TSTP Solution File: LAT387+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT387+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 15.03s 3.94s
% Output : Refutation 15.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 60
% Syntax : Number of formulae : 147 ( 29 unt; 30 typ; 0 def)
% Number of atoms : 569 ( 55 equ; 0 cnn)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 1569 ( 62 ~; 74 |; 188 &;1067 @)
% ( 10 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 12 con; 0-3 aty)
% Number of variables : 198 ( 0 ^; 185 !; 13 ?; 198 :)
% 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(xT_type,type,
xT: $i ).
thf(xS_type,type,
xS: $i ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(xP_type,type,
xP: $i ).
thf(xU_type,type,
xU: $i ).
thf(cS1241_type,type,
cS1241: $i > $i > $i > $i ).
thf(cS1142_type,type,
cS1142: $i > $i ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
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/sandbox/benchmark/theBenchmark.p',mTrans) ).
thf(101,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(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/sandbox/benchmark/theBenchmark.p',m__1123) ).
thf(111,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(132,plain,
( ( szRzazndt0 @ xf )
= xU ),
inference(cnf,[status(esa)],[111]) ).
thf(142,plain,
( ( szRzazndt0 @ xf )
= xU ),
inference(lifteq,[status(thm)],[132]) ).
thf(8,axiom,
( ! [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/sandbox/benchmark/theBenchmark.p',m__1299) ).
thf(52,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)],[8]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',m__1144) ).
thf(87,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)],[13]) ).
thf(88,plain,
( ( aSet0 @ xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ A )
= A )
& ( aFixedPointOf0 @ A @ xf ) ) )
& ! [A: $i] :
( ( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ A )
= A ) )
| ( aFixedPointOf0 @ A @ xf ) )
=> ( aElementOf0 @ A @ xS ) )
& ( xS
= ( cS1142 @ xf ) ) ),
inference(miniscope,[status(thm)],[87]) ).
thf(89,plain,
( xS
= ( cS1142 @ xf ) ),
inference(cnf,[status(esa)],[88]) ).
thf(97,plain,
( ( cS1142 @ xf )
= xS ),
inference(lifteq,[status(thm)],[89]) ).
thf(27,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mARefl) ).
thf(212,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(134,plain,
aFunction0 @ xf,
inference(cnf,[status(esa)],[111]) ).
thf(6,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(49,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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/sandbox/benchmark/theBenchmark.p',mDefLB) ).
thf(103,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(10,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/sandbox/benchmark/theBenchmark.p',m__1244) ).
thf(60,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)],[10]) ).
thf(61,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 ) ) )
& ! [A: $i] :
( ( ( 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(miniscope,[status(thm)],[60]) ).
thf(65,plain,
( xP
= ( cS1241 @ xU @ xf @ xT ) ),
inference(cnf,[status(esa)],[61]) ).
thf(72,plain,
( ( cS1241 @ xU @ xf @ xT )
= xP ),
inference(lifteq,[status(thm)],[65]) ).
thf(1,conjecture,
( ( ( ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ xp )
= xp ) )
| ( aFixedPointOf0 @ xp @ xf ) )
& ( ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( sdtlseqdt0 @ A @ xp ) )
| ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xS )
& ! [B: $i] :
( ( aElementOf0 @ B @ xT )
=> ( sdtlseqdt0 @ B @ A ) )
& ( aUpperBoundOfIn0 @ A @ xT @ xS ) )
=> ( sdtlseqdt0 @ xp @ A ) ) )
| ( aSupremumOfIn0 @ xp @ xT @ xS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ xp )
= xp ) )
| ( aFixedPointOf0 @ xp @ xf ) )
& ( ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( sdtlseqdt0 @ A @ xp ) )
| ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xS )
& ! [B: $i] :
( ( aElementOf0 @ B @ xT )
=> ( sdtlseqdt0 @ B @ A ) )
& ( aUpperBoundOfIn0 @ A @ xT @ xS ) )
=> ( sdtlseqdt0 @ xp @ A ) ) )
| ( aSupremumOfIn0 @ xp @ xT @ xS ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(32,plain,
~ ( ( ( ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ xp )
= xp ) )
| ( aFixedPointOf0 @ xp @ xf ) )
& ( ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( sdtlseqdt0 @ A @ xp ) )
| ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xS )
& ! [B: $i] :
( ( aElementOf0 @ B @ xT )
=> ( sdtlseqdt0 @ B @ A ) )
& ( aUpperBoundOfIn0 @ A @ xT @ xS ) )
=> ( sdtlseqdt0 @ xp @ A ) ) )
| ( aSupremumOfIn0 @ xp @ xT @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,plain,
( sk1
| sk2
| ( aUpperBoundOfIn0 @ sk4 @ xT @ xS ) ),
inference(cnf,[status(esa)],[32]) ).
