%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET579^3 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 10:40:23 AM UTC 2026
% Result : Theorem 31.98s 5.68s
% Output : CNFRefutation 31.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of formulae : 221 ( 143 unt; 0 typ; 10 def)
% Number of atoms : 1291 ( 294 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 2927 ( 378 ~; 333 |; 30 &;2162 @)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 595 ( 64 ^; 529 !; 2 ?; 595 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_difference,type,
difference: $i > $i > $i ).
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_SY40,type,
sK1_SY40: $i ).
thf(tp_sK2_SY361,type,
sK2_SY361: $i ).
thf(tp_sK3_SY364,type,
sK3_SY364: $i ).
thf(tp_sK4_SY80,type,
sK4_SY80: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > mworld > $o ).
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] : ( 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] : ( 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
@ ( mforall_di
@ ^ [B: $i] : ( subset @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(2,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/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(3,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ D @ ( difference @ B @ C ) ) @ ( mand @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_2) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_1) ).
thf(11,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(12,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(13,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(15,conjecture,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] :
( mimplies
@ ( mforall_di
@ ^ [E: $i] : ( mequiv @ ( member @ E @ B ) @ ( mand @ ( member @ E @ C ) @ ( mnot @ ( member @ E @ D ) ) ) ) )
@ ( qmltpeq @ B @ ( difference @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th20) ).
thf(16,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] :
( mimplies
@ ( mforall_di
@ ^ [E: $i] : ( mequiv @ ( member @ E @ B ) @ ( mand @ ( member @ E @ C ) @ ( mnot @ ( member @ E @ D ) ) ) ) )
@ ( qmltpeq @ B @ ( difference @ C @ D ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[15]) ).
thf(17,plain,
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ! [SY43: $i] :
( ( member @ SY43 @ SY40 @ mactual )
<=> ( ( member @ SY43 @ SY41 @ mactual )
& ~ ( member @ SY43 @ SY42 @ mactual ) ) )
=> ( qmltpeq @ SY40 @ ( difference @ SY41 @ SY42 ) @ mactual ) ) )
= $false ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(18,plain,
( ( ! [SY51: $i] : ( subset @ SY51 @ SY51 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(19,plain,
( ( ! [SY78: $i,SY79: $i] :
( ( subset @ SY78 @ SY79 @ mactual )
<=> ! [SY80: $i] :
( ( member @ SY80 @ SY78 @ mactual )
=> ( member @ SY80 @ SY79 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(20,plain,
( ( ! [SY100: $i,SY101: $i] :
( ( qmltpeq @ SY100 @ SY101 @ mactual )
<=> ( ( subset @ SY100 @ SY101 @ mactual )
& ( subset @ SY101 @ SY100 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(21,plain,
( ( ! [SY129: $i,SY130: $i,SY131: $i] :
( ( member @ SY131 @ ( difference @ SY129 @ SY130 ) @ mactual )
<=> ( ( member @ SY131 @ SY129 @ mactual )
& ~ ( member @ SY131 @ SY130 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(22,plain,
( ( ! [SY159: $i,SY160: $i,SY161: $i] :
( ( ( qmltpeq @ SY159 @ SY160 @ mactual )
& ( subset @ SY161 @ SY159 @ mactual ) )
=> ( subset @ SY161 @ SY160 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(23,plain,
( ( ! [SY189: $i,SY190: $i,SY191: $i] :
( ( ( qmltpeq @ SY189 @ SY190 @ mactual )
& ( subset @ SY189 @ SY191 @ mactual ) )
=> ( subset @ SY190 @ SY191 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(24,plain,
( ( ! [SY219: $i,SY220: $i,SY221: $i] :
( ( ( qmltpeq @ SY219 @ SY220 @ mactual )
& ( member @ SY221 @ SY219 @ mactual ) )
=> ( member @ SY221 @ SY220 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(25,plain,
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ( ( qmltpeq @ SY249 @ SY250 @ mactual )
& ( member @ SY249 @ SY251 @ mactual ) )
=> ( member @ SY250 @ SY251 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(26,plain,
( ( ! [SY276: $i,SY277: $i,SY278: $i] :
( ( qmltpeq @ SY276 @ SY277 @ mactual )
=> ( qmltpeq @ ( difference @ SY278 @ SY276 ) @ ( difference @ SY278 @ SY277 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(27,plain,
( ( ! [SY303: $i,SY304: $i,SY305: $i] :
( ( qmltpeq @ SY303 @ SY304 @ mactual )
=> ( qmltpeq @ ( difference @ SY303 @ SY305 ) @ ( difference @ SY304 @ SY305 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(28,plain,
( ( ! [SY333: $i,SY334: $i,SY335: $i] :
( ( ( qmltpeq @ SY333 @ SY334 @ mactual )
& ( qmltpeq @ SY334 @ SY335 @ mactual ) )
=> ( qmltpeq @ SY333 @ SY335 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(29,plain,
( ( ! [SY352: $i,SY353: $i] :
( ( qmltpeq @ SY352 @ SY353 @ mactual )
=> ( qmltpeq @ SY353 @ SY352 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(30,plain,
( ( ! [SY359: $i] : ( qmltpeq @ SY359 @ SY359 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(31,plain,
( ( ! [SY361: $i,SY362: $i] :
( ! [SY363: $i] :
( ( member @ SY363 @ sK1_SY40 @ mactual )
<=> ( ( member @ SY363 @ SY361 @ mactual )
& ~ ( member @ SY363 @ SY362 @ mactual ) ) )
=> ( qmltpeq @ sK1_SY40 @ ( difference @ SY361 @ SY362 ) @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(32,plain,
( ( ! [SY364: $i] :
( ! [SY365: $i] :
( ( member @ SY365 @ sK1_SY40 @ mactual )
<=> ( ( member @ SY365 @ sK2_SY361 @ mactual )
& ~ ( member @ SY365 @ SY364 @ mactual ) ) )
=> ( qmltpeq @ sK1_SY40 @ ( difference @ sK2_SY361 @ SY364 ) @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(33,plain,
( ( ! [SY366: $i] :
( ( member @ SY366 @ sK1_SY40 @ mactual )
<=> ( ( member @ SY366 @ sK2_SY361 @ mactual )
& ~ ( member @ SY366 @ sK3_SY364 @ mactual ) ) )
=> ( qmltpeq @ sK1_SY40 @ ( difference @ sK2_SY361 @ sK3_SY364 ) @ mactual ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(34,plain,
( ( ! [SY366: $i] :
( ( member @ SY366 @ sK1_SY40 @ mactual )
<=> ( ( member @ SY366 @ sK2_SY361 @ mactual )
& ~ ( member @ SY366 @ sK3_SY364 @ mactual ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[33]) ).
