TSTP Solution File: LAT388+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LAT388+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 05:48:13 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 47
% Syntax : Number of formulae : 214 ( 110 unt; 26 typ; 0 def)
% Number of atoms : 1190 ( 357 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1618 ( 272 ~; 317 |; 31 &; 954 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 8 con; 0-3 aty)
% Number of variables : 308 ( 0 ^ 304 !; 4 ?; 308 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aCompleteLattice0,type,
aCompleteLattice0: $i > $o ).
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aFixedPointOf0,type,
aFixedPointOf0: $i > $i > $o ).
thf(tp_aFunction0,type,
aFunction0: $i > $o ).
thf(tp_aInfimumOfIn0,type,
aInfimumOfIn0: $i > $i > $i > $o ).
thf(tp_aLowerBoundOfIn0,type,
aLowerBoundOfIn0: $i > $i > $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_aSubsetOf0,type,
aSubsetOf0: $i > $i > $o ).
thf(tp_aSupremumOfIn0,type,
aSupremumOfIn0: $i > $i > $i > $o ).
thf(tp_aUpperBoundOfIn0,type,
aUpperBoundOfIn0: $i > $i > $i > $o ).
thf(tp_cS1142,type,
cS1142: $i > $i ).
thf(tp_cS1241,type,
cS1241: $i > $i > $i > $i ).
thf(tp_isEmpty0,type,
isEmpty0: $i > $o ).
thf(tp_isMonotone0,type,
isMonotone0: $i > $o ).
thf(tp_isOn0,type,
isOn0: $i > $i > $o ).
thf(tp_sdtlpdtrp0,type,
sdtlpdtrp0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_szDzozmdt0,type,
szDzozmdt0: $i > $i ).
thf(tp_szRzazndt0,type,
szRzazndt0: $i > $i ).
thf(tp_xP,type,
xP: $i ).
thf(tp_xS,type,
xS: $i ).
thf(tp_xT,type,
xT: $i ).
thf(tp_xU,type,
xU: $i ).
thf(tp_xf,type,
xf: $i ).
thf(tp_xp,type,
xp: $i ).
thf(1,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( szRzazndt0 @ W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgSort) ).
thf(2,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szRzazndt0 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mRanSort) ).
thf(3,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDomSort) ).
thf(4,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConMap) ).
thf(5,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aInfimumOfIn0 @ W2 @ W1 @ W0 )
& ( aInfimumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mInfUn) ).
thf(6,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
& ( aSupremumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSupUn) ).
thf(7,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTrans) ).
thf(8,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mASymm) ).
thf(9,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mARefl) ).
thf(10,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRel) ).
thf(11,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(12,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(13,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetSort) ).
thf(14,axiom,
( ( aFixedPointOf0 @ xp @ xf )
& ( aSupremumOfIn0 @ xp @ xT @ xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1330) ).
thf(15,axiom,
( ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
& ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1299) ).
thf(16,axiom,
aInfimumOfIn0 @ xp @ xP @ xU,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1261) ).
thf(17,axiom,
( xP
= ( cS1241 @ xU @ xf @ xT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1244) ).
thf(18,axiom,
aSubsetOf0 @ xT @ xS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1173) ).
thf(19,axiom,
( xS
= ( cS1142 @ xf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1144) ).
thf(20,axiom,
( ( aCompleteLattice0 @ xU )
& ( aFunction0 @ xf )
& ( isMonotone0 @ xf )
& ( isOn0 @ xf @ xU ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1123) ).
