual )
| ( member @ SY412 @ SV25 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(126,plain,
! [SV25: $i,SV10: $i] :
( ( ~ ( ~ ! [SY413: $i] :
( ~ ( member @ SY413 @ SV10 @ mactual )
| ( member @ SY413 @ SV25 @ mactual ) )
| ( subset @ SV10 @ SV25 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(127,plain,
! [SV37: $i,SV26: $i,SV11: $i] :
( ( ( ~ ( qmltpeq @ SV11 @ SV26 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( union @ SV37 @ SV11 ) @ ( union @ SV37 @ SV26 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(128,plain,
! [SV38: $i,SV27: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV12 @ SV27 @ mactual )
| ~ ( subset @ SV12 @ SV38 @ mactual ) ) )
= $true )
| ( ( subset @ SV27 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(129,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( ~ ( qmltpeq @ SV13 @ SV28 @ mactual )
| ! [SY416: $i] :
~ ( ~ ( ~ ( member @ SY416 @ SV13 @ mactual )
| ( member @ SY416 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY416 @ SV28 @ mactual )
| ( member @ SY416 @ SV13 @ mactual ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(130,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( ~ ! [SY417: $i] :
~ ( ~ ( ~ ( member @ SY417 @ SV13 @ mactual )
| ( member @ SY417 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY417 @ SV28 @ mactual )
| ( member @ SY417 @ SV13 @ mactual ) ) )
| ( qmltpeq @ SV13 @ SV28 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(131,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( ~ ( qmltpeq @ SV14 @ SV29 @ mactual )
| ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(132,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) )
| ( qmltpeq @ SV14 @ SV29 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(133,plain,
! [SV39: $i,SV30: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV15 @ SV30 @ mactual )
| ~ ( subset @ SV39 @ SV15 @ mactual ) ) )
= $true )
| ( ( subset @ SV39 @ SV30 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV16: mworld] :
( ( mrel @ SV16 @ ( sK2_SY405 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(135,plain,
! [SV31: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV31 @ mactual )
= $false )
| ( ( qmltpeq @ ( union @ SV17 @ SV31 ) @ SV31 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(136,plain,
! [SV32: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV4 @ SV19 @ mactual )
| ~ ( qmltpeq @ SV19 @ SV32 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV4 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(137,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ~ ( ~ ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
| ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(138,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ~ ( ~ ( ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
| ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(139,plain,
! [SV34: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV6 @ SV21 @ mactual )
| ~ ( member @ SV6 @ SV34 @ mactual ) ) )
= $false )
| ( ( member @ SV21 @ SV34 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(140,plain,
! [SV35: $i,SV23: $i,SV8: $i] :
( ( ( qmltpeq @ SV8 @ SV23 @ mactual )
= $false )
| ( ( qmltpeq @ ( union @ SV8 @ SV35 ) @ ( union @ SV23 @ SV35 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(141,plain,
! [SV36: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV9 @ SV24 @ mactual )
| ~ ( member @ SV36 @ SV9 @ mactual ) ) )
= $false )
| ( ( member @ SV36 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(142,plain,
! [SV25: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV25 @ mactual )
| ! [SY412: $i] :
( ~ ( member @ SY412 @ SV10 @ mactual )
| ( member @ SY412 @ SV25 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(143,plain,
! [SV25: $i,SV10: $i] :
( ( ~ ! [SY413: $i] :
( ~ ( member @ SY413 @ SV10 @ mactual )
| ( member @ SY413 @ SV25 @ mactual ) )
| ( subset @ SV10 @ SV25 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(144,plain,
! [SV37: $i,SV26: $i,SV11: $i] :
( ( ( qmltpeq @ SV11 @ SV26 @ mactual )
= $false )
| ( ( qmltpeq @ ( union @ SV37 @ SV11 ) @ ( union @ SV37 @ SV26 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(145,plain,
! [SV38: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV12 @ SV27 @ mactual )
| ~ ( subset @ SV12 @ SV38 @ mactual ) ) )
= $false )
