TSTP Solution File: LAT386+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT386+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 : 300s
% DateTime : Fri May 19 11:28:14 EDT 2023
% Result : Theorem 38.03s 9.61s
% Output : Refutation 38.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 55
% Syntax : Number of formulae : 86 ( 5 unt; 26 typ; 0 def)
% Number of atoms : 399 ( 27 equ; 0 cnn)
% Maximal formula atoms : 37 ( 6 avg)
% Number of connectives : 1168 ( 5 ~; 18 |; 156 &; 824 @)
% ( 10 <=>; 155 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 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 : 166 ( 0 ^; 153 !; 13 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(isEmpty0_type,type,
isEmpty0: $i > $o ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_type,type,
aSubsetOf0: $i > $i > $o ).
thf(aLowerBoundOfIn0_type,type,
aLowerBoundOfIn0: $i > $i > $i > $o ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(aUpperBoundOfIn0_type,type,
aUpperBoundOfIn0: $i > $i > $i > $o ).
thf(aInfimumOfIn0_type,type,
aInfimumOfIn0: $i > $i > $i > $o ).
thf(aSupremumOfIn0_type,type,
aSupremumOfIn0: $i > $i > $i > $o ).
thf(aCompleteLattice0_type,type,
aCompleteLattice0: $i > $o ).
thf(aFunction0_type,type,
aFunction0: $i > $o ).
thf(isOn0_type,type,
isOn0: $i > $i > $o ).
thf(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
thf(szRzazndt0_type,type,
szRzazndt0: $i > $i ).
thf(aFixedPointOf0_type,type,
aFixedPointOf0: $i > $i > $o ).
thf(sdtlpdtrp0_type,type,
sdtlpdtrp0: $i > $i > $i ).
thf(isMonotone0_type,type,
isMonotone0: $i > $o ).
thf(xP_type,type,
xP: $i ).
thf(xf_type,type,
xf: $i ).
thf(xp_type,type,
xp: $i ).
thf(xU_type,type,
xU: $i ).
thf(xT_type,type,
xT: $i ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(cS1241_type,type,
cS1241: $i > $i > $i > $i ).
thf(xS_type,type,
xS: $i ).
thf(cS1142_type,type,
cS1142: $i > $i ).
thf(18,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( aUpperBoundOfIn0 @ C @ B @ A )
<=> ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefUB) ).
thf(142,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( ( aUpperBoundOfIn0 @ C @ B @ A )
=> ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ D @ C ) ) ) )
& ( ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ D @ C ) ) )
=> ( aUpperBoundOfIn0 @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
( ( aSet0 @ xS )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xS )
=> ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ A )
= A )
& ( aFixedPointOf0 @ A @ xf ) ) )
& ( ( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ A )
= A ) )
| ( aFixedPointOf0 @ A @ xf ) )
=> ( aElementOf0 @ A @ xS ) ) )
& ( xS
= ( cS1142 @ xf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1144) ).
thf(189,plain,
( ( aSet0 @ xS )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xS )
=> ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ A )
= A )
& ( aFixedPointOf0 @ A @ xf ) ) )
& ( ( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ A )
= A ) )
| ( aFixedPointOf0 @ A @ xf ) )
=> ( aElementOf0 @ A @ xS ) ) )
& ( xS
= ( cS1142 @ xf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(24,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
thf(179,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ A )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) )
=> ( aSubsetOf0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(38,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( szRzazndt0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgSort) ).
thf(205,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( szRzazndt0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
! [A: $i] :
( ( aCompleteLattice0 @ A )
<=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ? [C: $i] :
( ( aInfimumOfIn0 @ C @ B @ A )
& ? [D: $i] : ( aSupremumOfIn0 @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCLat) ).
thf(45,plain,
! [A: $i] :
( ( ( aCompleteLattice0 @ A )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ? [C: $i] :
( ( aInfimumOfIn0 @ C @ B @ A )
& ? [D: $i] : ( aSupremumOfIn0 @ D @ B @ A ) ) ) ) )
& ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ? [C: $i] :
( ( aInfimumOfIn0 @ C @ B @ A )
& ? [D: $i] : ( aSupremumOfIn0 @ D @ B @ A ) ) ) )
=> ( aCompleteLattice0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mASymm) ).
thf(176,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( ( isMonotone0 @ A )
<=> ! [B: $i,C: $i] :
( ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) ) )
=> ( ( sdtlseqdt0 @ B @ C )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlpdtrp0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMonot) ).
