%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET019^4 : 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 : n016.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 10:38:57 AM UTC 2026
% Result : Theorem 0.64s 0.32s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 178 ( 71 unt; 0 typ; 10 def)
% Number of atoms : 1698 ( 407 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 3300 ( 469 ~; 588 |; 23 &;2179 @)
% ( 2 <=>; 39 =>; 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 : 31 ( 28 usr; 6 con; 0-3 aty)
% Number of variables : 409 ( 47 ^; 360 !; 2 ?; 409 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_equal_set,type,
equal_set: $i > $i > mworld > $o ).
thf(tp_intersection,type,
intersection: $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_power_set,type,
power_set: $i > $i ).
thf(tp_product,type,
product: $i > $i ).
thf(tp_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(tp_sK1_SY16,type,
sK1_SY16: $i ).
thf(tp_sK2_SY212,type,
sK2_SY212: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > mworld > $o ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $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] :
( ( eiw_di @ X @ W )
& ( 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] :
( ( eiw_di @ X @ W )
=> ( 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(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set_0) ).
thf(12,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(13,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(16,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set_substitution_2) ).
thf(17,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set_substitution_1) ).
thf(30,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(31,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(32,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(36,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI02) ).
thf(37,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [SY16: $i] :
( ( eiw_di @ SY16 @ mactual )
=> ! [SY17: $i] :
( ( eiw_di @ SY17 @ mactual )
=> ( ( ( subset @ SY16 @ SY17 @ mactual )
& ( subset @ SY17 @ SY16 @ mactual ) )
=> ( equal_set @ SY16 @ SY17 @ mactual ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(39,plain,
( ( ! [SY36: $i] :
( ( eiw_di @ SY36 @ mactual )
=> ! [SY37: $i] :
( ( eiw_di @ SY37 @ mactual )
=> ( ( equal_set @ SY36 @ SY37 @ mactual )
<=> ( ( subset @ SY36 @ SY37 @ mactual )
& ( subset @ SY37 @ SY36 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(40,plain,
( ( ! [SY64: $i] :
( ( eiw_di @ SY64 @ mactual )
=> ! [SY65: $i] :
( ( eiw_di @ SY65 @ mactual )
=> ! [SY66: $i] :
( ( eiw_di @ SY66 @ mactual )
=> ( ( ( qmltpeq @ SY64 @ SY65 @ mactual )
& ( subset @ SY66 @ SY64 @ mactual ) )
=> ( subset @ SY66 @ SY65 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(41,plain,
( ( ! [SY94: $i] :
( ( eiw_di @ SY94 @ mactual )
=> ! [SY95: $i] :
( ( eiw_di @ SY95 @ mactual )
=> ! [SY96: $i] :
( ( eiw_di @ SY96 @ mactual )
=> ( ( ( qmltpeq @ SY94 @ SY95 @ mactual )
& ( subset @ SY94 @ SY96 @ mactual ) )
=> ( subset @ SY95 @ SY96 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(42,plain,
( ( ! [SY124: $i] :
( ( eiw_di @ SY124 @ mactual )
=> ! [SY125: $i] :
( ( eiw_di @ SY125 @ mactual )
=> ! [SY126: $i] :
( ( eiw_di @ SY126 @ mactual )
=> ( ( ( qmltpeq @ SY124 @ SY125 @ mactual )
& ( equal_set @ SY126 @ SY124 @ mactual ) )
=> ( equal_set @ SY126 @ SY125 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(43,plain,
( ( ! [SY154: $i] :
( ( eiw_di @ SY154 @ mactual )
=> ! [SY155: $i] :
( ( eiw_di @ SY155 @ mactual )
=> ! [SY156: $i] :
( ( eiw_di @ SY156 @ mactual )
=> ( ( ( qmltpeq @ SY154 @ SY155 @ mactual )
& ( equal_set @ SY154 @ SY156 @ mactual ) )
=> ( equal_set @ SY155 @ SY156 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(44,plain,
( ( ! [SY184: $i] :
( ( eiw_di @ SY184 @ mactual )
=> ! [SY185: $i] :
( ( eiw_di @ SY185 @ mactual )
=> ! [SY186: $i] :
( ( eiw_di @ SY186 @ mactual )
=> ( ( ( qmltpeq @ SY184 @ SY185 @ mactual )
& ( qmltpeq @ SY185 @ SY186 @ mactual ) )
=> ( qmltpeq @ SY184 @ SY186 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(45,plain,
( ( ! [SY203: $i] :
( ( eiw_di @ SY203 @ mactual )
=> ! [SY204: $i] :
( ( eiw_di @ SY204 @ mactual )
=> ( ( qmltpeq @ SY203 @ SY204 @ mactual )
=> ( qmltpeq @ SY204 @ SY203 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(46,plain,
( ( ! [SY210: $i] :
( ( eiw_di @ SY210 @ mactual )
=> ( qmltpeq @ SY210 @ SY210 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(47,plain,
( ( ( eiw_di @ sK1_SY16 @ mactual )
=> ! [SY212: $i] :
( ( eiw_di @ SY212 @ mactual )
=> ( ( ( subset @ sK1_SY16 @ SY212 @ mactual )
& ( subset @ SY212 @ sK1_SY16 @ mactual ) )
=> ( equal_set @ sK1_SY16 @ SY212 @ mactual ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(48,plain,
( ( eiw_di @ sK1_SY16 @ mactual )
= $true ),
inference(standard_cnf,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [SY212: $i] :
( ( eiw_di @ SY212 @ mactual )
=> ( ( ( subset @ sK1_SY16 @ SY212 @ mactual )
& ( subset @ SY212 @ sK1_SY16 @ mactual ) )
=> ( equal_set @ sK1_SY16 @ SY212 @ mactual ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[47]) ).
thf(50,plain,
( ( ~ ! [SY212: $i] :
( ( eiw_di @ SY212 @ mactual )
=> ( ( ( subset @ sK1_SY16 @ SY212 @ mactual )
& ( subset @ SY212 @ sK1_SY16 @ mactual ) )
=> ( equal_set @ sK1_SY16 @ SY212 @ mactual ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[49]) ).
