TSTP Solution File: NUM474+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM474+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 11:40:45 EDT 2023
% Result : Theorem 4.94s 2.16s
% Output : Refutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 57
% Syntax : Number of formulae : 100 ( 18 unt; 16 typ; 0 def)
% Number of atoms : 336 ( 111 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 887 ( 32 ~; 12 |; 133 &; 603 @)
% ( 4 <=>; 103 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 139 ( 0 ^; 133 !; 6 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
thf(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtmndt0_type,type,
sdtmndt0: $i > $i > $i ).
thf(doDivides0_type,type,
doDivides0: $i > $i > $o ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(sz00_type,type,
sz00: $i ).
thf(sdtsldt0_type,type,
sdtsldt0: $i > $i > $i ).
thf(xl_type,type,
xl: $i ).
thf(xp_type,type,
xp: $i ).
thf(xr_type,type,
xr: $i ).
thf(xn_type,type,
xn: $i ).
thf(sz10_type,type,
sz10: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(xq_type,type,
xq: $i ).
thf(xm_type,type,
xm: $i ).
thf(7,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
thf(56,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
thf(174,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(22,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
thf(121,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(10,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
thf(60,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( ( B != A )
& ( sdtlseqdt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( ( B != A )
& ( sdtlseqdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
( xp
= ( sdtsldt0 @ xm @ xl ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
thf(156,plain,
( xp
= ( sdtsldt0 @ xm @ xl ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
thf(45,plain,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
( xr
= ( sdtmndt0 @ xq @ xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1422) ).
thf(172,plain,
( xr
= ( sdtmndt0 @ xq @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(66,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1,conjecture,
( ( sdtpldt0 @ ( sdtasdt0 @ xl @ xp ) @ ( sdtasdt0 @ xl @ xr ) )
= ( sdtpldt0 @ ( sdtasdt0 @ xl @ xp ) @ xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
( ( sdtpldt0 @ ( sdtasdt0 @ xl @ xp ) @ ( sdtasdt0 @ xl @ xr ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ xl @ xp ) @ xn ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
( ( sdtpldt0 @ ( sdtasdt0 @ xl @ xp ) @ ( sdtasdt0 @ xl @ xr ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ xl @ xp ) @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,axiom,
( ( doDivides0 @ xl @ xm )
& ( doDivides0 @ xl @ ( sdtpldt0 @ xm @ xn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
thf(183,plain,
( ( doDivides0 @ xl @ xm )
& ( doDivides0 @ xl @ ( sdtpldt0 @ xm @ xn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ B @ C ) )
=> ( doDivides0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ B @ C ) )
=> ( doDivides0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtsldt0 @ B @ A ) )
<=> ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtsldt0 @ B @ A ) )
=> ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) )
& ( ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) )
=> ( C
= ( sdtsldt0 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
thf(93,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(30,axiom,
( ( aNaturalNumber0 @ xl )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
thf(152,plain,
( ( aNaturalNumber0 @ xl )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
thf(147,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ C ) )
=> ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ C ) )
=> ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( doDivides0 @ A @ B )
<=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( doDivides0 @ A @ B )
=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) )
=> ( doDivides0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> ! [C: $i] :
( ( C
= ( sdtmndt0 @ B @ A ) )
<=> ( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
thf(96,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> ! [C: $i] :
( ( ( C
= ( sdtmndt0 @ B @ A ) )
=> ( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) )
& ( ( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) )
=> ( C
= ( sdtmndt0 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
thf(191,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(9,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(59,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
thf(54,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,axiom,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
thf(144,plain,
xl != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
<=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) )
& ( ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) )
=> ( sdtlseqdt0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( A != sz00 )
& ( B != C )
& ( sdtlseqdt0 @ B @ C ) )
=> ( ( ( sdtasdt0 @ A @ B )
!= ( sdtasdt0 @ A @ C ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) )
& ( ( sdtasdt0 @ B @ A )
!= ( sdtasdt0 @ C @ A ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
thf(135,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( A != sz00 )
& ( B != C )
& ( sdtlseqdt0 @ B @ C ) )
=> ( ( ( sdtasdt0 @ A @ B )
!= ( sdtasdt0 @ A @ C ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) )
& ( ( sdtasdt0 @ B @ A )
!= ( sdtasdt0 @ C @ A ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ( iLess0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ( iLess0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ A @ C ) )
| ( ( sdtpldt0 @ B @ A )
= ( sdtpldt0 @ C @ A ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
thf(177,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ A @ C ) )
| ( ( sdtpldt0 @ B @ A )
= ( sdtpldt0 @ C @ A ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(37,axiom,
sdtlseqdt0 @ xp @ xq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1395) ).