thf(162,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( ( ( isMonotone0 @ A )
=> ! [B: $i,C: $i] :
( ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) ) )
=> ( ( sdtlseqdt0 @ B @ C )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlpdtrp0 @ A @ C ) ) ) ) )
& ( ! [B: $i,C: $i] :
( ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) ) )
=> ( ( sdtlseqdt0 @ B @ C )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlpdtrp0 @ A @ C ) ) ) )
=> ( isMonotone0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ A ) )
| ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
& ( ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( sdtlseqdt0 @ A @ ( sdtlpdtrp0 @ xf @ xp ) ) )
| ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ A ) )
| ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
& ( ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( sdtlseqdt0 @ A @ ( sdtlpdtrp0 @ xf @ xp ) ) )
| ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ A ) )
| ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
& ( ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( sdtlseqdt0 @ A @ ( sdtlpdtrp0 @ xf @ xp ) ) )
| ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSort) ).
thf(43,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRel) ).
thf(207,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(22,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aFixedPointOf0 @ B @ A )
<=> ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefFix) ).
thf(168,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( ( aFixedPointOf0 @ B @ A )
=> ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ B )
= B ) ) )
& ( ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ B )
= B ) )
=> ( aFixedPointOf0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
( ( aSet0 @ xP )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xP )
=> ( ( aElementOf0 @ A @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ A ) @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ xT )
=> ( sdtlseqdt0 @ B @ A ) )
& ( aUpperBoundOfIn0 @ A @ xT @ xU ) ) )
& ( ( ( aElementOf0 @ A @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ A ) @ A )
& ( ! [B: $i] :
( ( aElementOf0 @ B @ xT )
=> ( sdtlseqdt0 @ B @ A ) )
| ( aUpperBoundOfIn0 @ A @ xT @ xU ) ) )
=> ( aElementOf0 @ A @ xP ) ) )
& ( xP
= ( cS1241 @ xU @ xf @ xT ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1244) ).
thf(68,plain,
( ( aSet0 @ xP )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xP )
=> ( ( aElementOf0 @ A @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ A ) @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ xT )
=> ( sdtlseqdt0 @ B @ A ) )
& ( aUpperBoundOfIn0 @ A @ xT @ xU ) ) )
& ( ( ( aElementOf0 @ A @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ A ) @ A )
& ( ! [B: $i] :
( ( aElementOf0 @ B @ xT )
=> ( sdtlseqdt0 @ B @ A ) )
| ( aUpperBoundOfIn0 @ A @ xT @ xU ) ) )
=> ( aElementOf0 @ A @ xP ) ) )
& ( xP
= ( cS1241 @ xU @ xf @ xT ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
( ( aSet0 @ xT )
& ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xT @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1173) ).
thf(83,plain,
( ( aSet0 @ xT )
& ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xT @ xS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( aLowerBoundOfIn0 @ C @ B @ A )
<=> ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLB) ).
thf(89,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( ( aLowerBoundOfIn0 @ C @ B @ A )
=> ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ C @ D ) ) ) )
& ( ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ C @ D ) ) )
=> ( aLowerBoundOfIn0 @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(17,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( aSupremumOfIn0 @ C @ B @ A )
<=> ( ( aElementOf0 @ C @ A )
& ( aUpperBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aUpperBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSup) ).
thf(133,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( ( aSupremumOfIn0 @ C @ B @ A )
=> ( ( aElementOf0 @ C @ A )
& ( aUpperBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aUpperBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ C @ D ) ) ) )
& ( ( ( aElementOf0 @ C @ A )
& ( aUpperBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aUpperBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ C @ D ) ) )
=> ( aSupremumOfIn0 @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( aSupremumOfIn0 @ C @ B @ A )
& ( aSupremumOfIn0 @ D @ B @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSupUn) ).