thf(51,plain,
( ( ( eiw_di @ sK2_SY212 @ mactual )
& ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
& ( subset @ sK2_SY212 @ sK1_SY16 @ mactual )
& ~ ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(52,plain,
( ( ! [SY36: $i] :
( ~ ( eiw_di @ SY36 @ mactual )
| ( ! [SY37: $i] :
( ~ ( eiw_di @ SY37 @ mactual )
| ~ ( subset @ SY36 @ SY37 @ mactual )
| ~ ( subset @ SY37 @ SY36 @ mactual )
| ( equal_set @ SY36 @ SY37 @ mactual ) )
& ! [SY37: $i] :
( ~ ( eiw_di @ SY37 @ mactual )
| ~ ( equal_set @ SY36 @ SY37 @ mactual )
| ( subset @ SY36 @ SY37 @ mactual ) )
& ! [SY37: $i] :
( ~ ( eiw_di @ SY37 @ mactual )
| ~ ( equal_set @ SY36 @ SY37 @ mactual )
| ( subset @ SY37 @ SY36 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(53,plain,
( ( ! [SY64: $i] :
( ~ ( eiw_di @ SY64 @ mactual )
| ! [SY65: $i] :
( ~ ( eiw_di @ SY65 @ mactual )
| ! [SY66: $i] :
( ~ ( eiw_di @ SY66 @ mactual )
| ~ ( qmltpeq @ SY64 @ SY65 @ mactual )
| ~ ( subset @ SY66 @ SY64 @ mactual )
| ( subset @ SY66 @ SY65 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(54,plain,
( ( ! [SY94: $i] :
( ~ ( eiw_di @ SY94 @ mactual )
| ! [SY95: $i] :
( ~ ( eiw_di @ SY95 @ mactual )
| ! [SY96: $i] :
( ~ ( eiw_di @ SY96 @ mactual )
| ~ ( qmltpeq @ SY94 @ SY95 @ mactual )
| ~ ( subset @ SY94 @ SY96 @ mactual )
| ( subset @ SY95 @ SY96 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(55,plain,
( ( ! [SY124: $i] :
( ~ ( eiw_di @ SY124 @ mactual )
| ! [SY125: $i] :
( ~ ( eiw_di @ SY125 @ mactual )
| ! [SY126: $i] :
( ~ ( eiw_di @ SY126 @ mactual )
| ~ ( equal_set @ SY126 @ SY124 @ mactual )
| ~ ( qmltpeq @ SY124 @ SY125 @ mactual )
| ( equal_set @ SY126 @ SY125 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(56,plain,
( ( ! [SY154: $i] :
( ~ ( eiw_di @ SY154 @ mactual )
| ! [SY155: $i] :
( ~ ( eiw_di @ SY155 @ mactual )
| ! [SY156: $i] :
( ~ ( eiw_di @ SY156 @ mactual )
| ~ ( equal_set @ SY154 @ SY156 @ mactual )
| ~ ( qmltpeq @ SY154 @ SY155 @ mactual )
| ( equal_set @ SY155 @ SY156 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(57,plain,
( ( ! [SY184: $i] :
( ~ ( eiw_di @ SY184 @ mactual )
| ! [SY185: $i] :
( ~ ( eiw_di @ SY185 @ mactual )
| ! [SY186: $i] :
( ~ ( eiw_di @ SY186 @ mactual )
| ~ ( qmltpeq @ SY184 @ SY185 @ mactual )
| ~ ( qmltpeq @ SY185 @ SY186 @ mactual )
| ( qmltpeq @ SY184 @ SY186 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(58,plain,
( ( ! [SY203: $i] :
( ~ ( eiw_di @ SY203 @ mactual )
| ! [SY204: $i] :
( ~ ( eiw_di @ SY204 @ mactual )
| ~ ( qmltpeq @ SY203 @ SY204 @ mactual )
| ( qmltpeq @ SY204 @ SY203 @ mactual ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(59,plain,
( ( ! [SY210: $i] :
( ~ ( eiw_di @ SY210 @ mactual )
| ( qmltpeq @ SY210 @ SY210 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(60,plain,
( ( ! [SY210: $i] :
( ~ ( eiw_di @ SY210 @ mactual )
| ( qmltpeq @ SY210 @ SY210 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(61,plain,
( ( ! [SY203: $i] :
( ~ ( eiw_di @ SY203 @ mactual )
| ! [SY204: $i] :
( ~ ( eiw_di @ SY204 @ mactual )
| ~ ( qmltpeq @ SY203 @ SY204 @ mactual )
| ( qmltpeq @ SY204 @ SY203 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(62,plain,
( ( ! [SY184: $i] :
( ~ ( eiw_di @ SY184 @ mactual )
| ! [SY185: $i] :
( ~ ( eiw_di @ SY185 @ mactual )
| ! [SY186: $i] :
( ~ ( eiw_di @ SY186 @ mactual )
| ~ ( qmltpeq @ SY184 @ SY185 @ mactual )
| ~ ( qmltpeq @ SY185 @ SY186 @ mactual )
| ( qmltpeq @ SY184 @ SY186 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(63,plain,
( ( ! [SY154: $i] :
( ~ ( eiw_di @ SY154 @ mactual )
| ! [SY155: $i] :
( ~ ( eiw_di @ SY155 @ mactual )
| ! [SY156: $i] :
( ~ ( eiw_di @ SY156 @ mactual )
| ~ ( equal_set @ SY154 @ SY156 @ mactual )
| ~ ( qmltpeq @ SY154 @ SY155 @ mactual )
| ( equal_set @ SY155 @ SY156 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(64,plain,
( ( ! [SY124: $i] :
( ~ ( eiw_di @ SY124 @ mactual )
| ! [SY125: $i] :
( ~ ( eiw_di @ SY125 @ mactual )
| ! [SY126: $i] :
( ~ ( eiw_di @ SY126 @ mactual )
| ~ ( equal_set @ SY126 @ SY124 @ mactual )
| ~ ( qmltpeq @ SY124 @ SY125 @ mactual )
| ( equal_set @ SY126 @ SY125 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(65,plain,
( ( ! [SY94: $i] :
( ~ ( eiw_di @ SY94 @ mactual )
| ! [SY95: $i] :
( ~ ( eiw_di @ SY95 @ mactual )
| ! [SY96: $i] :
( ~ ( eiw_di @ SY96 @ mactual )
| ~ ( qmltpeq @ SY94 @ SY95 @ mactual )
| ~ ( subset @ SY94 @ SY96 @ mactual )
| ( subset @ SY95 @ SY96 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(66,plain,
( ( ! [SY64: $i] :
( ~ ( eiw_di @ SY64 @ mactual )
| ! [SY65: $i] :
( ~ ( eiw_di @ SY65 @ mactual )
| ! [SY66: $i] :
( ~ ( eiw_di @ SY66 @ mactual )
| ~ ( qmltpeq @ SY64 @ SY65 @ mactual )
| ~ ( subset @ SY66 @ SY64 @ mactual )
| ( subset @ SY66 @ SY65 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(67,plain,
( ( ! [SY36: $i] :
( ~ ( eiw_di @ SY36 @ mactual )
| ( ! [SY37: $i] :
( ~ ( eiw_di @ SY37 @ mactual )
| ~ ( subset @ SY36 @ SY37 @ mactual )
| ~ ( subset @ SY37 @ SY36 @ mactual )
| ( equal_set @ SY36 @ SY37 @ mactual ) )
& ! [SY37: $i] :
( ~ ( eiw_di @ SY37 @ mactual )
| ~ ( equal_set @ SY36 @ SY37 @ mactual )
| ( subset @ SY36 @ SY37 @ mactual ) )
& ! [SY37: $i] :
( ~ ( eiw_di @ SY37 @ mactual )
| ~ ( equal_set @ SY36 @ SY37 @ mactual )
| ( subset @ SY37 @ SY36 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(68,plain,
( ( eiw_di @ sK1_SY16 @ mactual )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(69,plain,
( ( ( eiw_di @ sK2_SY212 @ mactual )
& ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
& ( subset @ sK2_SY212 @ sK1_SY16 @ mactual )
& ~ ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(70,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ~ ( ~ ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual )
| ( equal_set @ SX0 @ SX1 @ mactual ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( equal_set @ SX0 @ SX1 @ mactual )
| ( subset @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( equal_set @ SX0 @ SX1 @ mactual )
| ( subset @ SX1 @ SX0 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(71,plain,
( ( ~ ( ~ ( eiw_di @ sK2_SY212 @ mactual )
| ~ ~ ( ~ ~ ( ~ ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
| ~ ( subset @ sK2_SY212 @ sK1_SY16 @ mactual ) )
| ~ ~ ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(72,plain,
! [SV1: $i] :
( ( ~ ( eiw_di @ SV1 @ mactual )
| ( qmltpeq @ SV1 @ SV1 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(73,plain,
! [SV2: $i] :
( ( ~ ( eiw_di @ SV2 @ mactual )
| ! [SY213: $i] :
( ~ ( eiw_di @ SY213 @ mactual )
| ~ ( qmltpeq @ SV2 @ SY213 @ mactual )
| ( qmltpeq @ SY213 @ SV2 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(74,plain,
! [SV3: $i] :
( ( ~ ( eiw_di @ SV3 @ mactual )
| ! [SY214: $i] :
( ~ ( eiw_di @ SY214 @ mactual )
| ! [SY215: $i] :
( ~ ( eiw_di @ SY215 @ mactual )
| ~ ( qmltpeq @ SV3 @ SY214 @ mactual )
| ~ ( qmltpeq @ SY214 @ SY215 @ mactual )
| ( qmltpeq @ SV3 @ SY215 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(75,plain,
! [SV4: $i] :
( ( ~ ( eiw_di @ SV4 @ mactual )
| ! [SY216: $i] :
( ~ ( eiw_di @ SY216 @ mactual )
| ! [SY217: $i] :
( ~ ( eiw_di @ SY217 @ mactual )
| ~ ( equal_set @ SV4 @ SY217 @ mactual )
| ~ ( qmltpeq @ SV4 @ SY216 @ mactual )
| ( equal_set @ SY216 @ SY217 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(76,plain,
! [SV5: $i] :
( ( ~ ( eiw_di @ SV5 @ mactual )
| ! [SY218: $i] :
( ~ ( eiw_di @ SY218 @ mactual )
| ! [SY219: $i] :
( ~ ( eiw_di @ SY219 @ mactual )
| ~ ( equal_set @ SY219 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SY218 @ mactual )
| ( equal_set @ SY219 @ SY218 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV6: $i] :
( ( ~ ( eiw_di @ SV6 @ mactual )
| ! [SY220: $i] :
( ~ ( eiw_di @ SY220 @ mactual )
| ! [SY221: $i] :
( ~ ( eiw_di @ SY221 @ mactual )
| ~ ( qmltpeq @ SV6 @ SY220 @ mactual )
| ~ ( subset @ SV6 @ SY221 @ mactual )
| ( subset @ SY220 @ SY221 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(78,plain,
! [SV7: $i] :
( ( ~ ( eiw_di @ SV7 @ mactual )
| ! [SY222: $i] :
( ~ ( eiw_di @ SY222 @ mactual )
| ! [SY223: $i] :
( ~ ( eiw_di @ SY223 @ mactual )
| ~ ( qmltpeq @ SV7 @ SY222 @ mactual )
| ~ ( subset @ SY223 @ SV7 @ mactual )
| ( subset @ SY223 @ SY222 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(79,plain,
! [SV8: $i] :
( ( ~ ( eiw_di @ SV8 @ mactual )
| ~ ( ~ ! [SY224: $i] :
( ~ ( eiw_di @ SY224 @ mactual )
| ~ ( subset @ SV8 @ SY224 @ mactual )
| ~ ( subset @ SY224 @ SV8 @ mactual )
| ( equal_set @ SV8 @ SY224 @ mactual ) )
| ~ ~ ( ~ ! [SY225: $i] :
( ~ ( eiw_di @ SY225 @ mactual )
| ~ ( equal_set @ SV8 @ SY225 @ mactual )
| ( subset @ SV8 @ SY225 @ mactual ) )
| ~ ! [SY226: $i] :
( ~ ( eiw_di @ SY226 @ mactual )
| ~ ( equal_set @ SV8 @ SY226 @ mactual )
| ( subset @ SY226 @ SV8 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(80,plain,
( ( ~ ( eiw_di @ sK2_SY212 @ mactual )
| ~ ~ ( ~ ~ ( ~ ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
| ~ ( subset @ sK2_SY212 @ sK1_SY16 @ mactual ) )
| ~ ~ ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV1: $i] :
( ( ( ~ ( eiw_di @ SV1 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV1 @ SV1 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV2: $i] :
( ( ( ~ ( eiw_di @ SV2 @ mactual ) )
= $true )
| ( ( ! [SY213: $i] :
( ~ ( eiw_di @ SY213 @ mactual )
| ~ ( qmltpeq @ SV2 @ SY213 @ mactual )
| ( qmltpeq @ SY213 @ SV2 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV3: $i] :
( ( ( ~ ( eiw_di @ SV3 @ mactual ) )
= $true )
| ( ( ! [SY214: $i] :
( ~ ( eiw_di @ SY214 @ mactual )
| ! [SY215: $i] :
( ~ ( eiw_di @ SY215 @ mactual )
| ~ ( qmltpeq @ SV3 @ SY214 @ mactual )
| ~ ( qmltpeq @ SY214 @ SY215 @ mactual )
| ( qmltpeq @ SV3 @ SY215 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV4: $i] :
( ( ( ~ ( eiw_di @ SV4 @ mactual ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( eiw_di @ SY216 @ mactual )
| ! [SY217: $i] :
( ~ ( eiw_di @ SY217 @ mactual )
| ~ ( equal_set @ SV4 @ SY217 @ mactual )
| ~ ( qmltpeq @ SV4 @ SY216 @ mactual )
| ( equal_set @ SY216 @ SY217 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV5: $i] :
( ( ( ~ ( eiw_di @ SV5 @ mactual ) )
= $true )
| ( ( ! [SY218: $i] :
( ~ ( eiw_di @ SY218 @ mactual )
| ! [SY219: $i] :
( ~ ( eiw_di @ SY219 @ mactual )
| ~ ( equal_set @ SY219 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SY218 @ mactual )
| ( equal_set @ SY219 @ SY218 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ mactual ) )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( eiw_di @ SY220 @ mactual )
| ! [SY221: $i] :
( ~ ( eiw_di @ SY221 @ mactual )
| ~ ( qmltpeq @ SV6 @ SY220 @ mactual )
| ~ ( subset @ SV6 @ SY221 @ mactual )
| ( subset @ SY220 @ SY221 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV7: $i] :
( ( ( ~ ( eiw_di @ SV7 @ mactual ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( eiw_di @ SY222 @ mactual )
| ! [SY223: $i] :
( ~ ( eiw_di @ SY223 @ mactual )
| ~ ( qmltpeq @ SV7 @ SY222 @ mactual )