thf(35,plain,
( ( qmltpeq @ sK1_SY40 @ ( difference @ sK2_SY361 @ sK3_SY364 ) @ mactual )
= $false ),
inference(standard_cnf,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ( qmltpeq @ sK1_SY40 @ ( difference @ sK2_SY361 @ sK3_SY364 ) @ mactual ) )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [SY366: $i] :
( ~ ( member @ SY366 @ sK2_SY361 @ mactual )
| ( member @ SY366 @ sK3_SY364 @ mactual )
| ( member @ SY366 @ sK1_SY40 @ mactual ) )
& ! [SY366: $i] :
( ~ ( member @ SY366 @ sK1_SY40 @ mactual )
| ( member @ SY366 @ sK2_SY361 @ mactual ) )
& ! [SY366: $i] :
( ~ ( member @ SY366 @ sK1_SY40 @ mactual )
| ~ ( member @ SY366 @ sK3_SY364 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(38,plain,
( ( ! [SY78: $i,SY79: $i] :
( ( ( member @ ( sK4_SY80 @ SY79 @ SY78 ) @ SY78 @ mactual )
& ~ ( member @ ( sK4_SY80 @ SY79 @ SY78 ) @ SY79 @ mactual ) )
| ( subset @ SY78 @ SY79 @ mactual ) )
& ! [SY78: $i,SY79: $i] :
( ~ ( subset @ SY78 @ SY79 @ mactual )
| ! [SY80: $i] :
( ~ ( member @ SY80 @ SY78 @ mactual )
| ( member @ SY80 @ SY79 @ mactual ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(39,plain,
( ( ! [SY100: $i,SY101: $i] :
( ~ ( subset @ SY100 @ SY101 @ mactual )
| ~ ( subset @ SY101 @ SY100 @ mactual )
| ( qmltpeq @ SY100 @ SY101 @ mactual ) )
& ! [SY100: $i,SY101: $i] :
( ~ ( qmltpeq @ SY100 @ SY101 @ mactual )
| ( subset @ SY100 @ SY101 @ mactual ) )
& ! [SY100: $i,SY101: $i] :
( ~ ( qmltpeq @ SY100 @ SY101 @ mactual )
| ( subset @ SY101 @ SY100 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(40,plain,
( ( ! [SY129: $i] :
( ! [SY130: $i,SY131: $i] :
( ~ ( member @ SY131 @ SY129 @ mactual )
| ( member @ SY131 @ SY130 @ mactual )
| ( member @ SY131 @ ( difference @ SY129 @ SY130 ) @ mactual ) )
& ! [SY130: $i,SY131: $i] :
( ~ ( member @ SY131 @ ( difference @ SY129 @ SY130 ) @ mactual )
| ( member @ SY131 @ SY129 @ mactual ) )
& ! [SY130: $i,SY131: $i] :
( ~ ( member @ SY131 @ ( difference @ SY129 @ SY130 ) @ mactual )
| ~ ( member @ SY131 @ SY130 @ mactual ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(41,plain,
( ( ! [SY159: $i,SY160: $i,SY161: $i] :
( ~ ( qmltpeq @ SY159 @ SY160 @ mactual )
| ~ ( subset @ SY161 @ SY159 @ mactual )
| ( subset @ SY161 @ SY160 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(42,plain,
( ( ! [SY189: $i,SY190: $i,SY191: $i] :
( ~ ( qmltpeq @ SY189 @ SY190 @ mactual )
| ~ ( subset @ SY189 @ SY191 @ mactual )
| ( subset @ SY190 @ SY191 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(43,plain,
( ( ! [SY219: $i,SY220: $i,SY221: $i] :
( ~ ( member @ SY221 @ SY219 @ mactual )
| ~ ( qmltpeq @ SY219 @ SY220 @ mactual )
| ( member @ SY221 @ SY220 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(44,plain,
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ~ ( member @ SY249 @ SY251 @ mactual )
| ~ ( qmltpeq @ SY249 @ SY250 @ mactual )
| ( member @ SY250 @ SY251 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(45,plain,
( ( ! [SY276: $i,SY277: $i] :
( ~ ( qmltpeq @ SY276 @ SY277 @ mactual )
| ! [SY278: $i] : ( qmltpeq @ ( difference @ SY278 @ SY276 ) @ ( difference @ SY278 @ SY277 ) @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(46,plain,
( ( ! [SY303: $i,SY304: $i] :
( ~ ( qmltpeq @ SY303 @ SY304 @ mactual )
| ! [SY305: $i] : ( qmltpeq @ ( difference @ SY303 @ SY305 ) @ ( difference @ SY304 @ SY305 ) @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(47,plain,
( ( ! [SY333: $i,SY334: $i,SY335: $i] :
( ~ ( qmltpeq @ SY333 @ SY334 @ mactual )
| ~ ( qmltpeq @ SY334 @ SY335 @ mactual )
| ( qmltpeq @ SY333 @ SY335 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(48,plain,
( ( ! [SY352: $i,SY353: $i] :
( ~ ( qmltpeq @ SY352 @ SY353 @ mactual )
| ( qmltpeq @ SY353 @ SY352 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(49,plain,
( ( ! [SY359: $i] : ( qmltpeq @ SY359 @ SY359 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(50,plain,
( ( ! [SY352: $i,SY353: $i] :
( ~ ( qmltpeq @ SY352 @ SY353 @ mactual )
| ( qmltpeq @ SY353 @ SY352 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(51,plain,
( ( ! [SY333: $i,SY334: $i,SY335: $i] :
( ~ ( qmltpeq @ SY333 @ SY334 @ mactual )
| ~ ( qmltpeq @ SY334 @ SY335 @ mactual )
| ( qmltpeq @ SY333 @ SY335 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(52,plain,
( ( ! [SY303: $i,SY304: $i] :
( ~ ( qmltpeq @ SY303 @ SY304 @ mactual )
| ! [SY305: $i] : ( qmltpeq @ ( difference @ SY303 @ SY305 ) @ ( difference @ SY304 @ SY305 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(53,plain,
( ( ! [SY276: $i,SY277: $i] :
( ~ ( qmltpeq @ SY276 @ SY277 @ mactual )
| ! [SY278: $i] : ( qmltpeq @ ( difference @ SY278 @ SY276 ) @ ( difference @ SY278 @ SY277 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(54,plain,
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ~ ( member @ SY249 @ SY251 @ mactual )
| ~ ( qmltpeq @ SY249 @ SY250 @ mactual )
| ( member @ SY250 @ SY251 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(55,plain,
( ( ! [SY219: $i,SY220: $i,SY221: $i] :
( ~ ( member @ SY221 @ SY219 @ mactual )
| ~ ( qmltpeq @ SY219 @ SY220 @ mactual )
| ( member @ SY221 @ SY220 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(56,plain,
( ( ! [SY189: $i,SY190: $i,SY191: $i] :
( ~ ( qmltpeq @ SY189 @ SY190 @ mactual )
| ~ ( subset @ SY189 @ SY191 @ mactual )
| ( subset @ SY190 @ SY191 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(57,plain,
( ( ! [SY159: $i,SY160: $i,SY161: $i] :
( ~ ( qmltpeq @ SY159 @ SY160 @ mactual )
| ~ ( subset @ SY161 @ SY159 @ mactual )
| ( subset @ SY161 @ SY160 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(58,plain,
