TSTP Solution File: RNG125+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 11:49:32 EDT 2023
% Result : Theorem 5.41s 2.39s
% Output : Refutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 75
% Syntax : Number of formulae : 127 ( 20 unt; 25 typ; 0 def)
% Number of atoms : 411 ( 86 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1080 ( 28 ~; 4 |; 166 &; 743 @)
% ( 12 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 9 con; 0-3 aty)
% Number of variables : 188 ( 0 ^; 158 !; 30 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(sdtpldt1_type,type,
sdtpldt1: $i > $i > $i ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtasasdt0_type,type,
sdtasasdt0: $i > $i > $i ).
thf(aIdeal0_type,type,
aIdeal0: $i > $o ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(doDivides0_type,type,
doDivides0: $i > $i > $o ).
thf(aDivisorOf0_type,type,
aDivisorOf0: $i > $i > $o ).
thf(aGcdOfAnd0_type,type,
aGcdOfAnd0: $i > $i > $i > $o ).
thf(misRelativelyPrime0_type,type,
misRelativelyPrime0: $i > $i > $o ).
thf(sz10_type,type,
sz10: $i ).
thf(slsdtgt0_type,type,
slsdtgt0: $i > $i ).
thf(sz00_type,type,
sz00: $i ).
thf(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
thf(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(xa_type,type,
xa: $i ).
thf(xb_type,type,
xb: $i ).
thf(xc_type,type,
xc: $i ).
thf(xI_type,type,
xI: $i ).
thf(xu_type,type,
xu: $i ).
thf(30,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetSort) ).
thf(249,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(41,axiom,
( ( aElement0 @ xa )
& ( aElement0 @ xb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
thf(288,plain,
( ( aElement0 @ xa )
& ( aElement0 @ xb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
thf(238,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtasasdt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSInt) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtasasdt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) ) )
& ( ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) ) )
& ( ( ( aElementOf0 @ D @ A )
& ( aElementOf0 @ D @ B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtasasdt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(271,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(50,axiom,
~ ~ ( doDivides0 @ xu @ xa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2479) ).
thf(323,plain,
doDivides0 @ xu @ xa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
thf(199,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(48,axiom,
~ ( ( aDivisorOf0 @ xu @ xa )
& ( aDivisorOf0 @ xu @ xb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2383) ).
thf(314,plain,
~ ( ( aDivisorOf0 @ xu @ xa )
& ( aDivisorOf0 @ xu @ xb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(31,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(250,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(46,axiom,
? [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
& ( A != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2228) ).
thf(304,plain,
? [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
& ( A != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(47,axiom,
( ( aElementOf0 @ xu @ xI )
& ( xu != sz00 )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xI )
& ( A != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ A ) @ ( sbrdtbr0 @ xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
thf(308,plain,
( ( aElementOf0 @ xu @ xI )
& ( xu != sz00 )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xI )
& ( A != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ A ) @ ( sbrdtbr0 @ xu ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
thf(217,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( B != sz00 ) )
=> ? [C: $i,D: $i] :
( ( aElement0 @ C )
& ( aElement0 @ D )
& ( A
= ( sdtpldt0 @ ( sdtasdt0 @ C @ B ) @ D ) )
& ( ( D != sz00 )
=> ( iLess0 @ ( sbrdtbr0 @ D ) @ ( sbrdtbr0 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivision) ).
thf(276,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( B != sz00 ) )
=> ? [C: $i,D: $i] :
( ( aElement0 @ C )
& ( aElement0 @ D )
& ( A
= ( sdtpldt0 @ ( sdtasdt0 @ C @ B ) @ D ) )
& ( ( D != sz00 )
=> ( iLess0 @ ( sbrdtbr0 @ D ) @ ( sbrdtbr0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1,conjecture,
$false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ $false,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(52,plain,
~ $false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtpldt1 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
thf(157,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtpldt1 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) ) )
& ( ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) ) )
& ( ? [E: $i,F: $i] :
( ( aElementOf0 @ E @ A )
& ( aElementOf0 @ F @ B )
& ( ( sdtpldt0 @ E @ F )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtpldt1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
thf(228,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( aIdeal0 @ A )
& ( aIdeal0 @ B ) )
=> ( aIdeal0 @ ( sdtpldt1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIdeSum) ).
thf(261,plain,
! [A: $i,B: $i] :
( ( ( aIdeal0 @ A )
& ( aIdeal0 @ B ) )
=> ( aIdeal0 @ ( sdtpldt1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCancel) ).
thf(243,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( aIdeal0 @ A )
& ( aIdeal0 @ B ) )
=> ( ! [C: $i] :
( ( aElement0 @ C )
=> ( aElementOf0 @ C @ ( sdtpldt1 @ A @ B ) ) )
=> ! [C: $i,D: $i] :
( ( ( aElement0 @ C )
& ( aElement0 @ D ) )
=> ? [E: $i] :
( ( aElement0 @ E )
& ( sdteqdtlpzmzozddtrp0 @ E @ C @ A )
& ( sdteqdtlpzmzozddtrp0 @ E @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mChineseRemainder) ).