| ~ ( subset @ SY223 @ SV7 @ mactual )
| ( subset @ SY223 @ SY222 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV8: $i] :
( ( ( ~ ( eiw_di @ SV8 @ mactual ) )
= $true )
| ( ( ~ ( ~ ! [SY224: $i] :
( ~ ( eiw_di @ SY224 @ mactual )
| ~ ( subset @ SV8 @ SY224 @ mactual )
| ~ ( subset @ SY224 @ SV8 @ mactual )
| ( equal_set @ SV8 @ SY224 @ mactual ) )
| ~ ~ ( ~ ! [SY225: $i] :
( ~ ( eiw_di @ SY225 @ mactual )
| ~ ( equal_set @ SV8 @ SY225 @ mactual )
| ( subset @ SV8 @ SY225 @ mactual ) )
| ~ ! [SY226: $i] :
( ~ ( eiw_di @ SY226 @ mactual )
| ~ ( equal_set @ SV8 @ SY226 @ mactual )
| ( subset @ SY226 @ SV8 @ mactual ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(89,plain,
( ( ~ ( eiw_di @ sK2_SY212 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(90,plain,
( ( ~ ~ ( ~ ~ ( ~ ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
| ~ ( subset @ sK2_SY212 @ sK1_SY16 @ mactual ) )
| ~ ~ ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(91,plain,
! [SV1: $i] :
( ( ( eiw_di @ SV1 @ mactual )
= $false )
| ( ( qmltpeq @ SV1 @ SV1 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV2: $i] :
( ( ( eiw_di @ SV2 @ mactual )
= $false )
| ( ( ! [SY213: $i] :
( ~ ( eiw_di @ SY213 @ mactual )
| ~ ( qmltpeq @ SV2 @ SY213 @ mactual )
| ( qmltpeq @ SY213 @ SV2 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV3: $i] :
( ( ( eiw_di @ SV3 @ mactual )
= $false )
| ( ( ! [SY214: $i] :
( ~ ( eiw_di @ SY214 @ mactual )
| ! [SY215: $i] :
( ~ ( eiw_di @ SY215 @ mactual )
| ~ ( qmltpeq @ SV3 @ SY214 @ mactual )
| ~ ( qmltpeq @ SY214 @ SY215 @ mactual )
| ( qmltpeq @ SV3 @ SY215 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV4: $i] :
( ( ( eiw_di @ SV4 @ mactual )
= $false )
| ( ( ! [SY216: $i] :
( ~ ( eiw_di @ SY216 @ mactual )
| ! [SY217: $i] :
( ~ ( eiw_di @ SY217 @ mactual )
| ~ ( equal_set @ SV4 @ SY217 @ mactual )
| ~ ( qmltpeq @ SV4 @ SY216 @ mactual )
| ( equal_set @ SY216 @ SY217 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(95,plain,
! [SV5: $i] :
( ( ( eiw_di @ SV5 @ mactual )
= $false )
| ( ( ! [SY218: $i] :
( ~ ( eiw_di @ SY218 @ mactual )
| ! [SY219: $i] :
( ~ ( eiw_di @ SY219 @ mactual )
| ~ ( equal_set @ SY219 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SY218 @ mactual )
| ( equal_set @ SY219 @ SY218 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(96,plain,
! [SV6: $i] :
( ( ( eiw_di @ SV6 @ mactual )
= $false )
| ( ( ! [SY220: $i] :
( ~ ( eiw_di @ SY220 @ mactual )
| ! [SY221: $i] :
( ~ ( eiw_di @ SY221 @ mactual )
| ~ ( qmltpeq @ SV6 @ SY220 @ mactual )
| ~ ( subset @ SV6 @ SY221 @ mactual )
| ( subset @ SY220 @ SY221 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(97,plain,
! [SV7: $i] :
( ( ( eiw_di @ SV7 @ mactual )
= $false )
| ( ( ! [SY222: $i] :
( ~ ( eiw_di @ SY222 @ mactual )
| ! [SY223: $i] :
( ~ ( eiw_di @ SY223 @ mactual )
| ~ ( qmltpeq @ SV7 @ SY222 @ mactual )
| ~ ( subset @ SY223 @ SV7 @ mactual )
| ( subset @ SY223 @ SY222 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(98,plain,
! [SV8: $i] :
( ( ( eiw_di @ SV8 @ mactual )
= $false )
| ( ( ~ ( ~ ! [SY224: $i] :
( ~ ( eiw_di @ SY224 @ mactual )
| ~ ( subset @ SV8 @ SY224 @ mactual )
| ~ ( subset @ SY224 @ SV8 @ mactual )
| ( equal_set @ SV8 @ SY224 @ mactual ) )
| ~ ~ ( ~ ! [SY225: $i] :
( ~ ( eiw_di @ SY225 @ mactual )
| ~ ( equal_set @ SV8 @ SY225 @ mactual )
| ( subset @ SV8 @ SY225 @ mactual ) )
| ~ ! [SY226: $i] :
( ~ ( eiw_di @ SY226 @ mactual )
| ~ ( equal_set @ SV8 @ SY226 @ mactual )
| ( subset @ SY226 @ SV8 @ mactual ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(99,plain,
( ( eiw_di @ sK2_SY212 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(100,plain,
( ( ~ ( ~ ~ ( ~ ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
| ~ ( subset @ sK2_SY212 @ sK1_SY16 @ mactual ) )
| ~ ~ ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(101,plain,
! [SV2: $i,SV9: $i] :
( ( ( ~ ( eiw_di @ SV9 @ mactual )
| ~ ( qmltpeq @ SV2 @ SV9 @ mactual )
| ( qmltpeq @ SV9 @ SV2 @ mactual ) )
= $true )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( eiw_di @ SV10 @ mactual )
| ! [SY227: $i] :
( ~ ( eiw_di @ SY227 @ mactual )
| ~ ( qmltpeq @ SV3 @ SV10 @ mactual )
| ~ ( qmltpeq @ SV10 @ SY227 @ mactual )
| ( qmltpeq @ SV3 @ SY227 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV4: $i,SV11: $i] :
( ( ( ~ ( eiw_di @ SV11 @ mactual )
| ! [SY228: $i] :
( ~ ( eiw_di @ SY228 @ mactual )
| ~ ( equal_set @ SV4 @ SY228 @ mactual )
| ~ ( qmltpeq @ SV4 @ SV11 @ mactual )
| ( equal_set @ SV11 @ SY228 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV5: $i,SV12: $i] :
( ( ( ~ ( eiw_di @ SV12 @ mactual )
| ! [SY229: $i] :
( ~ ( eiw_di @ SY229 @ mactual )
| ~ ( equal_set @ SY229 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV12 @ mactual )
| ( equal_set @ SY229 @ SV12 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( eiw_di @ SV13 @ mactual )
| ! [SY230: $i] :
( ~ ( eiw_di @ SY230 @ mactual )
| ~ ( qmltpeq @ SV6 @ SV13 @ mactual )
| ~ ( subset @ SV6 @ SY230 @ mactual )
| ( subset @ SV13 @ SY230 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV7: $i,SV14: $i] :
( ( ( ~ ( eiw_di @ SV14 @ mactual )
| ! [SY231: $i] :
( ~ ( eiw_di @ SY231 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV14 @ mactual )
| ~ ( subset @ SY231 @ SV7 @ mactual )
| ( subset @ SY231 @ SV14 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV8: $i] :
( ( ( ~ ! [SY224: $i] :
( ~ ( eiw_di @ SY224 @ mactual )