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/sandbox/benchmark/theBenchmark.p',m__1261) ).
thf(217,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(34,plain,
( sk1
| sk2
| ( aElementOf0 @ sk4 @ xS ) ),
inference(cnf,[status(esa)],[32]) ).
thf(20,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isEmpty0 @ A )
<=> ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmpty) ).
thf(173,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(174,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isEmpty0 @ A )
| ~ ( aElementOf0 @ B @ A ) ),
inference(cnf,[status(esa)],[173]) ).
thf(236,plain,
! [B: $i,A: $i] :
( sk1
| sk2
| ~ ( aSet0 @ A )
| ~ ( isEmpty0 @ A )
| ( ( aElementOf0 @ sk4 @ xS )
!= ( aElementOf0 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,174]) ).
thf(237,plain,
( sk1
| sk2
| ~ ( aSet0 @ xS )
| ~ ( isEmpty0 @ xS ) ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( xS )),bind(B,$thf( sk4 ))]]) ).
thf(95,plain,
aSet0 @ xS,
inference(cnf,[status(esa)],[88]) ).
thf(268,plain,
( sk1
| sk2
| ~ $true
| ~ ( isEmpty0 @ xS ) ),
inference(rewrite,[status(thm)],[237,95]) ).
thf(269,plain,
( sk1
| sk2
| ~ ( isEmpty0 @ xS ) ),
inference(simp,[status(thm)],[268]) ).
thf(25,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
thf(202,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)],[25]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',mDefMonot) ).
thf(185,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)],[22]) ).
thf(37,plain,
! [A: $i] :
( sk1
| sk2
| ~ ( aElementOf0 @ A @ xT )
| ( sdtlseqdt0 @ A @ sk4 ) ),
inference(cnf,[status(esa)],[32]) ).
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/sandbox/benchmark/theBenchmark.p',mInfUn) ).
thf(46,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(31,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/sandbox/benchmark/theBenchmark.p',mSupUn) ).
thf(228,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)],[31]) ).
thf(11,axiom,
( ( aSet0 @ xT )
& ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xT @ xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1173) ).
thf(75,plain,
( ( aSet0 @ xT )
& ! [A: $i] :
( ( aElementOf0 @ A @ xT )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xT @ xS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(78,plain,
aSet0 @ xT,
inference(cnf,[status(esa)],[75]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRel) ).
thf(216,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
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/sandbox/benchmark/theBenchmark.p',mDefInf) ).
thf(164,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(121,plain,
aSet0 @ xU,
inference(cnf,[status(esa)],[111]) ).
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/sandbox/benchmark/theBenchmark.p',mDefSup) ).
thf(147,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(221,plain,
aLowerBoundOfIn0 @ xp @ xP @ xU,
inference(cnf,[status(esa)],[217]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ~ ( isEmpty0 @ A )
| ~ ( aElementOf0 @ B @ A )
| ( ( aSet0 @ xT )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[78,174]) ).
thf(233,plain,
! [A: $i] :
( ~ ( isEmpty0 @ xT )
| ~ ( aElementOf0 @ A @ xT ) ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( xT ))]]) ).
thf(243,plain,
! [A: $i] :
( ~ ( isEmpty0 @ xT )
| ~ ( aElementOf0 @ A @ xT ) ),
inference(simp,[status(thm)],[233]) ).