thf(21,conjecture,
? [W0: $i] : ( aSupremumOfIn0 @ W0 @ xT @ xS ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(22,negated_conjecture,
( ( ? [W0: $i] : ( aSupremumOfIn0 @ W0 @ xT @ xS ) )
= $false ),
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,plain,
( ( ? [W0: $i] : ( aSupremumOfIn0 @ W0 @ xT @ xS ) )
= $false ),
inference(unfold_def,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( szRzazndt0 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(25,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szRzazndt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(26,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(28,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aInfimumOfIn0 @ W2 @ W1 @ W0 )
& ( aInfimumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(29,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
& ( aSupremumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(30,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(31,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(32,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(33,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(34,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(35,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(36,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(37,plain,
( ( ( aFixedPointOf0 @ xp @ xf )
& ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(38,plain,
( ( ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
& ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(39,plain,
( ( aInfimumOfIn0 @ xp @ xP @ xU )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(40,plain,
( ( xP
= ( cS1241 @ xU @ xf @ xT ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(41,plain,
( ( aSubsetOf0 @ xT @ xS )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(42,plain,
( ( xS
= ( cS1142 @ xf ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(43,plain,
( ( ( aCompleteLattice0 @ xU )
& ( aFunction0 @ xf )
& ( isMonotone0 @ xf )
& ( isOn0 @ xf @ xU ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(44,plain,
( ( ~ ? [W0: $i] : ( aSupremumOfIn0 @ W0 @ xT @ xS ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(45,plain,
( ( ! [W0: $i] :
~ ( aSupremumOfIn0 @ W0 @ xT @ xS ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(46,plain,
( ( ! [W0: $i] :
( ~ ( aFunction0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( szRzazndt0 @ W0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(47,plain,
( ( ! [W0: $i] :
( ~ ( aFunction0 @ W0 )
| ( aSet0 @ ( szRzazndt0 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(48,plain,
( ( ! [W0: $i] :
( ~ ( aFunction0 @ W0 )
| ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(49,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(50,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aSubsetOf0 @ W1 @ W0 )
| ! [W2: $i,W3: $i] :
( ~ ( aInfimumOfIn0 @ W2 @ W1 @ W0 )
| ~ ( aInfimumOfIn0 @ W3 @ W1 @ W0 )
| ( W2 = W3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(51,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aSubsetOf0 @ W1 @ W0 )
| ! [W2: $i,W3: $i] :
( ~ ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
| ~ ( aSupremumOfIn0 @ W3 @ W1 @ W0 )
| ( W2 = W3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(52,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ W0 @ W2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(53,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(54,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(55,plain,
( ( ! [W0: $i] :
~ ( aElement0 @ W0 )
| ! [W1: $i] :
~ ( aElement0 @ W1 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(56,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ W0 )
| ( aElement0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(57,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(58,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(59,plain,
( ( ( aCompleteLattice0 @ xU )
& ( aFunction0 @ xf )
& ( isMonotone0 @ xf )
& ( isOn0 @ xf @ xU ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(60,plain,
( ( xS
= ( cS1142 @ xf ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(61,plain,
( ( aSubsetOf0 @ xT @ xS )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(62,plain,