| ~ ( subset @ SV8 @ SY224 @ mactual )
| ~ ( subset @ SY224 @ SV8 @ mactual )
| ( equal_set @ SV8 @ SY224 @ mactual ) )
| ~ ~ ( ~ ! [SY225: $i] :
( ~ ( eiw_di @ SY225 @ mactual )
| ~ ( equal_set @ SV8 @ SY225 @ mactual )
| ( subset @ SV8 @ SY225 @ mactual ) )
| ~ ! [SY226: $i] :
( ~ ( eiw_di @ SY226 @ mactual )
| ~ ( equal_set @ SV8 @ SY226 @ mactual )
| ( subset @ SY226 @ SV8 @ mactual ) ) ) )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(108,plain,
( ( ~ ~ ( ~ ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
| ~ ( subset @ sK2_SY212 @ sK1_SY16 @ mactual ) )
| ~ ~ ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV2: $i,SV9: $i] :
( ( ( ~ ( eiw_di @ SV9 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV2 @ SV9 @ mactual )
| ( qmltpeq @ SV9 @ SV2 @ mactual ) )
= $true )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( eiw_di @ SV10 @ mactual ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( eiw_di @ SY227 @ mactual )
| ~ ( qmltpeq @ SV3 @ SV10 @ mactual )
| ~ ( qmltpeq @ SV10 @ SY227 @ mactual )
| ( qmltpeq @ SV3 @ SY227 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV4: $i,SV11: $i] :
( ( ( ~ ( eiw_di @ SV11 @ mactual ) )
= $true )
| ( ( ! [SY228: $i] :
( ~ ( eiw_di @ SY228 @ mactual )
| ~ ( equal_set @ SV4 @ SY228 @ mactual )
| ~ ( qmltpeq @ SV4 @ SV11 @ mactual )
| ( equal_set @ SV11 @ SY228 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV5: $i,SV12: $i] :
( ( ( ~ ( eiw_di @ SV12 @ mactual ) )
= $true )
| ( ( ! [SY229: $i] :
( ~ ( eiw_di @ SY229 @ mactual )
| ~ ( equal_set @ SY229 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV12 @ mactual )
| ( equal_set @ SY229 @ SV12 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV6: $i,SV13: $i] :
( ( ( ~ ( eiw_di @ SV13 @ mactual ) )
= $true )
| ( ( ! [SY230: $i] :
( ~ ( eiw_di @ SY230 @ mactual )
| ~ ( qmltpeq @ SV6 @ SV13 @ mactual )
| ~ ( subset @ SV6 @ SY230 @ mactual )
| ( subset @ SV13 @ SY230 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV7: $i,SV14: $i] :
( ( ( ~ ( eiw_di @ SV14 @ mactual ) )
= $true )
| ( ( ! [SY231: $i] :
( ~ ( eiw_di @ SY231 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV14 @ mactual )
| ~ ( subset @ SY231 @ SV7 @ mactual )
| ( subset @ SY231 @ SV14 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(115,plain,
! [SV8: $i] :
( ( ( ~ ! [SY224: $i] :
( ~ ( eiw_di @ SY224 @ mactual )
| ~ ( subset @ SV8 @ SY224 @ mactual )
| ~ ( subset @ SY224 @ SV8 @ mactual )
| ( equal_set @ SV8 @ SY224 @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(116,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ! [SY225: $i] :
( ~ ( eiw_di @ SY225 @ mactual )
| ~ ( equal_set @ SV8 @ SY225 @ mactual )
| ( subset @ SV8 @ SY225 @ mactual ) )
| ~ ! [SY226: $i] :
( ~ ( eiw_di @ SY226 @ mactual )
| ~ ( equal_set @ SV8 @ SY226 @ mactual )
| ( subset @ SY226 @ SV8 @ mactual ) ) ) )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(117,plain,
( ( ~ ~ ( ~ ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
| ~ ( subset @ sK2_SY212 @ sK1_SY16 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(118,plain,
( ( ~ ~ ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(119,plain,
! [SV2: $i,SV9: $i] :
( ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV2 @ SV9 @ mactual )
| ( qmltpeq @ SV9 @ SV2 @ mactual ) )
= $true )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV3: $i,SV10: $i] :
( ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( ! [SY227: $i] :
( ~ ( eiw_di @ SY227 @ mactual )
| ~ ( qmltpeq @ SV3 @ SV10 @ mactual )
| ~ ( qmltpeq @ SV10 @ SY227 @ mactual )
| ( qmltpeq @ SV3 @ SY227 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV4: $i,SV11: $i] :
( ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( ! [SY228: $i] :
( ~ ( eiw_di @ SY228 @ mactual )
| ~ ( equal_set @ SV4 @ SY228 @ mactual )
| ~ ( qmltpeq @ SV4 @ SV11 @ mactual )
| ( equal_set @ SV11 @ SY228 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV5: $i,SV12: $i] :
( ( ( eiw_di @ SV12 @ mactual )
= $false )
| ( ( ! [SY229: $i] :
( ~ ( eiw_di @ SY229 @ mactual )
| ~ ( equal_set @ SY229 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV12 @ mactual )
| ( equal_set @ SY229 @ SV12 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV6: $i,SV13: $i] :
( ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( ! [SY230: $i] :
( ~ ( eiw_di @ SY230 @ mactual )
| ~ ( qmltpeq @ SV6 @ SV13 @ mactual )
| ~ ( subset @ SV6 @ SY230 @ mactual )
| ( subset @ SV13 @ SY230 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV7: $i,SV14: $i] :
( ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( ! [SY231: $i] :
( ~ ( eiw_di @ SY231 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV14 @ mactual )
| ~ ( subset @ SY231 @ SV7 @ mactual )
| ( subset @ SY231 @ SV14 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV8: $i] :
( ( ( ! [SY224: $i] :
( ~ ( eiw_di @ SY224 @ mactual )
| ~ ( subset @ SV8 @ SY224 @ mactual )
| ~ ( subset @ SY224 @ SV8 @ mactual )
| ( equal_set @ SV8 @ SY224 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(126,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ! [SY225: $i] :
( ~ ( eiw_di @ SY225 @ mactual )
| ~ ( equal_set @ SV8 @ SY225 @ mactual )
| ( subset @ SV8 @ SY225 @ mactual ) )
| ~ ! [SY226: $i] :
( ~ ( eiw_di @ SY226 @ mactual )
| ~ ( equal_set @ SV8 @ SY226 @ mactual )
| ( subset @ SY226 @ SV8 @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(127,plain,
( ( ~ ( ~ ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
