TSTP Solution File: NUM441+6 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:40:35 EDT 2023
% Result : Theorem 6.12s 2.54s
% Output : Refutation 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 64
% Syntax : Number of formulae : 107 ( 10 unt; 23 typ; 0 def)
% Number of atoms : 760 ( 106 equ; 0 cnn)
% Maximal formula atoms : 74 ( 9 avg)
% Number of connectives : 2340 ( 66 ~; 37 |; 401 &;1598 @)
% ( 33 <=>; 205 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 255 ( 0 ^; 220 !; 35 ?; 255 :)
% Comments :
%------------------------------------------------------------------------------
thf(aInteger0_type,type,
aInteger0: $i > $o ).
thf(aDivisorOf0_type,type,
aDivisorOf0: $i > $i > $o ).
thf(sz00_type,type,
sz00: $i ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(aSubsetOf0_type,type,
aSubsetOf0: $i > $i > $o ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(cS1395_type,type,
cS1395: $i ).
thf(sdtbsmnsldt0_type,type,
sdtbsmnsldt0: $i > $i > $i ).
thf(sdtslmnbsdt0_type,type,
sdtslmnbsdt0: $i > $i > $i ).
thf(sbsmnsldt0_type,type,
sbsmnsldt0: $i > $i ).
thf(stldt0_type,type,
stldt0: $i > $i ).
thf(szAzrzSzezqlpdtcmdtrp0_type,type,
szAzrzSzezqlpdtcmdtrp0: $i > $i > $i ).
thf(isOpen0_type,type,
isOpen0: $i > $o ).
thf(isClosed0_type,type,
isClosed0: $i > $o ).
thf(xA_type,type,
xA: $i ).
thf(xB_type,type,
xB: $i ).
thf(isPrime0_type,type,
isPrime0: $i > $o ).
thf(sz10_type,type,
sz10: $i ).
thf(isFinite0_type,type,
isFinite0: $i > $o ).
thf(27,axiom,
! [A: $i] :
( ( aSubsetOf0 @ A @ cS1395 )
=> ! [B: $i] :
( ( B
= ( stldt0 @ A ) )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
<=> ( ( aInteger0 @ C )
& ~ ( aElementOf0 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mComplement) ).
thf(385,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ cS1395 )
=> ! [B: $i] :
( ( ( B
= ( stldt0 @ A ) )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aInteger0 @ C )
& ~ ( aElementOf0 @ C @ A ) ) )
& ( ( ( aInteger0 @ C )
& ~ ( aElementOf0 @ C @ A ) )
=> ( aElementOf0 @ C @ B ) ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aInteger0 @ C )
& ~ ( aElementOf0 @ C @ A ) ) )
& ( ( ( aInteger0 @ C )
& ~ ( aElementOf0 @ C @ A ) )
=> ( aElementOf0 @ C @ B ) ) ) )
=> ( B
= ( stldt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
thf(316,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(19,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElements) ).
thf(321,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ! [B: $i] :
( ( aDivisorOf0 @ B @ A )
<=> ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
thf(302,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ! [B: $i] :
( ( ( aDivisorOf0 @ B @ A )
=> ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) ) )
& ( ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) )
=> ( aDivisorOf0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ cS1395 )
& ( aSubsetOf0 @ B @ cS1395 )
& ( isOpen0 @ A )
& ( isOpen0 @ B ) )
=> ( isOpen0 @ ( sdtslmnbsdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mInterOpen) ).
thf(343,plain,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ cS1395 )
& ( aSubsetOf0 @ B @ cS1395 )
& ( isOpen0 @ A )
& ( isOpen0 @ B ) )
=> ( isOpen0 @ ( sdtslmnbsdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(40,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
thf(540,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ cS1395 )
& ( aSubsetOf0 @ B @ cS1395 ) )
=> ! [C: $i] :
( ( C
= ( sdtslmnbsdt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aInteger0 @ D )
& ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntersection) ).