thf(220,plain,
aElementOf0 @ xp @ xU,
inference(cnf,[status(esa)],[217]) ).
thf(117,plain,
aCompleteLattice0 @ xU,
inference(cnf,[status(esa)],[111]) ).
thf(38,plain,
( sk1
| ( aElementOf0 @ sk3 @ xT )
| ~ sk2 ),
inference(cnf,[status(esa)],[32]) ).
thf(70,plain,
aSet0 @ xP,
inference(cnf,[status(esa)],[61]) ).
thf(33,plain,
( sk1
| ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS )
| ~ sk2 ),
inference(cnf,[status(esa)],[32]) ).
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/sandbox/benchmark/theBenchmark.p',mDefUB) ).
thf(156,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(53,plain,
aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU,
inference(cnf,[status(esa)],[52]) ).
thf(41,plain,
( ~ ( aFixedPointOf0 @ xp @ xf )
| ~ sk1 ),
inference(cnf,[status(esa)],[32]) ).
thf(124,plain,
( ( szDzozmdt0 @ xf )
= ( szRzazndt0 @ xf ) ),
inference(cnf,[status(esa)],[111]) ).
thf(137,plain,
( ( szRzazndt0 @ xf )
= ( szDzozmdt0 @ xf ) ),
inference(lifteq,[status(thm)],[124]) ).
thf(264,plain,
( ( szDzozmdt0 @ xf )
= xU ),
inference(rewrite,[status(thm)],[137,142]) ).
thf(4,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConMap) ).
thf(45,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',mDefCLat) ).
thf(176,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)],[21]) ).
thf(23,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aFixedPointOf0 @ B @ A )
<=> ( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefFix) ).
thf(191,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)],[23]) ).
thf(3,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetSort) ).
thf(44,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(113,plain,
isOn0 @ xf @ xU,
inference(cnf,[status(esa)],[111]) ).
thf(76,plain,
aSubsetOf0 @ xT @ xS,
inference(cnf,[status(esa)],[75]) ).
thf(39,plain,
( sk1
| ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) ),
inference(cnf,[status(esa)],[32]) ).
thf(130,plain,
isMonotone0 @ xf,
inference(cnf,[status(esa)],[111]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isEmpty0 @ A )
| ( ( aElementOf0 @ xp @ xU )
!= ( aElementOf0 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[220,174]) ).
thf(257,plain,
( ~ ( aSet0 @ xU )
| ~ ( isEmpty0 @ xU ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( xU )),bind(B,$thf( xp ))]]) ).
thf(266,plain,
( ~ $true
| ~ ( isEmpty0 @ xU ) ),
inference(rewrite,[status(thm)],[257,121]) ).
thf(267,plain,
~ ( isEmpty0 @ xU ),
inference(simp,[status(thm)],[266]) ).
thf(35,plain,
( sk1
| ~ ( sdtlseqdt0 @ sk3 @ xp )
| ~ sk2 ),
inference(cnf,[status(esa)],[32]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ~ ( isEmpty0 @ A )
| ~ ( aElementOf0 @ B @ A )
| ( ( aSet0 @ xP )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70,174]) ).
thf(241,plain,
! [A: $i] :
( ~ ( isEmpty0 @ xP )
| ~ ( aElementOf0 @ A @ xP ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( xP ))]]) ).
thf(242,plain,
! [A: $i] :
( ~ ( isEmpty0 @ xP )
| ~ ( aElementOf0 @ A @ xP ) ),
inference(simp,[status(thm)],[241]) ).
thf(259,plain,
! [A: $i] :
( ~ ( isEmpty0 @ xP )
| ( ( aElementOf0 @ xp @ xU )
!= ( aElementOf0 @ A @ xP ) ) ),
inference(paramod_ordered,[status(thm)],[220,242]) ).
thf(261,plain,
! [A: $i] :
( ~ ( isEmpty0 @ xP )
| ( xp != A )
| ( xU != xP ) ),
inference(simp,[status(thm)],[259]) ).