thf(182,plain,
sdtlseqdt0 @ xp @ xq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A != sz00 )
=> ! [B: $i,C: $i] :
( ( ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ A @ C ) )
| ( ( sdtasdt0 @ B @ A )
= ( sdtasdt0 @ C @ A ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
thf(158,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A != sz00 )
=> ! [B: $i,C: $i] :
( ( ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ A @ C ) )
| ( ( sdtasdt0 @ B @ A )
= ( sdtasdt0 @ C @ A ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
thf(186,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(14,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
thf(75,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(58,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
thf(107,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ 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(126,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ 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)],[23]) ).
thf(24,axiom,
( xq
= ( sdtsldt0 @ ( sdtpldt0 @ xm @ xn ) @ xl ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
thf(131,plain,
( xq
= ( sdtsldt0 @ ( sdtpldt0 @ xm @ xn ) @ xl ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ C @ A ) @ ( sdtpldt0 @ C @ B ) )
& ( ( sdtpldt0 @ A @ C )
!= ( sdtpldt0 @ B @ C ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ C @ A ) @ ( sdtpldt0 @ C @ B ) )
& ( ( sdtpldt0 @ A @ C )
!= ( sdtpldt0 @ B @ C ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtpldt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
& ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
thf(200,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtpldt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
& ( B = sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(319,plain,
$false,
inference(cvc4,[status(thm)],[56,174,121,60,70,156,45,172,66,150,43,183,83,52,110,93,152,147,133,193,96,191,59,54,144,49,86,135,80,67,177,182,158,186,75,58,107,126,131,163,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM474+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n023.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 16:57:30 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.95/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.96 % [INFO] Parsing done (134ms).
% 1.39/0.97 % [INFO] Running in sequential loop mode.
% 1.71/1.17 % [INFO] eprover registered as external prover.
% 1.71/1.17 % [INFO] cvc4 registered as external prover.
% 1.79/1.18 % [INFO] Scanning for conjecture ...
% 1.79/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.00/1.26 % [INFO] Found a conjecture and 40 axioms. Running axiom selection ...
% 2.00/1.30 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 2.23/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.23/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.23/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.23/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.23/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.23/1.36 % [INFO] Type checking passed.
% 2.23/1.36 % [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 ...
% 4.94/2.16 % External prover 'cvc4' found a proof!
% 4.94/2.16 % [INFO] Killing All external provers ...
% 4.94/2.16 % Time passed: 1646ms (effective reasoning time: 1178ms)
% 4.94/2.16 % 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)>
% 4.94/2.16 % Axioms used in derivation (40): mSortsC, mAddComm, m_MulUnit, m_MulZero, mZeroMul, mZeroAdd, mMonMul, mIH_03, mDefQuot, m__1360, mAMDistr, mLETotal, mLEAsym, mAddCanc, m__1324_04, m__1347, mDivSum, mDivTrans, mSortsC_01, mMulCanc, mLETran, mDefDiff, mMonMul2, mAddAsso, m__1422, mIH, mMulAsso, mDefDiv, mDefLE, m__1395, mLENTr, mSortsB_02, m_AddZero, mSortsB, mNatSort, mMulComm, m__1379, mLERefl, mMonAdd, m__1324
% 4.94/2.16 % No. of inferences in proof: 84
% 4.94/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1646 ms resp. 1178 ms w/o parsing
% 4.94/2.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.94/2.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------