thf(265,plain,
! [A: $i,B: $i] :
( ( ( aIdeal0 @ A )
& ( aIdeal0 @ B ) )
=> ( ! [C: $i] :
( ( aElement0 @ C )
=> ( aElementOf0 @ C @ ( sdtpldt1 @ A @ B ) ) )
=> ! [C: $i,D: $i] :
( ( ( aElement0 @ C )
& ( aElement0 @ D ) )
=> ? [E: $i] :
( ( aElement0 @ E )
& ( sdteqdtlpzmzozddtrp0 @ E @ C @ A )
& ( sdteqdtlpzmzozddtrp0 @ E @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(26,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).
thf(233,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
thf(220,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( doDivides0 @ A @ B )
<=> ? [C: $i] :
( ( aElement0 @ C )
& ( ( sdtasdt0 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
thf(102,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( doDivides0 @ A @ B )
=> ? [C: $i] :
( ( aElement0 @ C )
& ( ( sdtasdt0 @ A @ C )
= B ) ) )
& ( ? [C: $i] :
( ( aElement0 @ C )
& ( ( sdtasdt0 @ A @ C )
= B ) )
=> ( doDivides0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( aGcdOfAnd0 @ C @ A @ B )
<=> ( ( aDivisorOf0 @ C @ A )
& ( aDivisorOf0 @ C @ B )
& ! [D: $i] :
( ( ( aDivisorOf0 @ D @ A )
& ( aDivisorOf0 @ D @ B ) )
=> ( doDivides0 @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefGCD) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( aGcdOfAnd0 @ C @ A @ B )
=> ( ( aDivisorOf0 @ C @ A )
& ( aDivisorOf0 @ C @ B )
& ! [D: $i] :
( ( ( aDivisorOf0 @ D @ A )
& ( aDivisorOf0 @ D @ B ) )
=> ( doDivides0 @ D @ C ) ) ) )
& ( ( ( aDivisorOf0 @ C @ A )
& ( aDivisorOf0 @ C @ B )
& ! [D: $i] :
( ( ( aDivisorOf0 @ D @ A )
& ( aDivisorOf0 @ D @ B ) )
=> ( doDivides0 @ D @ C ) ) )
=> ( aGcdOfAnd0 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(192,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatLess) ).
thf(275,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ C @ B ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetEq) ).
thf(252,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ C @ B ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
thf(197,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(51,axiom,
~ ~ ( doDivides0 @ xu @ xb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2612) ).
thf(324,plain,
doDivides0 @ xu @ xb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(49,axiom,
? [A: $i,B: $i] :
( ( aElement0 @ A )
& ( aElement0 @ B )
& ( xu
= ( sdtpldt0 @ ( sdtasdt0 @ xa @ A ) @ ( sdtasdt0 @ xb @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2416) ).
thf(317,plain,
? [A: $i,B: $i] :
( ( aElement0 @ A )
& ( aElement0 @ B )
& ( xu
= ( sdtpldt0 @ ( sdtasdt0 @ xa @ A ) @ ( sdtasdt0 @ xb @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(3,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( B
= ( slsdtgt0 @ A ) )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
<=> ? [D: $i] :
( ( aElement0 @ D )
& ( ( sdtasdt0 @ A @ D )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
thf(53,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( B
= ( slsdtgt0 @ A ) )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ? [D: $i] :
( ( aElement0 @ D )
& ( ( sdtasdt0 @ A @ D )
= C ) ) )
& ( ? [D: $i] :
( ( aElement0 @ D )
& ( ( sdtasdt0 @ A @ D )
= C ) )
=> ( aElementOf0 @ C @ B ) ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ? [D: $i] :
( ( aElement0 @ D )
& ( ( sdtasdt0 @ A @ D )
= C ) ) )
& ( ? [D: $i] :
( ( aElement0 @ D )
& ( ( sdtasdt0 @ A @ D )
= C ) )
=> ( aElementOf0 @ C @ B ) ) ) )
=> ( B
= ( slsdtgt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aIdeal0 @ C ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
<=> ( aElementOf0 @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMod) ).
thf(109,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aIdeal0 @ C ) )
=> ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
=> ( aElementOf0 @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) @ C ) )
& ( ( aElementOf0 @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) @ C )
=> ( sdteqdtlpzmzozddtrp0 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
aElement0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(193,plain,
aElement0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddInvr) ).
thf(212,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(6,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( aDivisorOf0 @ B @ A )
<=> ( ( aElement0 @ B )
& ( doDivides0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
thf(96,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aDivisorOf0 @ B @ A )
=> ( ( aElement0 @ B )
& ( doDivides0 @ B @ A ) ) )
& ( ( ( aElement0 @ B )
& ( doDivides0 @ B @ A ) )
=> ( aDivisorOf0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( aIdeal0 @ ( slsdtgt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrIdeal) ).