thf(345,plain,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ cS1395 )
& ( aSubsetOf0 @ B @ cS1395 ) )
=> ! [C: $i] :
( ( ( C
= ( sdtslmnbsdt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aInteger0 @ D )
& ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) ) )
& ( ( ( aInteger0 @ D )
& ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aInteger0 @ D )
& ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) ) )
& ( ( ( aInteger0 @ D )
& ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtslmnbsdt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 )
& ( aInteger0 @ D )
& ( D != sz00 ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ ( sdtasdt0 @ C @ D ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
& ( sdteqdtlpzmzozddtrp0 @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModMul) ).
thf(505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 )
& ( aInteger0 @ D )
& ( D != sz00 ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ ( sdtasdt0 @ C @ D ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
& ( sdteqdtlpzmzozddtrp0 @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( B != sz00 ) )
=> ! [C: $i] :
( ( C
= ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aInteger0 @ D )
& ( sdteqdtlpzmzozddtrp0 @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
thf(510,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( B != sz00 ) )
=> ! [C: $i] :
( ( ( C
= ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aInteger0 @ D )
& ( sdteqdtlpzmzozddtrp0 @ D @ A @ B ) ) )
& ( ( ( aInteger0 @ D )
& ( sdteqdtlpzmzozddtrp0 @ D @ A @ B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aInteger0 @ D )
& ( sdteqdtlpzmzozddtrp0 @ D @ A @ B ) ) )
& ( ( ( aInteger0 @ D )
& ( sdteqdtlpzmzozddtrp0 @ D @ A @ B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(30,axiom,
aInteger0 @ sz10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
thf(422,plain,
aInteger0 @ sz10,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(8,axiom,
( ( aSet0 @ ( stldt0 @ xA ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
<=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xA ) ) )
& ( aSet0 @ cS1395 )
& ! [A: $i] :
( ( aElementOf0 @ A @ cS1395 )
<=> ( aInteger0 @ A ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
=> ( aElementOf0 @ A @ cS1395 ) )
& ( aSubsetOf0 @ ( stldt0 @ xA ) @ cS1395 )
& ( aSet0 @ ( stldt0 @ xB ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
<=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xB ) ) )
& ( aSet0 @ cS1395 )
& ! [A: $i] :
( ( aElementOf0 @ A @ cS1395 )
<=> ( aInteger0 @ A ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
=> ( aElementOf0 @ A @ cS1395 ) )
& ( aSubsetOf0 @ ( stldt0 @ xB ) @ cS1395 )
& ( aSet0 @ ( sdtbsmnsldt0 @ xA @ xB ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) )
<=> ( ( aInteger0 @ A )
& ( ( aElementOf0 @ A @ xA )
| ( aElementOf0 @ A @ xB ) ) ) )
& ( aSet0 @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
<=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
<=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xA ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
<=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xB ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
<=> ( ( aInteger0 @ A )
& ( aElementOf0 @ A @ ( stldt0 @ xA ) )
& ( aElementOf0 @ A @ ( stldt0 @ xB ) ) ) )
& ( ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) )
= ( sdtslmnbsdt0 @ ( stldt0 @ xA ) @ ( stldt0 @ xB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
thf(210,plain,
( ( aSet0 @ ( stldt0 @ xA ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xA ) ) )
& ( ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xA ) )
=> ( aElementOf0 @ A @ ( stldt0 @ xA ) ) ) )
& ( aSet0 @ cS1395 )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ cS1395 )
=> ( aInteger0 @ A ) )
& ( ( aInteger0 @ A )
=> ( aElementOf0 @ A @ cS1395 ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
=> ( aElementOf0 @ A @ cS1395 ) )
& ( aSubsetOf0 @ ( stldt0 @ xA ) @ cS1395 )
& ( aSet0 @ ( stldt0 @ xB ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xB ) ) )
& ( ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xB ) )
=> ( aElementOf0 @ A @ ( stldt0 @ xB ) ) ) )
& ( aSet0 @ cS1395 )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ cS1395 )
=> ( aInteger0 @ A ) )
& ( ( aInteger0 @ A )
=> ( aElementOf0 @ A @ cS1395 ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
=> ( aElementOf0 @ A @ cS1395 ) )