thf(263,plain,
( ~ ( isEmpty0 @ xP )
| ( xU != xP ) ),
inference(simp,[status(thm)],[261]) ).
thf(7,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szRzazndt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mRanSort) ).
thf(50,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szRzazndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mASymm) ).
thf(199,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)],[24]) ).
thf(218,plain,
aInfimumOfIn0 @ xp @ xP @ xU,
inference(cnf,[status(esa)],[217]) ).
thf(40,plain,
( sk1
| sk2
| ~ ( sdtlseqdt0 @ xp @ sk4 ) ),
inference(cnf,[status(esa)],[32]) ).
thf(55,plain,
aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU,
inference(cnf,[status(esa)],[52]) ).
thf(28,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( szRzazndt0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgSort) ).
thf(214,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(284,plain,
! [A: $i] :
( ~ ( isEmpty0 @ xT )
| ( ( aElementOf0 @ xp @ xU )
!= ( aElementOf0 @ A @ xT ) ) ),
inference(paramod_ordered,[status(thm)],[220,243]) ).
thf(288,plain,
! [A: $i] :
( ~ ( isEmpty0 @ xT )
| ( xp != A )
| ( xU != xT ) ),
inference(simp,[status(thm)],[284]) ).
thf(290,plain,
( ~ ( isEmpty0 @ xT )
| ( xU != xT ) ),
inference(simp,[status(thm)],[288]) ).
thf(9,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDomSort) ).
thf(58,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(210,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aSet0 @ B ) )
=> ( ( isOn0 @ A @ B )
<=> ( ( ( szDzozmdt0 @ A )
= ( szRzazndt0 @ A ) )
& ( ( szRzazndt0 @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDom) ).
thf(79,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)],[12]) ).
thf(3800,plain,
$false,
inference(cvc4,[status(thm)],[101,142,52,97,212,134,49,103,72,36,111,217,269,202,174,185,37,46,228,78,216,164,121,147,221,243,220,60,117,38,70,33,156,53,173,41,264,45,32,34,176,191,44,113,76,39,130,267,35,95,263,50,199,87,218,40,55,75,214,290,58,210,242,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT387+4 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 14:20:43 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.97/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.06 % [INFO] Parsing done (156ms).
% 1.38/1.07 % [INFO] Running in sequential loop mode.
% 1.91/1.27 % [INFO] eprover registered as external prover.
% 1.91/1.27 % [INFO] cvc4 registered as external prover.
% 1.91/1.28 % [INFO] Scanning for conjecture ...
% 1.91/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.11/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.11/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.11/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.11/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.11/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.11/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.11/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.11/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.29/1.37 % [INFO] Found a conjecture and 29 axioms. Running axiom selection ...
% 2.29/1.43 % [INFO] Axiom selection finished. Selected 29 axioms (removed 0 axioms).
% 2.29/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.29/1.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.47 % [INFO] Problem is first-order (TPTP FOF).
% 2.63/1.48 % [INFO] Type checking passed.
% 2.63/1.48 % [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 ...
% 15.03/3.93 % External prover 'cvc4' found a proof!
% 15.03/3.93 % [INFO] Killing All external provers ...
% 15.03/3.94 % Time passed: 3412ms (effective reasoning time: 2866ms)
% 15.03/3.94 % 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)>
% 15.03/3.94 % Axioms used in derivation (29): mDefSup, mDefLB, mInfUn, mSetSort, mImgSort, mDefInf, mConMap, mLessRel, m__1261, mASymm, mElmSort, mRanSort, mDefSub, mSupUn, m__1244, mDefUB, mTrans, mDefFix, m__1144, m__1299, mARefl, mDefDom, mEOfElem, mDefEmpty, mDefCLat, m__1123, mDefMonot, mDomSort, m__1173
% 15.03/3.94 % No. of inferences in proof: 117
% 15.03/3.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3412 ms resp. 2866 ms w/o parsing
% 15.03/3.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.03/3.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------