| ~ ( subset @ sK2_SY212 @ sK1_SY16 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(128,plain,
( ( ~ ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(129,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( qmltpeq @ SV2 @ SV9 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV9 @ SV2 @ mactual )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV10: $i,SV3: $i,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ mactual )
| ~ ( qmltpeq @ SV3 @ SV10 @ mactual )
| ~ ( qmltpeq @ SV10 @ SV15 @ mactual )
| ( qmltpeq @ SV3 @ SV15 @ mactual ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV11: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( eiw_di @ SV16 @ mactual )
| ~ ( equal_set @ SV4 @ SV16 @ mactual )
| ~ ( qmltpeq @ SV4 @ SV11 @ mactual )
| ( equal_set @ SV11 @ SV16 @ mactual ) )
= $true )
| ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV12: $i,SV5: $i,SV17: $i] :
( ( ( ~ ( eiw_di @ SV17 @ mactual )
| ~ ( equal_set @ SV17 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV12 @ mactual )
| ( equal_set @ SV17 @ SV12 @ mactual ) )
= $true )
| ( ( eiw_di @ SV12 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ( ~ ( eiw_di @ SV18 @ mactual )
| ~ ( qmltpeq @ SV6 @ SV13 @ mactual )
| ~ ( subset @ SV6 @ SV18 @ mactual )
| ( subset @ SV13 @ SV18 @ mactual ) )
= $true )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV14: $i,SV7: $i,SV19: $i] :
( ( ( ~ ( eiw_di @ SV19 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV14 @ mactual )
| ~ ( subset @ SV19 @ SV7 @ mactual )
| ( subset @ SV19 @ SV14 @ mactual ) )
= $true )
| ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV8: $i,SV20: $i] :
( ( ( ~ ( eiw_di @ SV20 @ mactual )
| ~ ( subset @ SV8 @ SV20 @ mactual )
| ~ ( subset @ SV20 @ SV8 @ mactual )
| ( equal_set @ SV8 @ SV20 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV8: $i] :
( ( ( ~ ! [SY225: $i] :
( ~ ( eiw_di @ SY225 @ mactual )
| ~ ( equal_set @ SV8 @ SY225 @ mactual )
| ( subset @ SV8 @ SY225 @ mactual ) )
| ~ ! [SY226: $i] :
( ~ ( eiw_di @ SY226 @ mactual )
| ~ ( equal_set @ SV8 @ SY226 @ mactual )
| ( subset @ SY226 @ SV8 @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(137,plain,
( ( ~ ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
| ~ ( subset @ sK2_SY212 @ sK1_SY16 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(138,plain,
( ( equal_set @ sK1_SY16 @ sK2_SY212 @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(139,plain,
! [SV9: $i,SV2: $i] :
( ( ( qmltpeq @ SV2 @ SV9 @ mactual )
= $false )
| ( ( qmltpeq @ SV9 @ SV2 @ mactual )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( eiw_di @ SV2 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(140,plain,
! [SV10: $i,SV3: $i,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV3 @ SV10 @ mactual )
| ~ ( qmltpeq @ SV10 @ SV15 @ mactual )
| ( qmltpeq @ SV3 @ SV15 @ mactual ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV11: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( eiw_di @ SV16 @ mactual ) )
= $true )
| ( ( ~ ( equal_set @ SV4 @ SV16 @ mactual )
| ~ ( qmltpeq @ SV4 @ SV11 @ mactual )
| ( equal_set @ SV11 @ SV16 @ mactual ) )
= $true )
| ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV12: $i,SV5: $i,SV17: $i] :
( ( ( ~ ( eiw_di @ SV17 @ mactual ) )
= $true )
| ( ( ~ ( equal_set @ SV17 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV12 @ mactual )
| ( equal_set @ SV17 @ SV12 @ mactual ) )
= $true )
| ( ( eiw_di @ SV12 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(143,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ( ~ ( eiw_di @ SV18 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV6 @ SV13 @ mactual )
| ~ ( subset @ SV6 @ SV18 @ mactual )
| ( subset @ SV13 @ SV18 @ mactual ) )
= $true )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(144,plain,
! [SV14: $i,SV7: $i,SV19: $i] :
( ( ( ~ ( eiw_di @ SV19 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV7 @ SV14 @ mactual )
| ~ ( subset @ SV19 @ SV7 @ mactual )
| ( subset @ SV19 @ SV14 @ mactual ) )
= $true )
| ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV8: $i,SV20: $i] :
( ( ( ~ ( eiw_di @ SV20 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV8 @ SV20 @ mactual )
| ~ ( subset @ SV20 @ SV8 @ mactual )
| ( equal_set @ SV8 @ SV20 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV8: $i] :
( ( ( ~ ! [SY225: $i] :
( ~ ( eiw_di @ SY225 @ mactual )
| ~ ( equal_set @ SV8 @ SY225 @ mactual )
| ( subset @ SV8 @ SY225 @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(147,plain,
! [SV8: $i] :
( ( ( ~ ! [SY226: $i] :
( ~ ( eiw_di @ SY226 @ mactual )
| ~ ( equal_set @ SV8 @ SY226 @ mactual )
| ( subset @ SY226 @ SV8 @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(148,plain,
( ( ~ ( subset @ sK1_SY16 @ sK2_SY212 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(149,plain,
( ( ~ ( subset @ sK2_SY212 @ sK1_SY16 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(150,plain,
! [SV10: $i,SV3: $i,SV15: $i] :
( ( ( eiw_di @ SV15 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV3 @ SV10 @ mactual )
| ~ ( qmltpeq @ SV10 @ SV15 @ mactual )
| ( qmltpeq @ SV3 @ SV15 @ mactual ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(151,plain,
! [SV11: $i,SV4: $i,SV16: $i] :
( ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( ~ ( equal_set @ SV4 @ SV16 @ mactual )
| ~ ( qmltpeq @ SV4 @ SV11 @ mactual )
| ( equal_set @ SV11 @ SV16 @ mactual ) )
= $true )
| ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(152,plain,