& ( aSubsetOf0 @ ( stldt0 @ xB ) @ cS1395 )
& ( aSet0 @ ( sdtbsmnsldt0 @ xA @ xB ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) )
=> ( ( aInteger0 @ A )
& ( ( aElementOf0 @ A @ xA )
| ( aElementOf0 @ A @ xB ) ) ) )
& ( ( ( aInteger0 @ A )
& ( ( aElementOf0 @ A @ xA )
| ( aElementOf0 @ A @ xB ) ) )
=> ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) )
& ( aSet0 @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) )
& ( ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
=> ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xA ) ) )
& ( ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xA ) )
=> ( aElementOf0 @ A @ ( stldt0 @ xA ) ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xB ) ) )
& ( ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xB ) )
=> ( aElementOf0 @ A @ ( stldt0 @ xB ) ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
=> ( ( aInteger0 @ A )
& ( aElementOf0 @ A @ ( stldt0 @ xA ) )
& ( aElementOf0 @ A @ ( stldt0 @ xB ) ) ) )
& ( ( ( aInteger0 @ A )
& ( aElementOf0 @ A @ ( stldt0 @ xA ) )
& ( aElementOf0 @ A @ ( stldt0 @ xB ) ) )
=> ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) )
& ( ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) )
= ( sdtslmnbsdt0 @ ( stldt0 @ xA ) @ ( stldt0 @ xB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
<=> ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
thf(322,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 ) )
=> ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
=> ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) )
& ( ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
thf(417,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(11,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( aSubsetOf0 @ B @ cS1395 )
& ( isOpen0 @ B ) ) ) )
=> ( isOpen0 @ ( sbsmnsldt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnionOpen) ).
thf(288,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( aSubsetOf0 @ B @ cS1395 )
& ( isOpen0 @ B ) ) ) )
=> ( isOpen0 @ ( sbsmnsldt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntegers) ).
thf(301,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,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',mSubset) ).
thf(280,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)],[10]) ).
thf(7,axiom,
( ( aSet0 @ cS1395 )
& ! [A: $i] :
( ( aElementOf0 @ A @ cS1395 )
<=> ( aInteger0 @ A ) )
& ( aSet0 @ xA )
& ! [A: $i] :
( ( aElementOf0 @ A @ xA )
=> ( aElementOf0 @ A @ cS1395 ) )
& ( aSubsetOf0 @ xA @ cS1395 )
& ( aSet0 @ cS1395 )
& ! [A: $i] :
( ( aElementOf0 @ A @ cS1395 )
<=> ( aInteger0 @ A ) )
& ( aSet0 @ xB )
& ! [A: $i] :
( ( aElementOf0 @ A @ xB )
=> ( aElementOf0 @ A @ cS1395 ) )
& ( aSubsetOf0 @ xB @ cS1395 )
& ( aSet0 @ ( stldt0 @ xA ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
<=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xA ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
=> ? [B: $i] :
( ( aInteger0 @ B )
& ( B != sz00 )
& ( aSet0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
& ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
& ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
& ( ( ( aInteger0 @ C )
& ( ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
| ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
| ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
=> ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( aElementOf0 @ C @ ( stldt0 @ xA ) ) )
& ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) @ ( stldt0 @ xA ) ) ) )
& ( isOpen0 @ ( stldt0 @ xA ) )
& ( isClosed0 @ xA )
& ( aSet0 @ ( stldt0 @ xB ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
<=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xB ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
=> ? [B: $i] :
( ( aInteger0 @ B )
& ( B != sz00 )
& ( aSet0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
& ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
& ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
& ( ( ( aInteger0 @ C )
& ( ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
| ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
| ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
=> ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( aElementOf0 @ C @ ( stldt0 @ xB ) ) )
& ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) @ ( stldt0 @ xB ) ) ) )
& ( isOpen0 @ ( stldt0 @ xB ) )
& ( isClosed0 @ xB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1826) ).