( ( xP
= ( cS1241 @ xU @ xf @ xT ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(63,plain,
( ( aInfimumOfIn0 @ xp @ xP @ xU )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(64,plain,
( ( ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
& ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(65,plain,
( ( ( aFixedPointOf0 @ xp @ xf )
& ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(66,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(67,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(68,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ W0 )
| ( aElement0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(69,plain,
( ( ! [W0: $i] :
~ ( aElement0 @ W0 )
| ! [W1: $i] :
~ ( aElement0 @ W1 )
| $true )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(70,plain,
( ( ! [W0: $i] :
( ~ ( aElement0 @ W0 )
| ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(71,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(72,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0 @ W0 )
| ~ ( aElement0 @ W1 )
| ~ ( aElement0 @ W2 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ W0 @ W2 ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(73,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aSubsetOf0 @ W1 @ W0 )
| ! [W2: $i,W3: $i] :
( ~ ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
| ~ ( aSupremumOfIn0 @ W3 @ W1 @ W0 )
| ( W2 = W3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(74,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aSubsetOf0 @ W1 @ W0 )
| ! [W2: $i,W3: $i] :
( ~ ( aInfimumOfIn0 @ W2 @ W1 @ W0 )
| ~ ( aInfimumOfIn0 @ W3 @ W1 @ W0 )
| ( W2 = W3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(75,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(76,plain,
( ( ! [W0: $i] :
( ~ ( aFunction0 @ W0 )
| ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(77,plain,
( ( ! [W0: $i] :
( ~ ( aFunction0 @ W0 )
| ( aSet0 @ ( szRzazndt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(78,plain,
( ( ! [W0: $i] :
( ~ ( aFunction0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( szRzazndt0 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(79,plain,
( ( ! [W0: $i] :
~ ( aSupremumOfIn0 @ W0 @ xT @ xS ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(80,plain,
( ( ~ ( ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
| ~ ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(81,plain,
( ( ~ ( ~ ( aFixedPointOf0 @ xp @ xf )
| ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(82,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aCompleteLattice0 @ xU )
| ~ ( aFunction0 @ xf ) )
| ~ ( isMonotone0 @ xf ) )
| ~ ( isOn0 @ xf @ xU ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(83,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(84,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(85,plain,
! [SV3: $i] :
( ( ~ ( aSet0 @ SV3 )
| ! [SY26: $i] :
( ~ ( aElementOf0 @ SY26 @ SV3 )
| ( aElement0 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(86,plain,
( ( ( ! [W0: $i] :
~ ( aElement0 @ W0 )
| ! [W1: $i] :
~ ( aElement0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(87,plain,
! [SV4: $i] :
( ( ~ ( aElement0 @ SV4 )
| ( sdtlseqdt0 @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(88,plain,
! [SV5: $i] :
( ( ! [SY27: $i] :
( ~ ( aElement0 @ SV5 )
| ~ ( aElement0 @ SY27 )
| ~ ( sdtlseqdt0 @ SV5 @ SY27 )
| ~ ( sdtlseqdt0 @ SY27 @ SV5 )
| ( SV5 = SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(89,plain,
! [SV6: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SY28 )
| ~ ( aElement0 @ SY29 )
| ~ ( sdtlseqdt0 @ SV6 @ SY28 )
| ~ ( sdtlseqdt0 @ SY28 @ SY29 )
| ( sdtlseqdt0 @ SV6 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(90,plain,
! [SV7: $i] :
( ( ~ ( aSet0 @ SV7 )
| ! [SY30: $i] :
( ~ ( aSubsetOf0 @ SY30 @ SV7 )
| ! [SY31: $i,SY32: $i] :
( ~ ( aSupremumOfIn0 @ SY31 @ SY30 @ SV7 )
| ~ ( aSupremumOfIn0 @ SY32 @ SY30 @ SV7 )
| ( SY31 = SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(91,plain,
! [SV8: $i] :
( ( ~ ( aSet0 @ SV8 )
| ! [SY33: $i] :
( ~ ( aSubsetOf0 @ SY33 @ SV8 )
| ! [SY34: $i,SY35: $i] :
( ~ ( aInfimumOfIn0 @ SY34 @ SY33 @ SV8 )
| ~ ( aInfimumOfIn0 @ SY35 @ SY33 @ SV8 )