! [SV12: $i,SV5: $i,SV17: $i] :
( ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( ~ ( equal_set @ SV17 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV12 @ mactual )
| ( equal_set @ SV17 @ SV12 @ mactual ) )
= $true )
| ( ( eiw_di @ SV12 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV13: $i,SV6: $i,SV18: $i] :
( ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV6 @ SV13 @ mactual )
| ~ ( subset @ SV6 @ SV18 @ mactual )
| ( subset @ SV13 @ SV18 @ mactual ) )
= $true )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV14: $i,SV7: $i,SV19: $i] :
( ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV7 @ SV14 @ mactual )
| ~ ( subset @ SV19 @ SV7 @ mactual )
| ( subset @ SV19 @ SV14 @ mactual ) )
= $true )
| ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV8: $i,SV20: $i] :
( ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( ~ ( subset @ SV8 @ SV20 @ mactual )
| ~ ( subset @ SV20 @ SV8 @ mactual )
| ( equal_set @ SV8 @ SV20 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV8: $i] :
( ( ( ! [SY225: $i] :
( ~ ( eiw_di @ SY225 @ mactual )
| ~ ( equal_set @ SV8 @ SY225 @ mactual )
| ( subset @ SV8 @ SY225 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(157,plain,
! [SV8: $i] :
( ( ( ! [SY226: $i] :
( ~ ( eiw_di @ SY226 @ mactual )
| ~ ( equal_set @ SV8 @ SY226 @ mactual )
| ( subset @ SY226 @ SV8 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(158,plain,
( ( subset @ sK1_SY16 @ sK2_SY212 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(159,plain,
( ( subset @ sK2_SY212 @ sK1_SY16 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(160,plain,
! [SV15: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( qmltpeq @ SV3 @ SV10 @ mactual )
| ~ ( qmltpeq @ SV10 @ SV15 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV15 @ mactual )
= $true )
| ( ( eiw_di @ SV15 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV11: $i,SV16: $i,SV4: $i] :
( ( ( ~ ( equal_set @ SV4 @ SV16 @ mactual )
| ~ ( qmltpeq @ SV4 @ SV11 @ mactual ) )
= $true )
| ( ( equal_set @ SV11 @ SV16 @ mactual )
= $true )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV12: $i,SV5: $i,SV17: $i] :
( ( ( ~ ( equal_set @ SV17 @ SV5 @ mactual )
| ~ ( qmltpeq @ SV5 @ SV12 @ mactual ) )
= $true )
| ( ( equal_set @ SV17 @ SV12 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV12 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV18: $i,SV13: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV13 @ mactual )
| ~ ( subset @ SV6 @ SV18 @ mactual ) )
= $true )
| ( ( subset @ SV13 @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV19: $i,SV14: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ SV7 @ SV14 @ mactual )
| ~ ( subset @ SV19 @ SV7 @ mactual ) )
= $true )
| ( ( subset @ SV19 @ SV14 @ mactual )
= $true )
| ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(165,plain,
! [SV20: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV20 @ mactual )
| ~ ( subset @ SV20 @ SV8 @ mactual ) )
= $true )
| ( ( equal_set @ SV8 @ SV20 @ mactual )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( eiw_di @ SV21 @ mactual )
| ~ ( equal_set @ SV8 @ SV21 @ mactual )
| ( subset @ SV8 @ SV21 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV8: $i,SV22: $i] :
( ( ( ~ ( eiw_di @ SV22 @ mactual )
| ~ ( equal_set @ SV8 @ SV22 @ mactual )
| ( subset @ SV22 @ SV8 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV15: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( qmltpeq @ SV3 @ SV10 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV10 @ SV15 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV15 @ mactual )
= $true )
| ( ( eiw_di @ SV15 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(169,plain,
! [SV11: $i,SV16: $i,SV4: $i] :
( ( ( ~ ( equal_set @ SV4 @ SV16 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV4 @ SV11 @ mactual ) )
= $true )
| ( ( equal_set @ SV11 @ SV16 @ mactual )
= $true )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV12: $i,SV5: $i,SV17: $i] :
( ( ( ~ ( equal_set @ SV17 @ SV5 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV5 @ SV12 @ mactual ) )
= $true )
| ( ( equal_set @ SV17 @ SV12 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV12 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV18: $i,SV13: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV13 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV6 @ SV18 @ mactual ) )
= $true )
| ( ( subset @ SV13 @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV19: $i,SV14: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ SV7 @ SV14 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV19 @ SV7 @ mactual ) )
= $true )
| ( ( subset @ SV19 @ SV14 @ mactual )
= $true )
| ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV20: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV20 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV20 @ SV8 @ mactual ) )
= $true )
| ( ( equal_set @ SV8 @ SV20 @ mactual )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(174,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( eiw_di @ SV21 @ mactual ) )
= $true )
| ( ( ~ ( equal_set @ SV8 @ SV21 @ mactual )
| ( subset @ SV8 @ SV21 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV8: $i,SV22: $i] :
( ( ( ~ ( eiw_di @ SV22 @ mactual ) )
= $true )
| ( ( ~ ( equal_set @ SV8 @ SV22 @ mactual )
| ( subset @ SV22 @ SV8 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV15: $i,SV10: $i,SV3: $i] :