| ( ( subset @ SV27 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(146,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( qmltpeq @ SV13 @ SV28 @ mactual )
| ! [SY416: $i] :
~ ( ~ ( ~ ( member @ SY416 @ SV13 @ mactual )
| ( member @ SY416 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY416 @ SV28 @ mactual )
| ( member @ SY416 @ SV13 @ mactual ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(147,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ! [SY417: $i] :
~ ( ~ ( ~ ( member @ SY417 @ SV13 @ mactual )
| ( member @ SY417 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY417 @ SV28 @ mactual )
| ( member @ SY417 @ SV13 @ mactual ) ) )
| ( qmltpeq @ SV13 @ SV28 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(148,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( qmltpeq @ SV14 @ SV29 @ mactual )
| ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(149,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) )
| ( qmltpeq @ SV14 @ SV29 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(150,plain,
! [SV39: $i,SV30: $i,SV15: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV15 @ SV30 @ mactual )
| ~ ( subset @ SV39 @ SV15 @ mactual ) ) )
= $false )
| ( ( subset @ SV39 @ SV30 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(151,plain,
! [SV32: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( qmltpeq @ SV4 @ SV19 @ mactual )
| ~ ( qmltpeq @ SV19 @ SV32 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV4 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(152,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ~ ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
| ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(153,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ~ ( ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
| ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(154,plain,
! [SV34: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV21 @ mactual )
| ~ ( member @ SV6 @ SV34 @ mactual ) )
= $true )
| ( ( member @ SV21 @ SV34 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(155,plain,
! [SV36: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV24 @ mactual )
| ~ ( member @ SV36 @ SV9 @ mactual ) )
= $true )
| ( ( member @ SV36 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(156,plain,
! [SV25: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV25 @ mactual ) )
= $true )
| ( ( ! [SY412: $i] :
( ~ ( member @ SY412 @ SV10 @ mactual )
| ( member @ SY412 @ SV25 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(157,plain,
! [SV25: $i,SV10: $i] :
( ( ( ~ ! [SY413: $i] :
( ~ ( member @ SY413 @ SV10 @ mactual )
| ( member @ SY413 @ SV25 @ mactual ) ) )
= $true )
| ( ( subset @ SV10 @ SV25 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV38: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( qmltpeq @ SV12 @ SV27 @ mactual )
| ~ ( subset @ SV12 @ SV38 @ mactual ) )
= $true )
| ( ( subset @ SV27 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(159,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( qmltpeq @ SV13 @ SV28 @ mactual ) )
= $true )
| ( ( ! [SY416: $i] :
~ ( ~ ( ~ ( member @ SY416 @ SV13 @ mactual )
| ( member @ SY416 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY416 @ SV28 @ mactual )
| ( member @ SY416 @ SV13 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ! [SY417: $i] :
~ ( ~ ( ~ ( member @ SY417 @ SV13 @ mactual )
| ( member @ SY417 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY417 @ SV28 @ mactual )
| ( member @ SY417 @ SV13 @ mactual ) ) ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( qmltpeq @ SV14 @ SV29 @ mactual ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV39: $i,SV30: $i,SV15: $i] :
( ( ( ~ ( qmltpeq @ SV15 @ SV30 @ mactual )
| ~ ( subset @ SV39 @ SV15 @ mactual ) )
= $true )
| ( ( subset @ SV39 @ SV30 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(164,plain,
! [SV32: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( qmltpeq @ SV4 @ SV19 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV19 @ SV32 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV4 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual ) )
= $true )
| ( ( ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ( ~ ( ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) ) )
= $true )
| ( ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV34: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV21 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV6 @ SV34 @ mactual ) )