( ( ! [SY129: $i] :
( ! [SY130: $i,SY131: $i] :
( ~ ( member @ SY131 @ SY129 @ mactual )
| ( member @ SY131 @ SY130 @ mactual )
| ( member @ SY131 @ ( difference @ SY129 @ SY130 ) @ mactual ) )
& ! [SY130: $i,SY131: $i] :
( ~ ( member @ SY131 @ ( difference @ SY129 @ SY130 ) @ mactual )
| ( member @ SY131 @ SY129 @ mactual ) )
& ! [SY130: $i,SY131: $i] :
( ~ ( member @ SY131 @ ( difference @ SY129 @ SY130 ) @ mactual )
| ~ ( member @ SY131 @ SY130 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(59,plain,
( ( ! [SY100: $i,SY101: $i] :
( ~ ( subset @ SY100 @ SY101 @ mactual )
| ~ ( subset @ SY101 @ SY100 @ mactual )
| ( qmltpeq @ SY100 @ SY101 @ mactual ) )
& ! [SY100: $i,SY101: $i] :
( ~ ( qmltpeq @ SY100 @ SY101 @ mactual )
| ( subset @ SY100 @ SY101 @ mactual ) )
& ! [SY100: $i,SY101: $i] :
( ~ ( qmltpeq @ SY100 @ SY101 @ mactual )
| ( subset @ SY101 @ SY100 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(60,plain,
( ( ! [SY78: $i,SY79: $i] :
( ( ( member @ ( sK4_SY80 @ SY79 @ SY78 ) @ SY78 @ mactual )
& ~ ( member @ ( sK4_SY80 @ SY79 @ SY78 ) @ SY79 @ mactual ) )
| ( subset @ SY78 @ SY79 @ mactual ) )
& ! [SY78: $i,SY79: $i] :
( ~ ( subset @ SY78 @ SY79 @ mactual )
| ! [SY80: $i] :
( ~ ( member @ SY80 @ SY78 @ mactual )
| ( member @ SY80 @ SY79 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(61,plain,
( ( ! [SY51: $i] : ( subset @ SY51 @ SY51 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(62,plain,
( ( ! [SY366: $i] :
( ~ ( member @ SY366 @ sK2_SY361 @ mactual )
| ( member @ SY366 @ sK3_SY364 @ mactual )
| ( member @ SY366 @ sK1_SY40 @ mactual ) )
& ! [SY366: $i] :
( ~ ( member @ SY366 @ sK1_SY40 @ mactual )
| ( member @ SY366 @ sK2_SY361 @ mactual ) )
& ! [SY366: $i] :
( ~ ( member @ SY366 @ sK1_SY40 @ mactual )
| ~ ( member @ SY366 @ sK3_SY364 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(63,plain,
( ( ~ ( qmltpeq @ sK1_SY40 @ ( difference @ sK2_SY361 @ sK3_SY364 ) @ mactual ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(64,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual )
| ( member @ SX2 @ ( difference @ SX0 @ SX1 ) @ mactual ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) @ mactual )
| ( member @ SX2 @ SX0 @ mactual ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) @ mactual )
| ~ ( member @ SX2 @ SX1 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(65,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual )
| ( qmltpeq @ SX0 @ SX1 @ mactual ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX1 @ SX0 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(66,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_SY80 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ~ ( member @ ( sK4_SY80 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ( subset @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(67,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK2_SY361 @ mactual )
| ( member @ SX0 @ sK3_SY364 @ mactual )
| ( member @ SX0 @ sK1_SY40 @ mactual ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ( member @ SX0 @ sK2_SY361 @ mactual ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ~ ( member @ SX0 @ sK3_SY364 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(68,plain,
! [SV1: $i] :
( ( qmltpeq @ SV1 @ SV1 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(69,plain,
! [SV2: $i] :
( ( ! [SY367: $i] :
( ~ ( qmltpeq @ SV2 @ SY367 @ mactual )
| ( qmltpeq @ SY367 @ SV2 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(70,plain,
! [SV3: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ~ ( qmltpeq @ SV3 @ SY368 @ mactual )
| ~ ( qmltpeq @ SY368 @ SY369 @ mactual )
| ( qmltpeq @ SV3 @ SY369 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(71,plain,
! [SV4: $i] :
( ( ! [SY370: $i] :
( ~ ( qmltpeq @ SV4 @ SY370 @ mactual )
| ! [SY371: $i] : ( qmltpeq @ ( difference @ SV4 @ SY371 ) @ ( difference @ SY370 @ SY371 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(72,plain,
! [SV5: $i] :
( ( ! [SY372: $i] :
( ~ ( qmltpeq @ SV5 @ SY372 @ mactual )
| ! [SY373: $i] : ( qmltpeq @ ( difference @ SY373 @ SV5 ) @ ( difference @ SY373 @ SY372 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(73,plain,
! [SV6: $i] :
( ( ! [SY374: $i,SY375: $i] :
( ~ ( member @ SV6 @ SY375 @ mactual )
| ~ ( qmltpeq @ SV6 @ SY374 @ mactual )
| ( member @ SY374 @ SY375 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(74,plain,
! [SV7: $i] :
( ( ! [SY376: $i,SY377: $i] :
( ~ ( member @ SY377 @ SV7 @ mactual )
| ~ ( qmltpeq @ SV7 @ SY376 @ mactual )
| ( member @ SY377 @ SY376 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(75,plain,
! [SV8: $i] :
( ( ! [SY378: $i,SY379: $i] :
( ~ ( qmltpeq @ SV8 @ SY378 @ mactual )
| ~ ( subset @ SV8 @ SY379 @ mactual )
| ( subset @ SY378 @ SY379 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(76,plain,
! [SV9: $i] :
( ( ! [SY380: $i,SY381: $i] :
( ~ ( qmltpeq @ SV9 @ SY380 @ mactual )
| ~ ( subset @ SY381 @ SV9 @ mactual )
| ( subset @ SY381 @ SY380 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(77,plain,
! [SV10: $i] :
( ( subset @ SV10 @ SV10 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
( ( qmltpeq @ sK1_SY40 @ ( difference @ sK2_SY361 @ sK3_SY364 ) @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(79,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ SV11 @ mactual )
| ( member @ SY383 @ SY382 @ mactual )
| ( member @ SY383 @ ( difference @ SV11 @ SY382 ) @ mactual ) )
| ~ ~ ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( difference @ SV11 @ SY384 ) @ mactual )
| ( member @ SY385 @ SV11 @ mactual ) )
| ~ ! [SY386: $i,SY387: $i] :