( ( ( qmltpeq @ SV3 @ SV10 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV10 @ SV15 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV15 @ mactual )
= $true )
| ( ( eiw_di @ SV15 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV11: $i,SV16: $i,SV4: $i] :
( ( ( equal_set @ SV4 @ SV16 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV4 @ SV11 @ mactual ) )
= $true )
| ( ( equal_set @ SV11 @ SV16 @ mactual )
= $true )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV12: $i,SV5: $i,SV17: $i] :
( ( ( equal_set @ SV17 @ SV5 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV5 @ SV12 @ mactual ) )
= $true )
| ( ( equal_set @ SV17 @ SV12 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV12 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV18: $i,SV13: $i,SV6: $i] :
( ( ( qmltpeq @ SV6 @ SV13 @ mactual )
= $false )
| ( ( ~ ( subset @ SV6 @ SV18 @ mactual ) )
= $true )
| ( ( subset @ SV13 @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(180,plain,
! [SV19: $i,SV14: $i,SV7: $i] :
( ( ( qmltpeq @ SV7 @ SV14 @ mactual )
= $false )
| ( ( ~ ( subset @ SV19 @ SV7 @ mactual ) )
= $true )
| ( ( subset @ SV19 @ SV14 @ mactual )
= $true )
| ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(181,plain,
! [SV20: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV20 @ mactual )
= $false )
| ( ( ~ ( subset @ SV20 @ SV8 @ mactual ) )
= $true )
| ( ( equal_set @ SV8 @ SV20 @ mactual )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV8: $i,SV21: $i] :
( ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( ~ ( equal_set @ SV8 @ SV21 @ mactual )
| ( subset @ SV8 @ SV21 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(183,plain,
! [SV8: $i,SV22: $i] :
( ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( ~ ( equal_set @ SV8 @ SV22 @ mactual )
| ( subset @ SV22 @ SV8 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(184,plain,
! [SV3: $i,SV15: $i,SV10: $i] :
( ( ( qmltpeq @ SV10 @ SV15 @ mactual )
= $false )
| ( ( qmltpeq @ SV3 @ SV10 @ mactual )
= $false )
| ( ( qmltpeq @ SV3 @ SV15 @ mactual )
= $true )
| ( ( eiw_di @ SV15 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV3 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(185,plain,
! [SV16: $i,SV11: $i,SV4: $i] :
( ( ( qmltpeq @ SV4 @ SV11 @ mactual )
= $false )
| ( ( equal_set @ SV4 @ SV16 @ mactual )
= $false )
| ( ( equal_set @ SV11 @ SV16 @ mactual )
= $true )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV17: $i,SV12: $i,SV5: $i] :
( ( ( qmltpeq @ SV5 @ SV12 @ mactual )
= $false )
| ( ( equal_set @ SV17 @ SV5 @ mactual )
= $false )
| ( ( equal_set @ SV17 @ SV12 @ mactual )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV12 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(187,plain,
! [SV13: $i,SV18: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV18 @ mactual )
= $false )
| ( ( qmltpeq @ SV6 @ SV13 @ mactual )
= $false )
| ( ( subset @ SV13 @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV13 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV14: $i,SV7: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV7 @ mactual )
= $false )
| ( ( qmltpeq @ SV7 @ SV14 @ mactual )
= $false )
| ( ( subset @ SV19 @ SV14 @ mactual )
= $true )
| ( ( eiw_di @ SV19 @ mactual )
= $false )
| ( ( eiw_di @ SV14 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(189,plain,
! [SV8: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV8 @ mactual )
= $false )
| ( ( subset @ SV8 @ SV20 @ mactual )
= $false )
| ( ( equal_set @ SV8 @ SV20 @ mactual )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV21: $i,SV8: $i] :
( ( ( ~ ( equal_set @ SV8 @ SV21 @ mactual ) )
= $true )
| ( ( subset @ SV8 @ SV21 @ mactual )
= $true )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( equal_set @ SV8 @ SV22 @ mactual ) )
= $true )
| ( ( subset @ SV22 @ SV8 @ mactual )
= $true )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV21: $i,SV8: $i] :
( ( ( equal_set @ SV8 @ SV21 @ mactual )
= $false )
| ( ( subset @ SV8 @ SV21 @ mactual )
= $true )
| ( ( eiw_di @ SV21 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(193,plain,
! [SV22: $i,SV8: $i] :
( ( ( equal_set @ SV8 @ SV22 @ mactual )
= $false )
| ( ( subset @ SV22 @ SV8 @ mactual )
= $true )
| ( ( eiw_di @ SV22 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(194,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,193,192,189,188,187,186,185,184,159,158,139,138,99,91]) ).
thf(195,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET019^4 : 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
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 14:31:29 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.32
% 0.64/0.32 No.of.Axioms: 35
% 0.64/0.32
% 0.64/0.32 Length.of.Defs: 1653
% 0.64/0.32
% 0.64/0.32 Contains.Choice.Funs: false
% 0.64/0.32 ........
% 0.64/0.32
% 0.64/0.32 ********************************
% 0.64/0.32 * All subproblems solved! *
% 0.64/0.32 ********************************
% 0.64/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:194,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.64/0.32
% 0.64/0.32 %**** Beginning of derivation protocol ****
% 0.64/0.32 % SZS output start CNFRefutation
% See solution above
% 0.64/0.32
% 0.64/0.32 %**** End of derivation protocol ****
% 0.64/0.32 %**** no. of clauses in derivation: 168 ****
% 0.64/0.32 %**** clause counter: 194 ****
% 0.64/0.32
% 0.64/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:194,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------