| ( SY34 = SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(92,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(93,plain,
! [SV10: $i] :
( ( ~ ( aFunction0 @ SV10 )
| ( aSet0 @ ( szDzozmdt0 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(94,plain,
! [SV11: $i] :
( ( ~ ( aFunction0 @ SV11 )
| ( aSet0 @ ( szRzazndt0 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(95,plain,
! [SV12: $i] :
( ( ~ ( aFunction0 @ SV12 )
| ! [SY36: $i] :
( ~ ( aElementOf0 @ SY36 @ ( szDzozmdt0 @ SV12 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV12 @ SY36 ) @ ( szRzazndt0 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(96,plain,
! [SV13: $i] :
( ( ~ ( aSupremumOfIn0 @ SV13 @ xT @ xS ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(97,plain,
( ( ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
| ~ ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(98,plain,
( ( ~ ( aFixedPointOf0 @ xp @ xf )
| ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(99,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aCompleteLattice0 @ xU )
| ~ ( aFunction0 @ xf ) )
| ~ ( isMonotone0 @ xf ) )
| ~ ( isOn0 @ xf @ xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(100,plain,
! [SV3: $i] :
( ( ( ~ ( aSet0 @ SV3 ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( aElementOf0 @ SY26 @ SV3 )
| ( aElement0 @ SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(101,plain,
( ( ( ! [W0: $i] :
~ ( aElement0 @ W0 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aElement0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV4: $i] :
( ( ( ~ ( aElement0 @ SV4 ) )
= $true )
| ( ( sdtlseqdt0 @ SV4 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV14: $i,SV5: $i] :
( ( ~ ( aElement0 @ SV5 )
| ~ ( aElement0 @ SV14 )
| ~ ( sdtlseqdt0 @ SV5 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV5 )
| ( SV5 = SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV15: $i,SV6: $i] :
( ( ! [SY37: $i] :
( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SV15 )
| ~ ( aElement0 @ SY37 )
| ~ ( sdtlseqdt0 @ SV6 @ SV15 )
| ~ ( sdtlseqdt0 @ SV15 @ SY37 )
| ( sdtlseqdt0 @ SV6 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV7: $i] :
( ( ( ~ ( aSet0 @ SV7 ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( aSubsetOf0 @ SY30 @ SV7 )
| ! [SY31: $i,SY32: $i] :
( ~ ( aSupremumOfIn0 @ SY31 @ SY30 @ SV7 )
| ~ ( aSupremumOfIn0 @ SY32 @ SY30 @ SV7 )
| ( SY31 = SY32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV8: $i] :
( ( ( ~ ( aSet0 @ SV8 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( aSubsetOf0 @ SY33 @ SV8 )
| ! [SY34: $i,SY35: $i] :
( ~ ( aInfimumOfIn0 @ SY34 @ SY33 @ SV8 )
| ~ ( aInfimumOfIn0 @ SY35 @ SY33 @ SV8 )
| ( SY34 = SY35 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV10: $i] :
( ( ( ~ ( aFunction0 @ SV10 ) )
= $true )
| ( ( aSet0 @ ( szDzozmdt0 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV11: $i] :
( ( ( ~ ( aFunction0 @ SV11 ) )
= $true )
| ( ( aSet0 @ ( szRzazndt0 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV12: $i] :
( ( ( ~ ( aFunction0 @ SV12 ) )
= $true )
| ( ( ! [SY36: $i] :
( ~ ( aElementOf0 @ SY36 @ ( szDzozmdt0 @ SV12 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV12 @ SY36 ) @ ( szRzazndt0 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV13: $i] :
( ( aSupremumOfIn0 @ SV13 @ xT @ xS )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(111,plain,
( ( ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(112,plain,
( ( ~ ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(113,plain,
( ( ~ ( aFixedPointOf0 @ xp @ xf ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(114,plain,
( ( ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(115,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aCompleteLattice0 @ xU )
| ~ ( aFunction0 @ xf ) )
| ~ ( isMonotone0 @ xf ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(116,plain,
( ( ~ ( isOn0 @ xf @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(117,plain,
! [SV3: $i] :
( ( ( aSet0 @ SV3 )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( aElementOf0 @ SY26 @ SV3 )
| ( aElement0 @ SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV16: $i] :