thf(116,plain,
( ( aSet0 @ cS1395 )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ cS1395 )
=> ( aInteger0 @ A ) )
& ( ( aInteger0 @ A )
=> ( aElementOf0 @ A @ cS1395 ) ) )
& ( aSet0 @ xA )
& ! [A: $i] :
( ( aElementOf0 @ A @ xA )
=> ( aElementOf0 @ A @ cS1395 ) )
& ( aSubsetOf0 @ xA @ cS1395 )
& ( aSet0 @ cS1395 )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ cS1395 )
=> ( aInteger0 @ A ) )
& ( ( aInteger0 @ A )
=> ( aElementOf0 @ A @ cS1395 ) ) )
& ( aSet0 @ xB )
& ! [A: $i] :
( ( aElementOf0 @ A @ xB )
=> ( aElementOf0 @ A @ cS1395 ) )
& ( aSubsetOf0 @ xB @ cS1395 )
& ( aSet0 @ ( stldt0 @ xA ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xA ) ) )
& ( ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xA ) )
=> ( aElementOf0 @ A @ ( stldt0 @ xA ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xA ) )
=> ? [B: $i] :
( ( aInteger0 @ B )
& ( B != sz00 )
& ( aSet0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
& ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
& ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
& ( ( ( aInteger0 @ C )
& ( ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
| ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
| ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
=> ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( aElementOf0 @ C @ ( stldt0 @ xA ) ) )
& ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) @ ( stldt0 @ xA ) ) ) )
& ( isOpen0 @ ( stldt0 @ xA ) )
& ( isClosed0 @ xA )
& ( aSet0 @ ( stldt0 @ xB ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xB ) ) )
& ( ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ xB ) )
=> ( aElementOf0 @ A @ ( stldt0 @ xB ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ xB ) )
=> ? [B: $i] :
( ( aInteger0 @ B )
& ( B != sz00 )
& ( aSet0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
& ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
& ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
& ( ( ( aInteger0 @ C )
& ( ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
| ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
| ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
=> ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( aElementOf0 @ C @ ( stldt0 @ xB ) ) )
& ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) @ ( stldt0 @ xB ) ) ) )
& ( isOpen0 @ ( stldt0 @ xB ) )
& ( isClosed0 @ xB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
thf(380,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ? [B: $i] :
( ( aDivisorOf0 @ B @ A )
& ( isPrime0 @ B ) )
<=> ( ( A != sz10 )
& ( A
!= ( smndt0 @ sz10 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimeDivisor) ).
thf(102,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ? [B: $i] :
( ( aDivisorOf0 @ B @ A )
& ( isPrime0 @ B ) )
=> ( ( A != sz10 )
& ( A
!= ( smndt0 @ sz10 ) ) ) )
& ( ( ( A != sz10 )
& ( A
!= ( smndt0 @ sz10 ) ) )
=> ? [B: $i] :
( ( aDivisorOf0 @ B @ A )
& ( isPrime0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ cS1395 )
& ( aSubsetOf0 @ B @ cS1395 ) )
=> ! [C: $i] :
( ( C
= ( sdtbsmnsldt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aInteger0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( aElementOf0 @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnion) ).
thf(467,plain,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ cS1395 )
& ( aSubsetOf0 @ B @ cS1395 ) )
=> ! [C: $i] :
( ( ( C
= ( sdtbsmnsldt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aInteger0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( aElementOf0 @ D @ B ) ) ) )
& ( ( ( aInteger0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( aElementOf0 @ D @ B ) ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aInteger0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( aElementOf0 @ D @ B ) ) ) )
& ( ( ( aInteger0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( aElementOf0 @ D @ B ) ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtbsmnsldt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(22,axiom,
! [A: $i] :
( ( aSubsetOf0 @ A @ cS1395 )
=> ( ( isOpen0 @ A )
<=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ? [C: $i] :
( ( aInteger0 @ C )
& ( C != sz00 )
& ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mOpen) ).