( ~ ( member @ SY387 @ ( difference @ SV11 @ SY386 ) @ mactual )
| ~ ( member @ SY387 @ SY386 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual )
| ( qmltpeq @ SX0 @ SX1 @ mactual ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX1 @ SX0 @ mactual ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(81,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_SY80 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ~ ( member @ ( sK4_SY80 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ( subset @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(82,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK2_SY361 @ mactual )
| ( member @ SX0 @ sK3_SY364 @ mactual )
| ( member @ SX0 @ sK1_SY40 @ mactual ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ( member @ SX0 @ sK2_SY361 @ mactual ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ~ ( member @ SX0 @ sK3_SY364 @ mactual ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(83,plain,
! [SV12: $i,SV2: $i] :
( ( ~ ( qmltpeq @ SV2 @ SV12 @ mactual )
| ( qmltpeq @ SV12 @ SV2 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(84,plain,
! [SV13: $i,SV3: $i] :
( ( ! [SY388: $i] :
( ~ ( qmltpeq @ SV3 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SY388 @ mactual )
| ( qmltpeq @ SV3 @ SY388 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(85,plain,
! [SV14: $i,SV4: $i] :
( ( ~ ( qmltpeq @ SV4 @ SV14 @ mactual )
| ! [SY389: $i] : ( qmltpeq @ ( difference @ SV4 @ SY389 ) @ ( difference @ SV14 @ SY389 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(86,plain,
! [SV15: $i,SV5: $i] :
( ( ~ ( qmltpeq @ SV5 @ SV15 @ mactual )
| ! [SY390: $i] : ( qmltpeq @ ( difference @ SY390 @ SV5 ) @ ( difference @ SY390 @ SV15 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(87,plain,
! [SV16: $i,SV6: $i] :
( ( ! [SY391: $i] :
( ~ ( member @ SV6 @ SY391 @ mactual )
| ~ ( qmltpeq @ SV6 @ SV16 @ mactual )
| ( member @ SV16 @ SY391 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(88,plain,
! [SV17: $i,SV7: $i] :
( ( ! [SY392: $i] :
( ~ ( member @ SY392 @ SV7 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV17 @ mactual )
| ( member @ SY392 @ SV17 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(89,plain,
! [SV18: $i,SV8: $i] :
( ( ! [SY393: $i] :
( ~ ( qmltpeq @ SV8 @ SV18 @ mactual )
| ~ ( subset @ SV8 @ SY393 @ mactual )
| ( subset @ SV18 @ SY393 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(90,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY394: $i] :
( ~ ( qmltpeq @ SV9 @ SV19 @ mactual )
| ~ ( subset @ SY394 @ SV9 @ mactual )
| ( subset @ SY394 @ SV19 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(91,plain,
! [SV11: $i] :
( ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ SV11 @ mactual )
| ( member @ SY383 @ SY382 @ mactual )
| ( member @ SY383 @ ( difference @ SV11 @ SY382 ) @ mactual ) )
| ~ ~ ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( difference @ SV11 @ SY384 ) @ mactual )
| ( member @ SY385 @ SV11 @ mactual ) )
| ~ ! [SY386: $i,SY387: $i] :
( ~ ( member @ SY387 @ ( difference @ SV11 @ SY386 ) @ mactual )
| ~ ( member @ SY387 @ SY386 @ mactual ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(92,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual )
| ( qmltpeq @ SX0 @ SX1 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(93,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX1 @ SX0 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(94,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_SY80 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ~ ( member @ ( sK4_SY80 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ( subset @ SX0 @ SX1 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(95,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(96,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK2_SY361 @ mactual )
| ( member @ SX0 @ sK3_SY364 @ mactual )
| ( member @ SX0 @ sK1_SY40 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(97,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ( member @ SX0 @ sK2_SY361 @ mactual ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ~ ( member @ SX0 @ sK3_SY364 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(98,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ( qmltpeq @ SV2 @ SV12 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV12 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV20: $i,SV13: $i,SV3: $i] :
( ( ~ ( qmltpeq @ SV3 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SV20 @ mactual )
| ( qmltpeq @ SV3 @ SV20 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV14: $i,SV4: $i] :
( ( ( ~ ( qmltpeq @ SV4 @ SV14 @ mactual ) )
= $true )
| ( ( ! [SY389: $i] : ( qmltpeq @ ( difference @ SV4 @ SY389 ) @ ( difference @ SV14 @ SY389 ) @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( qmltpeq @ SV5 @ SV15 @ mactual ) )
= $true )
| ( ( ! [SY390: $i] : ( qmltpeq @ ( difference @ SY390 @ SV5 ) @ ( difference @ SY390 @ SV15 ) @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV16: $i,SV21: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ SV21 @ mactual )
| ~ ( qmltpeq @ SV6 @ SV16 @ mactual )
| ( member @ SV16 @ SV21 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV17: $i,SV7: $i,SV22: $i] :
( ( ~ ( member @ SV22 @ SV7 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV17 @ mactual )
| ( member @ SV22 @ SV17 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV23: $i,SV18: $i,SV8: $i] :
( ( ~ ( qmltpeq @ SV8 @ SV18 @ mactual )
| ~ ( subset @ SV8 @ SV23 @ mactual )
| ( subset @ SV18 @ SV23 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ~ ( qmltpeq @ SV9 @ SV19 @ mactual )