= $true )
| ( ( member @ SV21 @ SV34 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV36: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV24 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV36 @ SV9 @ mactual ) )
= $true )
| ( ( member @ SV36 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV25: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV25 @ mactual )
= $false )
| ( ( ! [SY412: $i] :
( ~ ( member @ SY412 @ SV10 @ mactual )
| ( member @ SY412 @ SV25 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(170,plain,
! [SV25: $i,SV10: $i] :
( ( ( ! [SY413: $i] :
( ~ ( member @ SY413 @ SV10 @ mactual )
| ( member @ SY413 @ SV25 @ mactual ) ) )
= $false )
| ( ( subset @ SV10 @ SV25 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV38: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( qmltpeq @ SV12 @ SV27 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV12 @ SV38 @ mactual ) )
= $true )
| ( ( subset @ SV27 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV28: $i,SV13: $i] :
( ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false )
| ( ( ! [SY416: $i] :
~ ( ~ ( ~ ( member @ SY416 @ SV13 @ mactual )
| ( member @ SY416 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY416 @ SV28 @ mactual )
| ( member @ SY416 @ SV13 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(173,plain,
! [SV28: $i,SV13: $i] :
( ( ( ! [SY417: $i] :
~ ( ~ ( ~ ( member @ SY417 @ SV13 @ mactual )
| ( member @ SY417 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SY417 @ SV28 @ mactual )
| ( member @ SY417 @ SV13 @ mactual ) ) ) )
= $false )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV29: $i,SV14: $i] :
( ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $false )
| ( ( ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(176,plain,
! [SV39: $i,SV30: $i,SV15: $i] :
( ( ( ~ ( qmltpeq @ SV15 @ SV30 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV39 @ SV15 @ mactual ) )
= $true )
| ( ( subset @ SV39 @ SV30 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(177,plain,
! [SV32: $i,SV19: $i,SV4: $i] :
( ( ( qmltpeq @ SV4 @ SV19 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV19 @ SV32 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV4 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(178,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
= $false )
| ( ( ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(179,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ( ( member @ SV33 @ SV5 @ mactual )
| ( member @ SV33 @ SV20 @ mactual ) )
= $false )
| ( ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(180,plain,
! [SV34: $i,SV21: $i,SV6: $i] :
( ( ( qmltpeq @ SV6 @ SV21 @ mactual )
= $false )
| ( ( ~ ( member @ SV6 @ SV34 @ mactual ) )
= $true )
| ( ( member @ SV21 @ SV34 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(181,plain,
! [SV36: $i,SV24: $i,SV9: $i] :
( ( ( qmltpeq @ SV9 @ SV24 @ mactual )
= $false )
| ( ( ~ ( member @ SV36 @ SV9 @ mactual ) )
= $true )
| ( ( member @ SV36 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(182,plain,
! [SV25: $i,SV10: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ SV10 @ mactual )
| ( member @ SV40 @ SV25 @ mactual ) )
= $true )
| ( ( subset @ SV10 @ SV25 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(183,plain,
! [SV10: $i,SV25: $i] :
( ( ( ~ ( member @ ( sK3_SY413 @ SV25 @ SV10 ) @ SV10 @ mactual )
| ( member @ ( sK3_SY413 @ SV25 @ SV10 ) @ SV25 @ mactual ) )
= $false )
| ( ( subset @ SV10 @ SV25 @ mactual )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[170]) ).
thf(184,plain,
! [SV38: $i,SV27: $i,SV12: $i] :
( ( ( qmltpeq @ SV12 @ SV27 @ mactual )
= $false )
| ( ( ~ ( subset @ SV12 @ SV38 @ mactual ) )
= $true )
| ( ( subset @ SV27 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(185,plain,
! [SV28: $i,SV13: $i,SV41: $i] :
( ( ( ~ ( ~ ( ~ ( member @ SV41 @ SV13 @ mactual )
| ( member @ SV41 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SV41 @ SV28 @ mactual )
| ( member @ SV41 @ SV13 @ mactual ) ) ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(186,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual ) )
| ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) ) ) )
= $false )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[173]) ).