thf(329,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ cS1395 )
=> ( ( ( isOpen0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ? [C: $i] :
( ( aInteger0 @ C )
& ( C != sz00 )
& ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ B @ C ) @ A ) ) ) )
& ( ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ? [C: $i] :
( ( aInteger0 @ C )
& ( C != sz00 )
& ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ B @ C ) @ A ) ) )
=> ( isOpen0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
! [A: $i] :
( ( aSubsetOf0 @ A @ cS1395 )
=> ( ( isClosed0 @ A )
<=> ( isOpen0 @ ( stldt0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mClosed) ).
thf(298,plain,
! [A: $i] :
( ( aSubsetOf0 @ A @ cS1395 )
=> ( ( ( isClosed0 @ A )
=> ( isOpen0 @ ( stldt0 @ A ) ) )
& ( ( isOpen0 @ ( stldt0 @ A ) )
=> ( isClosed0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
thf(296,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
thf(423,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
thf(291,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( B != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModRef) ).
thf(545,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( B != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 )
& ( aInteger0 @ D ) )
=> ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
& ( sdteqdtlpzmzozddtrp0 @ B @ D @ C ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModTrn) ).
thf(113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 )
& ( aInteger0 @ D ) )
=> ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
& ( sdteqdtlpzmzozddtrp0 @ B @ D @ C ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i] :
( ( ( aInteger0 @ A )
& ( A != sz00 ) )
=> ( ( isPrime0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrime) ).
thf(98,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aSubsetOf0 @ B @ cS1395 ) ) )
=> ! [B: $i] :
( ( B
= ( sbsmnsldt0 @ A ) )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
<=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnionSet) ).
thf(426,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aSubsetOf0 @ B @ cS1395 ) ) )
=> ! [B: $i] :
( ( ( B
= ( sbsmnsldt0 @ A ) )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ C @ D ) ) ) )
& ( ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ C @ D ) ) )
=> ( aElementOf0 @ C @ B ) ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ C @ D ) ) ) )
& ( ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ C @ D ) ) )
=> ( aElementOf0 @ C @ B ) ) ) )
=> ( B
= ( sbsmnsldt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(42,axiom,
aInteger0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
thf(548,plain,
aInteger0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
thf(414,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
thf(327,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) )
= ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
thf(502,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) )
= ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(33,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSets) ).
thf(463,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(23,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
thf(338,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( aInteger0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
thf(314,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( aInteger0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
( ( ( aSet0 @ ( sdtbsmnsldt0 @ xA @ xB ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) )
<=> ( ( aInteger0 @ A )
& ( ( aElementOf0 @ A @ xA )
| ( aElementOf0 @ A @ xB ) ) ) ) )
=> ( ( ( ( aSet0 @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
<=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
=> ? [B: $i] :
( ( aInteger0 @ B )
& ( B != sz00 )
& ( ( ( aSet0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
& ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
& ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
& ( ( ( aInteger0 @ C )
& ( ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
| ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
| ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
=> ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) ) ) ) )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( aElementOf0 @ C @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) )
| ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) ) ) )
| ( isOpen0 @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) )
| ( isClosed0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( aSet0 @ ( sdtbsmnsldt0 @ xA @ xB ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) )
<=> ( ( aInteger0 @ A )
& ( ( aElementOf0 @ A @ xA )
| ( aElementOf0 @ A @ xB ) ) ) ) )
=> ( ( ( ( aSet0 @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
<=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
=> ? [B: $i] :
( ( aInteger0 @ B )
& ( B != sz00 )
& ( ( ( aSet0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
& ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
& ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