| ~ ( subset @ SV24 @ SV9 @ mactual )
| ( subset @ SV24 @ SV19 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV11: $i] :
( ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ SV11 @ mactual )
| ( member @ SY383 @ SY382 @ mactual )
| ( member @ SY383 @ ( difference @ SV11 @ SY382 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(107,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( difference @ SV11 @ SY384 ) @ mactual )
| ( member @ SY385 @ SV11 @ mactual ) )
| ~ ! [SY386: $i,SY387: $i] :
( ~ ( member @ SY387 @ ( difference @ SV11 @ SY386 ) @ mactual )
| ~ ( member @ SY387 @ SY386 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual )
| ( qmltpeq @ SX0 @ SX1 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(109,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX1 @ SX0 @ mactual ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_SY80 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ~ ( member @ ( sK4_SY80 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ( subset @ SX0 @ SX1 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(112,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ sK2_SY361 @ mactual )
| ( member @ SX0 @ sK3_SY364 @ mactual )
| ( member @ SX0 @ sK1_SY40 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(113,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ( member @ SX0 @ sK2_SY361 @ mactual ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ~ ( member @ SX0 @ sK3_SY364 @ mactual ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(114,plain,
! [SV12: $i,SV2: $i] :
( ( ( qmltpeq @ SV2 @ SV12 @ mactual )
= $false )
| ( ( qmltpeq @ SV12 @ SV2 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(115,plain,
! [SV20: $i,SV13: $i,SV3: $i] :
( ( ( ~ ( qmltpeq @ SV3 @ SV13 @ mactual )
| ~ ( qmltpeq @ SV13 @ SV20 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(116,plain,
! [SV14: $i,SV4: $i] :
( ( ( qmltpeq @ SV4 @ SV14 @ mactual )
= $false )
| ( ( ! [SY389: $i] : ( qmltpeq @ ( difference @ SV4 @ SY389 ) @ ( difference @ SV14 @ SY389 ) @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(117,plain,
! [SV15: $i,SV5: $i] :
( ( ( qmltpeq @ SV5 @ SV15 @ mactual )
= $false )
| ( ( ! [SY390: $i] : ( qmltpeq @ ( difference @ SY390 @ SV5 ) @ ( difference @ SY390 @ SV15 ) @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(118,plain,
! [SV16: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ SV21 @ mactual )
| ~ ( qmltpeq @ SV6 @ SV16 @ mactual ) )
= $true )
| ( ( member @ SV16 @ SV21 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV17: $i,SV7: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV7 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV17 @ mactual ) )
= $true )
| ( ( member @ SV22 @ SV17 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(120,plain,
! [SV23: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( qmltpeq @ SV8 @ SV18 @ mactual )
| ~ ( subset @ SV8 @ SV23 @ mactual ) )
= $true )
| ( ( subset @ SV18 @ SV23 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV19 @ mactual )
| ~ ( subset @ SV24 @ SV9 @ mactual ) )
= $true )
| ( ( subset @ SV24 @ SV19 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(122,plain,
! [SV11: $i] :
( ( ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ SV11 @ mactual )
| ( member @ SY383 @ SY382 @ mactual )
| ( member @ SY383 @ ( difference @ SV11 @ SY382 ) @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(123,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( difference @ SV11 @ SY384 ) @ mactual )
| ( member @ SY385 @ SV11 @ mactual ) )
| ~ ! [SY386: $i,SY387: $i] :
( ~ ( member @ SY387 @ ( difference @ SV11 @ SY386 ) @ mactual )
| ~ ( member @ SY387 @ SY386 @ mactual ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(124,plain,
! [SV25: $i] :
( ( ! [SY395: $i] :
( ~ ( subset @ SV25 @ SY395 @ mactual )
| ~ ( subset @ SY395 @ SV25 @ mactual )
| ( qmltpeq @ SV25 @ SY395 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(125,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX1 @ SX0 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV26: $i] :
( ( ! [SY396: $i] :
( ~ ( ~ ( member @ ( sK4_SY80 @ SY396 @ SV26 ) @ SV26 @ mactual )
| ~ ~ ( member @ ( sK4_SY80 @ SY396 @ SV26 ) @ SY396 @ mactual ) )
| ( subset @ SV26 @ SY396 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV27: $i] :
( ( ! [SY397: $i] :
( ~ ( subset @ SV27 @ SY397 @ mactual )
| ! [SY398: $i] :
( ~ ( member @ SY398 @ SV27 @ mactual )
| ( member @ SY398 @ SY397 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV28: $i] :
( ( ~ ( member @ SV28 @ sK2_SY361 @ mactual )
| ( member @ SV28 @ sK3_SY364 @ mactual )
| ( member @ SV28 @ sK1_SY40 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(129,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ( member @ SX0 @ sK2_SY361 @ mactual ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ~ ( member @ SX0 @ sK3_SY364 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV20: $i,SV13: $i,SV3: $i] :
( ( ( ~ ( qmltpeq @ SV3 @ SV13 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV13 @ SV20 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(131,plain,
! [SV14: $i,SV29: $i,SV4: $i] :
( ( ( qmltpeq @ ( difference @ SV4 @ SV29 ) @ ( difference @ SV14 @ SV29 ) @ mactual )
= $true )
| ( ( qmltpeq @ SV4 @ SV14 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(132,plain,
! [SV15: $i,SV5: $i,SV30: $i] :
( ( ( qmltpeq @ ( difference @ SV30 @ SV5 ) @ ( difference @ SV30 @ SV15 ) @ mactual )
= $true )
| ( ( qmltpeq @ SV5 @ SV15 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(133,plain,