thf(187,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) )
= $false )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(188,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV29 @ mactual )
| ~ ( subset @ SV29 @ SV14 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(189,plain,
! [SV39: $i,SV30: $i,SV15: $i] :
( ( ( qmltpeq @ SV15 @ SV30 @ mactual )
= $false )
| ( ( ~ ( subset @ SV39 @ SV15 @ mactual ) )
= $true )
| ( ( subset @ SV39 @ SV30 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV4: $i,SV32: $i,SV19: $i] :
( ( ( qmltpeq @ SV19 @ SV32 @ mactual )
= $false )
| ( ( qmltpeq @ SV4 @ SV19 @ mactual )
= $false )
| ( ( qmltpeq @ SV4 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(191,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ( member @ SV33 @ SV5 @ mactual )
= $true )
| ( ( member @ SV33 @ SV20 @ mactual )
= $true )
| ( ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(192,plain,
! [SV20: $i,SV5: $i,SV33: $i] :
( ( ( member @ SV33 @ SV5 @ mactual )
= $false )
| ( ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(193,plain,
! [SV5: $i,SV20: $i,SV33: $i] :
( ( ( member @ SV33 @ SV20 @ mactual )
= $false )
| ( ( member @ SV33 @ ( union @ SV5 @ SV20 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(194,plain,
! [SV21: $i,SV34: $i,SV6: $i] :
( ( ( member @ SV6 @ SV34 @ mactual )
= $false )
| ( ( qmltpeq @ SV6 @ SV21 @ mactual )
= $false )
| ( ( member @ SV21 @ SV34 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(195,plain,
! [SV24: $i,SV9: $i,SV36: $i] :
( ( ( member @ SV36 @ SV9 @ mactual )
= $false )
| ( ( qmltpeq @ SV9 @ SV24 @ mactual )
= $false )
| ( ( member @ SV36 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(196,plain,
! [SV25: $i,SV10: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ SV10 @ mactual ) )
= $true )
| ( ( member @ SV40 @ SV25 @ mactual )
= $true )
| ( ( subset @ SV10 @ SV25 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(197,plain,
! [SV10: $i,SV25: $i] :
( ( ( ~ ( member @ ( sK3_SY413 @ SV25 @ SV10 ) @ SV10 @ mactual ) )
= $false )
| ( ( subset @ SV10 @ SV25 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(198,plain,
! [SV10: $i,SV25: $i] :
( ( ( member @ ( sK3_SY413 @ SV25 @ SV10 ) @ SV25 @ mactual )
= $false )
| ( ( subset @ SV10 @ SV25 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(199,plain,
! [SV27: $i,SV38: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV38 @ mactual )
= $false )
| ( ( qmltpeq @ SV12 @ SV27 @ mactual )
= $false )
| ( ( subset @ SV27 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(200,plain,
! [SV28: $i,SV13: $i,SV41: $i] :
( ( ( ~ ( ~ ( member @ SV41 @ SV13 @ mactual )
| ( member @ SV41 @ SV28 @ mactual ) )
| ~ ( ~ ( member @ SV41 @ SV28 @ mactual )
| ( member @ SV41 @ SV13 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(201,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual ) )
| ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(202,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV29 @ mactual ) )
= $false )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(203,plain,
! [SV14: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV14 @ mactual ) )
= $false )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(204,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV29 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV29 @ SV14 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(205,plain,
! [SV30: $i,SV15: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV15 @ mactual )
= $false )
| ( ( qmltpeq @ SV15 @ SV30 @ mactual )
= $false )
| ( ( subset @ SV39 @ SV30 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(206,plain,
! [SV25: $i,SV10: $i,SV40: $i] :
( ( ( member @ SV40 @ SV10 @ mactual )
= $false )
| ( ( member @ SV40 @ SV25 @ mactual )
= $true )
| ( ( subset @ SV10 @ SV25 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(207,plain,
! [SV10: $i,SV25: $i] :
( ( ( member @ ( sK3_SY413 @ SV25 @ SV10 ) @ SV10 @ mactual )
= $true )
| ( ( subset @ SV10 @ SV25 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(208,plain,
! [SV28: $i,SV13: $i,SV41: $i] :
( ( ( ~ ( ~ ( member @ SV41 @ SV13 @ mactual )
| ( member @ SV41 @ SV28 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(209,plain,
! [SV13: $i,SV28: $i,SV41: $i] :
( ( ( ~ ( ~ ( member @ SV41 @ SV28 @ mactual )
| ( member @ SV41 @ SV13 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(210,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(211,plain,
! [SV29: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV29 @ mactual )
= $true )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(212,plain,
! [SV14: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV14 @ mactual )
= $true )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(213,plain,