( ( ( ~ ( aElement0 @ SV16 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aElement0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(119,plain,
! [SV4: $i] :
( ( ( aElement0 @ SV4 )
= $false )
| ( ( sdtlseqdt0 @ SV4 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( aElement0 @ SV5 )
| ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV5 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV5 )
| ( SV5 = SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(121,plain,
! [SV17: $i,SV15: $i,SV6: $i] :
( ( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SV15 )
| ~ ( aElement0 @ SV17 )
| ~ ( sdtlseqdt0 @ SV6 @ SV15 )
| ~ ( sdtlseqdt0 @ SV15 @ SV17 )
| ( sdtlseqdt0 @ SV6 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(122,plain,
! [SV7: $i] :
( ( ( aSet0 @ SV7 )
= $false )
| ( ( ! [SY30: $i] :
( ~ ( aSubsetOf0 @ SY30 @ SV7 )
| ! [SY31: $i,SY32: $i] :
( ~ ( aSupremumOfIn0 @ SY31 @ SY30 @ SV7 )
| ~ ( aSupremumOfIn0 @ SY32 @ SY30 @ SV7 )
| ( SY31 = SY32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(123,plain,
! [SV8: $i] :
( ( ( aSet0 @ SV8 )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( aSubsetOf0 @ SY33 @ SV8 )
| ! [SY34: $i,SY35: $i] :
( ~ ( aInfimumOfIn0 @ SY34 @ SY33 @ SV8 )
| ~ ( aInfimumOfIn0 @ SY35 @ SY33 @ SV8 )
| ( SY34 = SY35 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(124,plain,
! [SV10: $i] :
( ( ( aFunction0 @ SV10 )
= $false )
| ( ( aSet0 @ ( szDzozmdt0 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(125,plain,
! [SV11: $i] :
( ( ( aFunction0 @ SV11 )
= $false )
| ( ( aSet0 @ ( szRzazndt0 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(126,plain,
! [SV12: $i] :
( ( ( aFunction0 @ SV12 )
= $false )
| ( ( ! [SY36: $i] :
( ~ ( aElementOf0 @ SY36 @ ( szDzozmdt0 @ SV12 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV12 @ SY36 ) @ ( szRzazndt0 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(127,plain,
( ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(128,plain,
( ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(129,plain,
( ( aFixedPointOf0 @ xp @ xf )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(130,plain,
( ( aSupremumOfIn0 @ xp @ xT @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(131,plain,
( ( ~ ( ~ ~ ( ~ ( aCompleteLattice0 @ xU )
| ~ ( aFunction0 @ xf ) )
| ~ ( isMonotone0 @ xf ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(132,plain,
( ( isOn0 @ xf @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(133,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ( aElementOf0 @ SV18 @ SV3 )
| ( aElement0 @ SV18 ) )
= $true )
| ( ( aSet0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(134,plain,
! [SV16: $i] :
( ( ( aElement0 @ SV16 )
= $false )
| ( ( ! [W1: $i] :
~ ( aElement0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( aElement0 @ SV5 ) )
= $true )
| ( ( ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV5 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV5 )
| ( SV5 = SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(136,plain,
! [SV17: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SV15 )
| ~ ( aElement0 @ SV17 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV15 )
| ~ ( sdtlseqdt0 @ SV15 @ SV17 )
| ( sdtlseqdt0 @ SV6 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(137,plain,
! [SV7: $i,SV19: $i] :
( ( ( ~ ( aSubsetOf0 @ SV19 @ SV7 )
| ! [SY38: $i,SY39: $i] :
( ~ ( aSupremumOfIn0 @ SY38 @ SV19 @ SV7 )
| ~ ( aSupremumOfIn0 @ SY39 @ SV19 @ SV7 )
| ( SY38 = SY39 ) ) )
= $true )
| ( ( aSet0 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(138,plain,
! [SV8: $i,SV20: $i] :
( ( ( ~ ( aSubsetOf0 @ SV20 @ SV8 )
| ! [SY40: $i,SY41: $i] :
( ~ ( aInfimumOfIn0 @ SY40 @ SV20 @ SV8 )
| ~ ( aInfimumOfIn0 @ SY41 @ SV20 @ SV8 )
| ( SY40 = SY41 ) ) )
= $true )
| ( ( aSet0 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(139,plain,
! [SV12: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ SV21 @ ( szDzozmdt0 @ SV12 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV12 @ SV21 ) @ ( szRzazndt0 @ SV12 ) ) )
= $true )
| ( ( aFunction0 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(140,plain,
( ( ~ ~ ( ~ ( aCompleteLattice0 @ xU )
| ~ ( aFunction0 @ xf ) )
| ~ ( isMonotone0 @ xf ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ( aElementOf0 @ SV18 @ SV3 ) )