! [SV16: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ SV21 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV6 @ SV16 @ mactual ) )
= $true )
| ( ( member @ SV16 @ SV21 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(134,plain,
! [SV17: $i,SV7: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV7 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV7 @ SV17 @ mactual ) )
= $true )
| ( ( member @ SV22 @ SV17 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(135,plain,
! [SV23: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( qmltpeq @ SV8 @ SV18 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV8 @ SV23 @ mactual ) )
= $true )
| ( ( subset @ SV18 @ SV23 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(136,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV19 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV24 @ SV9 @ mactual ) )
= $true )
| ( ( subset @ SV24 @ SV19 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(137,plain,
! [SV31: $i,SV11: $i] :
( ( ! [SY399: $i] :
( ~ ( member @ SY399 @ SV11 @ mactual )
| ( member @ SY399 @ SV31 @ mactual )
| ( member @ SY399 @ ( difference @ SV11 @ SV31 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(138,plain,
! [SV11: $i] :
( ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( difference @ SV11 @ SY384 ) @ mactual )
| ( member @ SY385 @ SV11 @ mactual ) )
| ~ ! [SY386: $i,SY387: $i] :
( ~ ( member @ SY387 @ ( difference @ SV11 @ SY386 ) @ mactual )
| ~ ( member @ SY387 @ SY386 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(139,plain,
! [SV32: $i,SV25: $i] :
( ( ~ ( subset @ SV25 @ SV32 @ mactual )
| ~ ( subset @ SV32 @ SV25 @ mactual )
| ( qmltpeq @ SV25 @ SV32 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(140,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX0 @ SX1 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(141,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX1 @ SX0 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(142,plain,
! [SV26: $i,SV33: $i] :
( ( ~ ( ~ ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV26 @ mactual )
| ~ ~ ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV33 @ mactual ) )
| ( subset @ SV26 @ SV33 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV34: $i,SV27: $i] :
( ( ~ ( subset @ SV27 @ SV34 @ mactual )
| ! [SY400: $i] :
( ~ ( member @ SY400 @ SV27 @ mactual )
| ( member @ SY400 @ SV34 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(144,plain,
! [SV28: $i] :
( ( ( ~ ( member @ SV28 @ sK2_SY361 @ mactual )
| ( member @ SV28 @ sK3_SY364 @ mactual ) )
= $true )
| ( ( member @ SV28 @ sK1_SY40 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(145,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ( member @ SX0 @ sK2_SY361 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(146,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ~ ( member @ SX0 @ sK3_SY364 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(147,plain,
! [SV20: $i,SV13: $i,SV3: $i] :
( ( ( qmltpeq @ SV3 @ SV13 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV13 @ SV20 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(148,plain,
! [SV16: $i,SV21: $i,SV6: $i] :
( ( ( member @ SV6 @ SV21 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV6 @ SV16 @ mactual ) )
= $true )
| ( ( member @ SV16 @ SV21 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(149,plain,
! [SV17: $i,SV7: $i,SV22: $i] :
( ( ( member @ SV22 @ SV7 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV7 @ SV17 @ mactual ) )
= $true )
| ( ( member @ SV22 @ SV17 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(150,plain,
! [SV23: $i,SV18: $i,SV8: $i] :
( ( ( qmltpeq @ SV8 @ SV18 @ mactual )
= $false )
| ( ( ~ ( subset @ SV8 @ SV23 @ mactual ) )
= $true )
| ( ( subset @ SV18 @ SV23 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(151,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ( qmltpeq @ SV9 @ SV19 @ mactual )
= $false )
| ( ( ~ ( subset @ SV24 @ SV9 @ mactual ) )
= $true )
| ( ( subset @ SV24 @ SV19 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(152,plain,
! [SV31: $i,SV11: $i,SV35: $i] :
( ( ~ ( member @ SV35 @ SV11 @ mactual )
| ( member @ SV35 @ SV31 @ mactual )
| ( member @ SV35 @ ( difference @ SV11 @ SV31 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(153,plain,
! [SV11: $i] :
( ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( difference @ SV11 @ SY384 ) @ mactual )
| ( member @ SY385 @ SV11 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(154,plain,
! [SV11: $i] :
( ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( member @ SY387 @ ( difference @ SV11 @ SY386 ) @ mactual )
| ~ ( member @ SY387 @ SY386 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(155,plain,
! [SV32: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV32 @ mactual )
| ~ ( subset @ SV32 @ SV25 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(156,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX0 @ SX1 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(157,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( subset @ SX1 @ SX0 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(158,plain,
! [SV26: $i,SV33: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV26 @ mactual )
| ~ ~ ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV33 @ mactual ) ) )
= $true )
| ( ( subset @ SV26 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(159,plain,
! [SV34: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV34 @ mactual ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( member @ SY400 @ SV27 @ mactual )
| ( member @ SY400 @ SV34 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(160,plain,