thf(65,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( aSupremumOfIn0 @ C @ B @ A )
& ( aSupremumOfIn0 @ D @ B @ A ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
( ( aSet0 @ xU )
& ! [A: $i] :
( ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xU ) ) )
| ( aSubsetOf0 @ A @ xU ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xU )
& ( aElementOf0 @ B @ xU )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) )
& ( aLowerBoundOfIn0 @ B @ A @ xU )
& ! [C: $i] :
( ( ( ( aElementOf0 @ C @ xU )
& ! [D: $i] :
( ( aElementOf0 @ D @ A )
=> ( sdtlseqdt0 @ C @ D ) ) )
| ( aLowerBoundOfIn0 @ C @ A @ xU ) )
=> ( sdtlseqdt0 @ C @ B ) )
& ( aInfimumOfIn0 @ B @ A @ xU )
& ? [C: $i] :
( ( aElementOf0 @ C @ xU )
& ( aElementOf0 @ C @ xU )
& ! [D: $i] :
( ( aElementOf0 @ D @ A )
=> ( sdtlseqdt0 @ D @ C ) )
& ( aUpperBoundOfIn0 @ C @ A @ xU )
& ! [D: $i] :
( ( ( ( aElementOf0 @ D @ xU )
& ! [E: $i] :
( ( aElementOf0 @ E @ A )
=> ( sdtlseqdt0 @ E @ D ) ) )
| ( aUpperBoundOfIn0 @ D @ A @ xU ) )
=> ( sdtlseqdt0 @ C @ D ) )
& ( aSupremumOfIn0 @ C @ A @ xU ) ) ) )
& ( aCompleteLattice0 @ xU )
& ( aFunction0 @ xf )
& ! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xf ) )
& ( aElementOf0 @ B @ ( szDzozmdt0 @ xf ) ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ A ) @ ( sdtlpdtrp0 @ xf @ B ) ) ) )
& ( isMonotone0 @ xf )
& ( ( szDzozmdt0 @ xf )
= ( szRzazndt0 @ xf ) )
& ( ( szRzazndt0 @ xf )
= xU )
& ( isOn0 @ xf @ xU ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1123) ).
thf(97,plain,
( ( aSet0 @ xU )
& ! [A: $i] :
( ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xU ) ) )
| ( aSubsetOf0 @ A @ xU ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xU )
& ( aElementOf0 @ B @ xU )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) )
& ( aLowerBoundOfIn0 @ B @ A @ xU )
& ! [C: $i] :
( ( ( ( aElementOf0 @ C @ xU )
& ! [D: $i] :
( ( aElementOf0 @ D @ A )
=> ( sdtlseqdt0 @ C @ D ) ) )
| ( aLowerBoundOfIn0 @ C @ A @ xU ) )
=> ( sdtlseqdt0 @ C @ B ) )
& ( aInfimumOfIn0 @ B @ A @ xU )
& ? [C: $i] :
( ( aElementOf0 @ C @ xU )
& ( aElementOf0 @ C @ xU )
& ! [D: $i] :
( ( aElementOf0 @ D @ A )
=> ( sdtlseqdt0 @ D @ C ) )
& ( aUpperBoundOfIn0 @ C @ A @ xU )
& ! [D: $i] :
( ( ( ( aElementOf0 @ D @ xU )
& ! [E: $i] :
( ( aElementOf0 @ E @ A )
=> ( sdtlseqdt0 @ E @ D ) ) )
| ( aUpperBoundOfIn0 @ D @ A @ xU ) )
=> ( sdtlseqdt0 @ C @ D ) )
& ( aSupremumOfIn0 @ C @ A @ xU ) ) ) )
& ( aCompleteLattice0 @ xU )
& ( aFunction0 @ xf )
& ! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xf ) )
& ( aElementOf0 @ B @ ( szDzozmdt0 @ xf ) ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ A ) @ ( sdtlpdtrp0 @ xf @ B ) ) ) )
& ( isMonotone0 @ xf )
& ( ( szDzozmdt0 @ xf )
= ( szRzazndt0 @ xf ) )
& ( ( szRzazndt0 @ xf )
= xU )
& ( isOn0 @ xf @ xU ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(54,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isEmpty0 @ A )
<=> ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmpty) ).
thf(159,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( isEmpty0 @ A )
=> ~ ? [B: $i] : ( aElementOf0 @ B @ A ) )
& ( ~ ? [B: $i] : ( aElementOf0 @ B @ A )
=> ( isEmpty0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(187,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConMap) ).