! [SV29: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV29 @ mactual )
= $false )
| ( ( ~ ( subset @ SV29 @ SV14 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(214,plain,
! [SV28: $i,SV13: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ SV13 @ mactual )
| ( member @ SV41 @ SV28 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(215,plain,
! [SV13: $i,SV28: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ SV28 @ mactual )
| ( member @ SV41 @ SV13 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(216,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(217,plain,
! [SV14: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV14 @ mactual )
= $false )
| ( ( subset @ SV14 @ SV29 @ mactual )
= $false )
| ( ( qmltpeq @ SV14 @ SV29 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(218,plain,
! [SV28: $i,SV13: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ SV13 @ mactual ) )
= $true )
| ( ( member @ SV41 @ SV28 @ mactual )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(219,plain,
! [SV13: $i,SV28: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ SV28 @ mactual ) )
= $true )
| ( ( member @ SV41 @ SV13 @ mactual )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(220,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(221,plain,
! [SV13: $i,SV28: $i] :
( ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(222,plain,
! [SV28: $i,SV13: $i,SV41: $i] :
( ( ( member @ SV41 @ SV13 @ mactual )
= $false )
| ( ( member @ SV41 @ SV28 @ mactual )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(223,plain,
! [SV13: $i,SV28: $i,SV41: $i] :
( ( ( member @ SV41 @ SV28 @ mactual )
= $false )
| ( ( member @ SV41 @ SV13 @ mactual )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(224,plain,
! [SV13: $i,SV28: $i] :
( ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
= $true )
| ( ( ~ ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(225,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) )
= $false )
| ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
= $false )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(226,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
| ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual ) )
= $false )
| ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(227,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual ) )
= $false )
| ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
= $false )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(228,plain,
! [SV13: $i,SV28: $i] :
( ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
= $false )
| ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
= $false )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(229,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual ) )
= $false )
| ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(230,plain,
! [SV13: $i,SV28: $i] :
( ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
= $false )
| ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(231,plain,
! [SV13: $i,SV28: $i] :
( ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
= $true )
| ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
= $false )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(232,plain,
! [SV13: $i,SV28: $i] :
( ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV28 @ mactual )
= $true )
| ( ( member @ ( sK4_SY417 @ SV28 @ SV13 ) @ SV13 @ mactual )
= $true )
| ( ( qmltpeq @ SV13 @ SV28 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(233,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[72,232,231,230,228,223,222,217,212,211,207,206,205,199,198,195,194,193,192,191,190,144,140,135,134,122,90,75,74]) ).
thf(234,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002^3 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n004.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 14:25:54 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.24
% 0.09/0.24 No.of.Axioms: 17
% 0.09/0.24
% 0.09/0.24 Length.of.Defs: 1614
% 0.09/0.24
% 0.09/0.24 Contains.Choice.Funs: false
% 0.09/0.24 ............
% 0.09/0.24
% 0.09/0.24 ********************************
% 0.09/0.24 * All subproblems solved! *
% 0.09/0.24 ********************************
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,ps:3,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:233,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.24
% 0.09/0.24 %**** Beginning of derivation protocol ****
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24
% 0.09/0.24 %**** End of derivation protocol ****
% 0.09/0.24 %**** no. of clauses in derivation: 234 ****
% 0.09/0.24 %**** clause counter: 233 ****
% 0.09/0.24
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,ps:3,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:233,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------