= $true )
| ( ( aElement0 @ SV18 )
= $true )
| ( ( aSet0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV16: $i,SV22: $i] :
( ( ( ~ ( aElement0 @ SV22 ) )
= $true )
| ( ( aElement0 @ SV16 )
= $false )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV14: $i,SV5: $i] :
( ( ( aElement0 @ SV5 )
= $false )
| ( ( ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV5 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV5 )
| ( SV5 = SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(144,plain,
! [SV17: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( aElement0 @ SV6 )
| ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( ~ ( aElement0 @ SV17 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV15 )
| ~ ( sdtlseqdt0 @ SV15 @ SV17 )
| ( sdtlseqdt0 @ SV6 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV7: $i,SV19: $i] :
( ( ( ~ ( aSubsetOf0 @ SV19 @ SV7 ) )
= $true )
| ( ( ! [SY38: $i,SY39: $i] :
( ~ ( aSupremumOfIn0 @ SY38 @ SV19 @ SV7 )
| ~ ( aSupremumOfIn0 @ SY39 @ SV19 @ SV7 )
| ( SY38 = SY39 ) ) )
= $true )
| ( ( aSet0 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(146,plain,
! [SV8: $i,SV20: $i] :
( ( ( ~ ( aSubsetOf0 @ SV20 @ SV8 ) )
= $true )
| ( ( ! [SY40: $i,SY41: $i] :
( ~ ( aInfimumOfIn0 @ SY40 @ SV20 @ SV8 )
| ~ ( aInfimumOfIn0 @ SY41 @ SV20 @ SV8 )
| ( SY40 = SY41 ) ) )
= $true )
| ( ( aSet0 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(147,plain,
! [SV12: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ SV21 @ ( szDzozmdt0 @ SV12 ) ) )
= $true )
| ( ( aElementOf0 @ ( sdtlpdtrp0 @ SV12 @ SV21 ) @ ( szRzazndt0 @ SV12 ) )
= $true )
| ( ( aFunction0 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(148,plain,
( ( ~ ~ ( ~ ( aCompleteLattice0 @ xU )
| ~ ( aFunction0 @ xf ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(149,plain,
( ( ~ ( isMonotone0 @ xf ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(150,plain,
! [SV3: $i,SV18: $i] :
( ( ( aElementOf0 @ SV18 @ SV3 )
= $false )
| ( ( aElement0 @ SV18 )
= $true )
| ( ( aSet0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(151,plain,
! [SV16: $i,SV22: $i] :
( ( ( aElement0 @ SV22 )
= $false )
| ( ( aElement0 @ SV16 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(152,plain,
! [SV5: $i,SV14: $i] :
( ( ( aElement0 @ SV14 )
= $false )
| ( ( aElement0 @ SV5 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV5 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV5 )
| ( SV5 = SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(153,plain,
! [SV17: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( aElement0 @ SV6 ) )
= $true )
| ( ( ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( ~ ( aElement0 @ SV17 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV15 )
| ~ ( sdtlseqdt0 @ SV15 @ SV17 )
| ( sdtlseqdt0 @ SV6 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(154,plain,
! [SV7: $i,SV19: $i] :
( ( ( aSubsetOf0 @ SV19 @ SV7 )
= $false )
| ( ( ! [SY38: $i,SY39: $i] :
( ~ ( aSupremumOfIn0 @ SY38 @ SV19 @ SV7 )
| ~ ( aSupremumOfIn0 @ SY39 @ SV19 @ SV7 )
| ( SY38 = SY39 ) ) )
= $true )
| ( ( aSet0 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(155,plain,
! [SV8: $i,SV20: $i] :
( ( ( aSubsetOf0 @ SV20 @ SV8 )
= $false )
| ( ( ! [SY40: $i,SY41: $i] :
( ~ ( aInfimumOfIn0 @ SY40 @ SV20 @ SV8 )
| ~ ( aInfimumOfIn0 @ SY41 @ SV20 @ SV8 )
| ( SY40 = SY41 ) ) )
= $true )
| ( ( aSet0 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(156,plain,
! [SV12: $i,SV21: $i] :
( ( ( aElementOf0 @ SV21 @ ( szDzozmdt0 @ SV12 ) )
= $false )
| ( ( aElementOf0 @ ( sdtlpdtrp0 @ SV12 @ SV21 ) @ ( szRzazndt0 @ SV12 ) )
= $true )
| ( ( aFunction0 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(157,plain,
( ( ~ ( ~ ( aCompleteLattice0 @ xU )
| ~ ( aFunction0 @ xf ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(158,plain,
( ( isMonotone0 @ xf )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(159,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV5 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV5 ) )
= $true )
| ( ( SV5 = SV14 )
= $true )
| ( ( aElement0 @ SV5 )
= $false )
| ( ( aElement0 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(160,plain,