thf(286,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( aIdeal0 @ ( slsdtgt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(42,axiom,
( ( xa != sz00 )
| ( xb != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2110) ).
thf(291,plain,
( ( xa != sz00 )
| ( xb != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
thf(204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(24,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
thf(223,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(45,axiom,
( ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) )
& ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).
thf(299,plain,
( ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) )
& ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(9,axiom,
! [A: $i] :
( ( aIdeal0 @ A )
<=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ ( sdtpldt0 @ B @ C ) @ A ) )
& ! [C: $i] :
( ( aElement0 @ C )
=> ( aElementOf0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
thf(112,plain,
! [A: $i] :
( ( ( aIdeal0 @ A )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ ( sdtpldt0 @ B @ C ) @ A ) )
& ! [C: $i] :
( ( aElement0 @ C )
=> ( aElementOf0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ) )
& ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( aElementOf0 @ ( sdtpldt0 @ B @ C ) @ A ) )
& ! [C: $i] :
( ( aElement0 @ C )
=> ( aElementOf0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) )
=> ( aIdeal0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
aElement0 @ sz10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
thf(194,plain,
aElement0 @ sz10,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(44,axiom,
( ( aIdeal0 @ xI )
& ( xI
= ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
thf(295,plain,
( ( aIdeal0 @ xI )
& ( xI
= ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( aIdeal0 @ A )
& ( aIdeal0 @ B ) )
=> ( aIdeal0 @ ( sdtasasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIdeInt) ).
thf(263,plain,
! [A: $i,B: $i] :
( ( ( aIdeal0 @ A )
& ( aIdeal0 @ B ) )
=> ( aIdeal0 @ ( sdtasasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(29,axiom,
sz10 != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnNeZr) ).
thf(246,plain,
sz10 != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
thf(207,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(37,axiom,
! [A: $i] :
( ( ( aElement0 @ A )
& ( A != sz00 ) )
=> ( aNaturalNumber0 @ ( sbrdtbr0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEucSort) ).
thf(272,plain,
! [A: $i] :
( ( ( aElement0 @ A )
& ( A != sz00 ) )
=> ( aNaturalNumber0 @ ( sbrdtbr0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( misRelativelyPrime0 @ A @ B )
<=> ( aGcdOfAnd0 @ sz10 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefRel) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( misRelativelyPrime0 @ A @ B )
=> ( aGcdOfAnd0 @ sz10 @ A @ B ) )
& ( ( aGcdOfAnd0 @ sz10 @ A @ B )
=> ( misRelativelyPrime0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,axiom,
aGcdOfAnd0 @ xc @ xa @ xb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2129) ).
thf(294,plain,
aGcdOfAnd0 @ xc @ xa @ xb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(15,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( aElement0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
thf(195,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( aElement0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(356,plain,
$false,
inference(cvc4,[status(thm)],[249,288,238,128,271,323,199,314,250,304,308,217,276,52,157,228,261,243,265,233,220,102,85,201,192,275,252,197,324,317,53,109,193,212,96,286,291,204,223,299,112,194,295,263,246,207,272,82,294,195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 20:18:18 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.00 % [INFO] Parsing done (145ms).
% 1.38/1.01 % [INFO] Running in sequential loop mode.
% 1.80/1.22 % [INFO] eprover registered as external prover.
% 1.80/1.22 % [INFO] cvc4 registered as external prover.
% 1.80/1.23 % [INFO] Scanning for conjecture ...
% 2.06/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.33 % [INFO] Found a conjecture and 49 axioms. Running axiom selection ...
% 2.24/1.35 % [INFO] Axiom selection finished. Selected 49 axioms (removed 0 axioms).
% 2.24/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.24/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.37/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.37/1.40 % [INFO] Type checking passed.
% 2.37/1.41 % [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 ...
% 5.41/2.38 % External prover 'cvc4' found a proof!
% 5.41/2.38 % [INFO] Killing All external provers ...
% 5.41/2.38 % Time passed: 1860ms (effective reasoning time: 1375ms)
% 5.41/2.38 % 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)>
% 5.41/2.39 % Axioms used in derivation (49): mAddComm, m__2416, mMulZero, mSetSort, mDivision, m__2091, mDefSSum, mMulUnit, mAddInvr, m__2383, m__2612, m__2110, mSortsC, mDefIdeal, mEucSort, mIdeInt, m__2479, mDefPrIdeal, mDefDvs, m__2174, mSortsC_01, mEOfElem, mNatLess, m__2273, m__2129, mAddZero, mIdeSum, mDefSInt, mAddAsso, mMulAsso, mDefDiv, mDefRel, mMulMnOne, mPrIdeal, mCancel, mSortsB_02, mSortsU, mDefGCD, mSetEq, mAMDistr, mElmSort, mUnNeZr, mChineseRemainder, mSortsB, mNatSort, mMulComm, m__2203, mDefMod, m__2228
% 5.41/2.39 % No. of inferences in proof: 102
% 5.41/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1860 ms resp. 1375 ms w/o parsing
% 5.94/2.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.94/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------