& ( ( ( aInteger0 @ C )
& ( ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
| ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
| ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
=> ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) ) ) ) )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( aElementOf0 @ C @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) )
| ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) ) ) )
| ( isOpen0 @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) )
| ( isClosed0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ ( ( ( aSet0 @ ( sdtbsmnsldt0 @ xA @ xB ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) )
=> ( ( aInteger0 @ A )
& ( ( aElementOf0 @ A @ xA )
| ( aElementOf0 @ A @ xB ) ) ) )
& ( ( ( aInteger0 @ A )
& ( ( aElementOf0 @ A @ xA )
| ( aElementOf0 @ A @ xB ) ) )
=> ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) )
=> ( ( ( ( aSet0 @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
=> ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) )
& ( ( ( aInteger0 @ A )
& ~ ( aElementOf0 @ A @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
=> ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) )
=> ? [B: $i] :
( ( aInteger0 @ B )
& ( B != sz00 )
& ( ( ( aSet0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( ( aInteger0 @ C )
& ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
& ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
& ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
& ( ( ( aInteger0 @ C )
& ( ? [D: $i] :
( ( aInteger0 @ D )
& ( ( sdtasdt0 @ B @ D )
= ( sdtpldt0 @ C @ ( smndt0 @ A ) ) ) )
| ( aDivisorOf0 @ B @ ( sdtpldt0 @ C @ ( smndt0 @ A ) ) )
| ( sdteqdtlpzmzozddtrp0 @ C @ A @ B ) ) )
=> ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) ) ) ) )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) )
=> ( aElementOf0 @ C @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) )
| ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ A @ B ) @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) ) ) )
| ( isOpen0 @ ( stldt0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ) )
| ( isClosed0 @ ( sdtbsmnsldt0 @ xA @ xB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
thf(99,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(39,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFinSet) ).
thf(539,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
=> ( sdteqdtlpzmzozddtrp0 @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
thf(464,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
=> ( sdteqdtlpzmzozddtrp0 @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
thf(277,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(554,plain,
$false,
inference(cvc4,[status(thm)],[385,316,321,302,343,540,345,505,510,422,210,322,417,288,301,280,116,380,102,467,329,298,296,423,291,545,113,98,426,548,414,327,502,463,338,314,43,99,539,464,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:26:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.06 % [INFO] Parsing done (175ms).
% 1.28/1.07 % [INFO] Running in sequential loop mode.
% 1.86/1.30 % [INFO] eprover registered as external prover.
% 1.86/1.30 % [INFO] cvc4 registered as external prover.
% 1.86/1.31 % [INFO] Scanning for conjecture ...
% 2.07/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.42 % [INFO] Found a conjecture and 40 axioms. Running axiom selection ...
% 2.51/1.49 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 2.68/1.53 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.53 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.53 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.53 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.53 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.68/1.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/1.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/1.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/1.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/1.55 % [INFO] Problem is first-order (TPTP FOF).
% 2.77/1.56 % [INFO] Type checking passed.
% 2.77/1.56 % [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 ...
% 6.12/2.53 % External prover 'cvc4' found a proof!
% 6.12/2.53 % [INFO] Killing All external provers ...
% 6.12/2.53 % Time passed: 2025ms (effective reasoning time: 1463ms)
% 6.12/2.53 % 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)>
% 6.12/2.54 % Axioms used in derivation (40): mSets, mEquModTrn, mUnionOpen, mAddNeg, mSubset, mAddZero, mPrimeDivisor, mIntMult, mDivisor, mMulMinOne, mFinSet, mComplement, mMulComm, mAddComm, mClosed, mMulZero, mEquMod, mPrime, mInterOpen, mEquModMul, mUnionSet, mArSeq, mZeroDiv, m__1826, mDistrib, mMulOne, mOpen, mAddAsso, mElements, mMulAsso, mEquModSym, mIntPlus, mIntNeg, m__1883, mEquModRef, mIntegers, mIntOne, mIntZero, mUnion, mIntersection
% 6.12/2.54 % No. of inferences in proof: 84
% 6.12/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2025 ms resp. 1463 ms w/o parsing
% 6.48/2.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.48/2.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------