! [SV28: $i] :
( ( ( ~ ( member @ SV28 @ sK2_SY361 @ mactual ) )
= $true )
| ( ( member @ SV28 @ sK3_SY364 @ mactual )
= $true )
| ( ( member @ SV28 @ sK1_SY40 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(161,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ( member @ SX0 @ sK2_SY361 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(162,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ sK1_SY40 @ mactual )
| ~ ( member @ SX0 @ sK3_SY364 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(163,plain,
! [SV3: $i,SV20: $i,SV13: $i] :
( ( ( qmltpeq @ SV13 @ SV20 @ mactual )
= $false )
| ( ( qmltpeq @ SV3 @ SV13 @ mactual )
= $false )
| ( ( qmltpeq @ SV3 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(164,plain,
! [SV21: $i,SV16: $i,SV6: $i] :
( ( ( qmltpeq @ SV6 @ SV16 @ mactual )
= $false )
| ( ( member @ SV6 @ SV21 @ mactual )
= $false )
| ( ( member @ SV16 @ SV21 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(165,plain,
! [SV22: $i,SV17: $i,SV7: $i] :
( ( ( qmltpeq @ SV7 @ SV17 @ mactual )
= $false )
| ( ( member @ SV22 @ SV7 @ mactual )
= $false )
| ( ( member @ SV22 @ SV17 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(166,plain,
! [SV18: $i,SV23: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV23 @ mactual )
= $false )
| ( ( qmltpeq @ SV8 @ SV18 @ mactual )
= $false )
| ( ( subset @ SV18 @ SV23 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(167,plain,
! [SV19: $i,SV9: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV9 @ mactual )
= $false )
| ( ( qmltpeq @ SV9 @ SV19 @ mactual )
= $false )
| ( ( subset @ SV24 @ SV19 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(168,plain,
! [SV31: $i,SV11: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ SV11 @ mactual )
| ( member @ SV35 @ SV31 @ mactual ) )
= $true )
| ( ( member @ SV35 @ ( difference @ SV11 @ SV31 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(169,plain,
! [SV11: $i] :
( ( ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( difference @ SV11 @ SY384 ) @ mactual )
| ( member @ SY385 @ SV11 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(170,plain,
! [SV11: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ~ ( member @ SY387 @ ( difference @ SV11 @ SY386 ) @ mactual )
| ~ ( member @ SY387 @ SY386 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(171,plain,
! [SV32: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV32 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV32 @ SV25 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(172,plain,
! [SV36: $i] :
( ( ! [SY401: $i] :
( ~ ( qmltpeq @ SV36 @ SY401 @ mactual )
| ( subset @ SV36 @ SY401 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(173,plain,
! [SV37: $i] :
( ( ! [SY402: $i] :
( ~ ( qmltpeq @ SV37 @ SY402 @ mactual )
| ( subset @ SY402 @ SV37 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(174,plain,
! [SV26: $i,SV33: $i] :
( ( ( ~ ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV26 @ mactual )
| ~ ~ ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV33 @ mactual ) )
= $false )
| ( ( subset @ SV26 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(175,plain,
! [SV34: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV34 @ mactual )
= $false )
| ( ( ! [SY400: $i] :
( ~ ( member @ SY400 @ SV27 @ mactual )
| ( member @ SY400 @ SV34 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(176,plain,
! [SV28: $i] :
( ( ( member @ SV28 @ sK2_SY361 @ mactual )
= $false )
| ( ( member @ SV28 @ sK3_SY364 @ mactual )
= $true )
| ( ( member @ SV28 @ sK1_SY40 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(177,plain,
! [SV38: $i] :
( ( ~ ( member @ SV38 @ sK1_SY40 @ mactual )
| ( member @ SV38 @ sK2_SY361 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(178,plain,
! [SV39: $i] :
( ( ~ ( member @ SV39 @ sK1_SY40 @ mactual )
| ~ ( member @ SV39 @ sK3_SY364 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(179,plain,
! [SV31: $i,SV11: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ SV11 @ mactual ) )
= $true )
| ( ( member @ SV35 @ SV31 @ mactual )
= $true )
| ( ( member @ SV35 @ ( difference @ SV11 @ SV31 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(180,plain,
! [SV40: $i,SV11: $i] :
( ( ! [SY403: $i] :
( ~ ( member @ SY403 @ ( difference @ SV11 @ SV40 ) @ mactual )
| ( member @ SY403 @ SV11 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(181,plain,
! [SV41: $i,SV11: $i] :
( ( ! [SY404: $i] :
( ~ ( member @ SY404 @ ( difference @ SV11 @ SV41 ) @ mactual )
| ~ ( member @ SY404 @ SV41 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV32: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV32 @ mactual )
= $false )
| ( ( ~ ( subset @ SV32 @ SV25 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV42: $i,SV36: $i] :
( ( ~ ( qmltpeq @ SV36 @ SV42 @ mactual )
| ( subset @ SV36 @ SV42 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV43: $i,SV37: $i] :
( ( ~ ( qmltpeq @ SV37 @ SV43 @ mactual )
| ( subset @ SV43 @ SV37 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV26: $i,SV33: $i] :
( ( ( ~ ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV26 @ mactual ) )
= $false )
| ( ( subset @ SV26 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(186,plain,
! [SV26: $i,SV33: $i] :
( ( ( ~ ~ ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV33 @ mactual ) )
= $false )
| ( ( subset @ SV26 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(187,plain,
! [SV34: $i,SV27: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ SV27 @ mactual )
| ( member @ SV44 @ SV34 @ mactual ) )
= $true )