! [SV17: $i,SV15: $i,SV6: $i] :
( ( ( aElement0 @ SV6 )
= $false )
| ( ( ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( ~ ( aElement0 @ SV17 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV15 )
| ~ ( sdtlseqdt0 @ SV15 @ SV17 )
| ( sdtlseqdt0 @ SV6 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV7: $i,SV19: $i,SV23: $i] :
( ( ( ! [SY42: $i] :
( ~ ( aSupremumOfIn0 @ SV23 @ SV19 @ SV7 )
| ~ ( aSupremumOfIn0 @ SY42 @ SV19 @ SV7 )
| ( SV23 = SY42 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV19 @ SV7 )
= $false )
| ( ( aSet0 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(162,plain,
! [SV8: $i,SV20: $i,SV24: $i] :
( ( ( ! [SY43: $i] :
( ~ ( aInfimumOfIn0 @ SV24 @ SV20 @ SV8 )
| ~ ( aInfimumOfIn0 @ SY43 @ SV20 @ SV8 )
| ( SV24 = SY43 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV8 )
= $false )
| ( ( aSet0 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(163,plain,
( ( ~ ( aCompleteLattice0 @ xU )
| ~ ( aFunction0 @ xf ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(164,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV5 @ SV14 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV5 ) )
= $true )
| ( ( SV5 = SV14 )
= $true )
| ( ( aElement0 @ SV5 )
= $false )
| ( ( aElement0 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(165,plain,
! [SV17: $i,SV6: $i,SV15: $i] :
( ( ( aElement0 @ SV15 )
= $false )
| ( ( aElement0 @ SV6 )
= $false )
| ( ( ~ ( aElement0 @ SV17 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV15 )
| ~ ( sdtlseqdt0 @ SV15 @ SV17 )
| ( sdtlseqdt0 @ SV6 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(166,plain,
! [SV25: $i,SV7: $i,SV19: $i,SV23: $i] :
( ( ( ~ ( aSupremumOfIn0 @ SV23 @ SV19 @ SV7 )
| ~ ( aSupremumOfIn0 @ SV25 @ SV19 @ SV7 )
| ( SV23 = SV25 ) )
= $true )
| ( ( aSubsetOf0 @ SV19 @ SV7 )
= $false )
| ( ( aSet0 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(167,plain,
! [SV26: $i,SV8: $i,SV20: $i,SV24: $i] :
( ( ( ~ ( aInfimumOfIn0 @ SV24 @ SV20 @ SV8 )
| ~ ( aInfimumOfIn0 @ SV26 @ SV20 @ SV8 )
| ( SV24 = SV26 ) )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV8 )
= $false )
| ( ( aSet0 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(168,plain,
( ( ~ ( aCompleteLattice0 @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(169,plain,
( ( ~ ( aFunction0 @ xf ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(170,plain,
! [SV14: $i,SV5: $i] :
( ( ( sdtlseqdt0 @ SV5 @ SV14 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV5 ) )
= $true )
| ( ( SV5 = SV14 )
= $true )
| ( ( aElement0 @ SV5 )
= $false )
| ( ( aElement0 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(171,plain,
! [SV15: $i,SV6: $i,SV17: $i] :
( ( ( aElement0 @ SV17 )
= $false )
| ( ( aElement0 @ SV6 )
= $false )
| ( ( aElement0 @ SV15 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV15 )
| ~ ( sdtlseqdt0 @ SV15 @ SV17 )
| ( sdtlseqdt0 @ SV6 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(172,plain,
! [SV25: $i,SV7: $i,SV19: $i,SV23: $i] :
( ( ( ~ ( aSupremumOfIn0 @ SV23 @ SV19 @ SV7 )
| ~ ( aSupremumOfIn0 @ SV25 @ SV19 @ SV7 ) )
= $true )
| ( ( SV23 = SV25 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ SV7 )
= $false )
| ( ( aSet0 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(173,plain,
! [SV26: $i,SV8: $i,SV20: $i,SV24: $i] :
( ( ( ~ ( aInfimumOfIn0 @ SV24 @ SV20 @ SV8 )
| ~ ( aInfimumOfIn0 @ SV26 @ SV20 @ SV8 ) )
= $true )
| ( ( SV24 = SV26 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV8 )
= $false )
| ( ( aSet0 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(174,plain,
( ( aCompleteLattice0 @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(175,plain,
( ( aFunction0 @ xf )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(176,plain,
! [SV5: $i,SV14: $i] :
( ( ( sdtlseqdt0 @ SV14 @ SV5 )
= $false )
| ( ( sdtlseqdt0 @ SV5 @ SV14 )
= $false )
| ( ( SV5 = SV14 )
= $true )
| ( ( aElement0 @ SV5 )
= $false )
| ( ( aElement0 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(177,plain,
! [SV17: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV6 @ SV15 )
| ~ ( sdtlseqdt0 @ SV15 @ SV17 ) )
= $true )
| ( ( sdtlseqdt0 @ SV6 @ SV17 )
= $true )
| ( ( aElement0 @ SV15 )
= $false )
| ( ( aElement0 @ SV6 )