thf(39,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
( ( aElementOf0 @ xp @ xU )
& ( aElementOf0 @ xp @ xU )
& ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( sdtlseqdt0 @ xp @ A ) )
& ( aLowerBoundOfIn0 @ xp @ xP @ xU )
& ! [A: $i] :
( ( ( ( aElementOf0 @ A @ xU )
& ! [B: $i] :
( ( aElementOf0 @ B @ xP )
=> ( sdtlseqdt0 @ A @ B ) ) )
| ( aLowerBoundOfIn0 @ A @ xP @ xU ) )
=> ( sdtlseqdt0 @ A @ xp ) )
& ( aInfimumOfIn0 @ xp @ xP @ xU ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1261) ).
thf(208,plain,
( ( aElementOf0 @ xp @ xU )
& ( aElementOf0 @ xp @ xU )
& ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( sdtlseqdt0 @ xp @ A ) )
& ( aLowerBoundOfIn0 @ xp @ xP @ xU )
& ! [A: $i] :
( ( ( ( aElementOf0 @ A @ xU )
& ! [B: $i] :
( ( aElementOf0 @ B @ xP )
=> ( sdtlseqdt0 @ A @ B ) ) )
| ( aLowerBoundOfIn0 @ A @ xP @ xU ) )
=> ( sdtlseqdt0 @ A @ xp ) )
& ( aInfimumOfIn0 @ xp @ xP @ xU ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(10,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szRzazndt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mRanSort) ).
thf(63,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szRzazndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( aInfimumOfIn0 @ C @ B @ A )
<=> ( ( aElementOf0 @ C @ A )
& ( aLowerBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aLowerBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInf) ).
thf(150,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( ( aInfimumOfIn0 @ C @ B @ A )
=> ( ( aElementOf0 @ C @ A )
& ( aLowerBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aLowerBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ D @ C ) ) ) )
& ( ( ( aElementOf0 @ C @ A )
& ( aLowerBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aLowerBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ D @ C ) ) )
=> ( aInfimumOfIn0 @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTrans) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(27,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mARefl) ).
thf(203,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(5,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( aInfimumOfIn0 @ C @ B @ A )
& ( aInfimumOfIn0 @ D @ B @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mInfUn) ).
thf(40,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( aInfimumOfIn0 @ C @ B @ A )
& ( aInfimumOfIn0 @ D @ B @ A ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aSet0 @ B ) )
=> ( ( isOn0 @ A @ B )
<=> ( ( ( szDzozmdt0 @ A )
= ( szRzazndt0 @ A ) )
& ( ( szRzazndt0 @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDom) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aSet0 @ B ) )
=> ( ( ( isOn0 @ A @ B )
=> ( ( ( szDzozmdt0 @ A )
= ( szRzazndt0 @ A ) )
& ( ( szRzazndt0 @ A )
= B ) ) )
& ( ( ( ( szDzozmdt0 @ A )
= ( szRzazndt0 @ A ) )
& ( ( szRzazndt0 @ A )
= B ) )
=> ( isOn0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26642,plain,
$false,
inference(cvc4,[status(thm)],[142,189,179,38,205,45,176,162,31,43,207,168,68,83,89,133,65,97,54,159,187,39,208,63,150,87,203,40,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT386+4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n006.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 14:17:37 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.87/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.99 % [INFO] Parsing done (135ms).
% 1.17/1.00 % [INFO] Running in sequential loop mode.
% 1.84/1.19 % [INFO] eprover registered as external prover.
% 1.84/1.19 % [INFO] cvc4 registered as external prover.
% 1.84/1.20 % [INFO] Scanning for conjecture ...
% 1.92/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.29 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ...
% 2.19/1.35 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.19/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.19/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.42/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.42/1.39 % [INFO] Type checking passed.
% 2.42/1.39 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 37.99/9.61 % External prover 'cvc4' found a proof!
% 37.99/9.61 % [INFO] Killing All external provers ...
% 37.99/9.61 % Time passed: 9086ms (effective reasoning time: 8610ms)
% 37.99/9.61 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 38.03/9.61 % Axioms used in derivation (28): mDefSup, mARefl, mDefLB, mInfUn, mSetSort, mImgSort, mDefInf, mConMap, mLessRel, m__1261, mASymm, mElmSort, mRanSort, mDefSub, mSupUn, m__1244, mDefUB, mTrans, mDefFix, m__1144, mDefDom, mEOfElem, mDefEmpty, mDefCLat, m__1123, mDefMonot, mDomSort, m__1173
% 38.03/9.61 % No. of inferences in proof: 60
% 38.03/9.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9086 ms resp. 8610 ms w/o parsing
% 38.03/9.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.03/9.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------