| ( ( subset @ SV27 @ SV34 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV38: $i] :
( ( ( ~ ( member @ SV38 @ sK1_SY40 @ mactual ) )
= $true )
| ( ( member @ SV38 @ sK2_SY361 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(189,plain,
! [SV39: $i] :
( ( ( ~ ( member @ SV39 @ sK1_SY40 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV39 @ sK3_SY364 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(190,plain,
! [SV31: $i,SV11: $i,SV35: $i] :
( ( ( member @ SV35 @ SV11 @ mactual )
= $false )
| ( ( member @ SV35 @ SV31 @ mactual )
= $true )
| ( ( member @ SV35 @ ( difference @ SV11 @ SV31 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(191,plain,
! [SV40: $i,SV11: $i,SV45: $i] :
( ( ~ ( member @ SV45 @ ( difference @ SV11 @ SV40 ) @ mactual )
| ( member @ SV45 @ SV11 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(192,plain,
! [SV41: $i,SV11: $i,SV46: $i] :
( ( ~ ( member @ SV46 @ ( difference @ SV11 @ SV41 ) @ mactual )
| ~ ( member @ SV46 @ SV41 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV25: $i,SV32: $i] :
( ( ( subset @ SV32 @ SV25 @ mactual )
= $false )
| ( ( subset @ SV25 @ SV32 @ mactual )
= $false )
| ( ( qmltpeq @ SV25 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV42: $i,SV36: $i] :
( ( ( ~ ( qmltpeq @ SV36 @ SV42 @ mactual ) )
= $true )
| ( ( subset @ SV36 @ SV42 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(195,plain,
! [SV43: $i,SV37: $i] :
( ( ( ~ ( qmltpeq @ SV37 @ SV43 @ mactual ) )
= $true )
| ( ( subset @ SV43 @ SV37 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV26: $i,SV33: $i] :
( ( ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV26 @ mactual )
= $true )
| ( ( subset @ SV26 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(197,plain,
! [SV26: $i,SV33: $i] :
( ( ( ~ ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV33 @ mactual ) )
= $true )
| ( ( subset @ SV26 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(198,plain,
! [SV34: $i,SV27: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ SV27 @ mactual ) )
= $true )
| ( ( member @ SV44 @ SV34 @ mactual )
= $true )
| ( ( subset @ SV27 @ SV34 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV38: $i] :
( ( ( member @ SV38 @ sK1_SY40 @ mactual )
= $false )
| ( ( member @ SV38 @ sK2_SY361 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV39: $i] :
( ( ( member @ SV39 @ sK1_SY40 @ mactual )
= $false )
| ( ( ~ ( member @ SV39 @ sK3_SY364 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV40: $i,SV11: $i,SV45: $i] :
( ( ( ~ ( member @ SV45 @ ( difference @ SV11 @ SV40 ) @ mactual ) )
= $true )
| ( ( member @ SV45 @ SV11 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(202,plain,
! [SV41: $i,SV11: $i,SV46: $i] :
( ( ( ~ ( member @ SV46 @ ( difference @ SV11 @ SV41 ) @ mactual ) )
= $true )
| ( ( ~ ( member @ SV46 @ SV41 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(203,plain,
! [SV42: $i,SV36: $i] :
( ( ( qmltpeq @ SV36 @ SV42 @ mactual )
= $false )
| ( ( subset @ SV36 @ SV42 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(204,plain,
! [SV43: $i,SV37: $i] :
( ( ( qmltpeq @ SV37 @ SV43 @ mactual )
= $false )
| ( ( subset @ SV43 @ SV37 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(205,plain,
! [SV26: $i,SV33: $i] :
( ( ( member @ ( sK4_SY80 @ SV33 @ SV26 ) @ SV33 @ mactual )
= $false )
| ( ( subset @ SV26 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(206,plain,
! [SV34: $i,SV27: $i,SV44: $i] :
( ( ( member @ SV44 @ SV27 @ mactual )
= $false )
| ( ( member @ SV44 @ SV34 @ mactual )
= $true )
| ( ( subset @ SV27 @ SV34 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(207,plain,
! [SV39: $i] :
( ( ( member @ SV39 @ sK3_SY364 @ mactual )
= $false )
| ( ( member @ SV39 @ sK1_SY40 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(208,plain,
! [SV40: $i,SV11: $i,SV45: $i] :
( ( ( member @ SV45 @ ( difference @ SV11 @ SV40 ) @ mactual )
= $false )
| ( ( member @ SV45 @ SV11 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(209,plain,
! [SV41: $i,SV11: $i,SV46: $i] :
( ( ( member @ SV46 @ ( difference @ SV11 @ SV41 ) @ mactual )
= $false )
| ( ( ~ ( member @ SV46 @ SV41 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(210,plain,
! [SV11: $i,SV41: $i,SV46: $i] :
( ( ( member @ SV46 @ SV41 @ mactual )
= $false )
| ( ( member @ SV46 @ ( difference @ SV11 @ SV41 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(211,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,210,208,207,206,205,204,203,199,196,193,190,176,167,166,165,164,163,132,131,114,78,77]) ).
thf(212,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET579^3 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n003.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 14:48:09 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.98/5.68
% 31.98/5.68 No.of.Axioms: 14
% 31.98/5.68
% 31.98/5.68 Length.of.Defs: 1624
% 31.98/5.68
% 31.98/5.68 Contains.Choice.Funs: false
% 31.98/5.68 ...........
% 31.98/5.68
% 31.98/5.68 ********************************
% 31.98/5.68 * All subproblems solved! *
% 31.98/5.68 ********************************
% 31.98/5.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:211,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 31.98/5.68
% 31.98/5.68 %**** Beginning of derivation protocol ****
% 31.98/5.68 % SZS output start CNFRefutation
% See solution above
% 31.98/5.68
% 31.98/5.68 %**** End of derivation protocol ****
% 31.98/5.68 %**** no. of clauses in derivation: 211 ****
% 31.98/5.68 %**** clause counter: 211 ****
% 31.98/5.68
% 31.98/5.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:211,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------