= $false )
| ( ( aElement0 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(178,plain,
! [SV25: $i,SV7: $i,SV19: $i,SV23: $i] :
( ( ( ~ ( aSupremumOfIn0 @ SV23 @ SV19 @ SV7 ) )
= $true )
| ( ( ~ ( aSupremumOfIn0 @ SV25 @ SV19 @ SV7 ) )
= $true )
| ( ( SV23 = SV25 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ SV7 )
= $false )
| ( ( aSet0 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(179,plain,
! [SV26: $i,SV8: $i,SV20: $i,SV24: $i] :
( ( ( ~ ( aInfimumOfIn0 @ SV24 @ SV20 @ SV8 ) )
= $true )
| ( ( ~ ( aInfimumOfIn0 @ SV26 @ SV20 @ SV8 ) )
= $true )
| ( ( SV24 = SV26 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV8 )
= $false )
| ( ( aSet0 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(180,plain,
! [SV17: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV6 @ SV15 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV17 ) )
= $true )
| ( ( sdtlseqdt0 @ SV6 @ SV17 )
= $true )
| ( ( aElement0 @ SV15 )
= $false )
| ( ( aElement0 @ SV6 )
= $false )
| ( ( aElement0 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV25: $i,SV7: $i,SV19: $i,SV23: $i] :
( ( ( aSupremumOfIn0 @ SV23 @ SV19 @ SV7 )
= $false )
| ( ( ~ ( aSupremumOfIn0 @ SV25 @ SV19 @ SV7 ) )
= $true )
| ( ( SV23 = SV25 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ SV7 )
= $false )
| ( ( aSet0 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(182,plain,
! [SV26: $i,SV8: $i,SV20: $i,SV24: $i] :
( ( ( aInfimumOfIn0 @ SV24 @ SV20 @ SV8 )
= $false )
| ( ( ~ ( aInfimumOfIn0 @ SV26 @ SV20 @ SV8 ) )
= $true )
| ( ( SV24 = SV26 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV8 )
= $false )
| ( ( aSet0 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(183,plain,
! [SV17: $i,SV15: $i,SV6: $i] :
( ( ( sdtlseqdt0 @ SV6 @ SV15 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV17 ) )
= $true )
| ( ( sdtlseqdt0 @ SV6 @ SV17 )
= $true )
| ( ( aElement0 @ SV15 )
= $false )
| ( ( aElement0 @ SV6 )
= $false )
| ( ( aElement0 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(184,plain,
! [SV23: $i,SV7: $i,SV19: $i,SV25: $i] :
( ( ( aSupremumOfIn0 @ SV25 @ SV19 @ SV7 )
= $false )
| ( ( aSupremumOfIn0 @ SV23 @ SV19 @ SV7 )
= $false )
| ( ( SV23 = SV25 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ SV7 )
= $false )
| ( ( aSet0 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(185,plain,
! [SV24: $i,SV8: $i,SV20: $i,SV26: $i] :
( ( ( aInfimumOfIn0 @ SV26 @ SV20 @ SV8 )
= $false )
| ( ( aInfimumOfIn0 @ SV24 @ SV20 @ SV8 )
= $false )
| ( ( SV24 = SV26 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV8 )
= $false )
| ( ( aSet0 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(186,plain,
! [SV6: $i,SV17: $i,SV15: $i] :
( ( ( sdtlseqdt0 @ SV15 @ SV17 )
= $false )
| ( ( sdtlseqdt0 @ SV6 @ SV15 )
= $false )
| ( ( sdtlseqdt0 @ SV6 @ SV17 )
= $true )
| ( ( aElement0 @ SV15 )
= $false )
| ( ( aElement0 @ SV6 )
= $false )
| ( ( aElement0 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(187,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,186,185,184,176,175,174,158,156,151,150,132,130,129,128,127,125,124,119,110,92,84,83,63,62,61]) ).
thf(188,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT388+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 28 22:43:31 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 20
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 0
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.14/0.37 (rf:0,axioms:20,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:0,translation:fof_full)........
% 0.20/0.44
% 0.20/0.44 ********************************
% 0.20/0.44 * All subproblems solved! *
% 0.20/0.44 ********************************
% 0.20/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:187,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.46
% 0.20/0.46 %**** Beginning of derivation protocol ****
% 0.20/0.46 % SZS output start CNFRefutation
% See solution above
% 0.20/0.46
% 0.20/0.46 %**** End of derivation protocol ****
% 0.20/0.46 %**** no. of clauses in derivation: 188 ****
% 0.20/0.46 %**** clause counter: 187 ****
% 0.20/0.46
% 0.20/0.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:187,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------