TSTP Solution File: NUM479+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM479+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:40:46 EDT 2023
% Result : Theorem 83.79s 22.26s
% Output : Refutation 83.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 54
% Syntax : Number of formulae : 623 ( 134 unt; 15 typ; 0 def)
% Number of atoms : 2060 ( 794 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 5543 ( 872 ~; 909 |; 150 &;3489 @)
% ( 4 <=>; 119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 603 ( 0 ^; 597 !; 6 ?; 603 :)
% 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(xn_type,type,
xn: $i ).
thf(xm_type,type,
xm: $i ).
thf(sz10_type,type,
sz10: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(8,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(63,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)],[8]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtpldt0 @ A @ C )
!= B )
| ( sdtlseqdt0 @ A @ B ) ),
inference(cnf,[status(esa)],[63]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ C )
!= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ( sdtlseqdt0 @ A @ ( sdtpldt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(37,axiom,
( ( aNaturalNumber0 @ xl )
& ( aNaturalNumber0 @ xm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524) ).
thf(178,plain,
( ( aNaturalNumber0 @ xl )
& ( aNaturalNumber0 @ xm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(180,plain,
aNaturalNumber0 @ xl,
inference(cnf,[status(esa)],[178]) ).
thf(14,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
thf(90,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(91,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sdtlseqdt0 @ A @ A ) ),
inference(cnf,[status(esa)],[90]) ).
thf(2076,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[180,91]) ).
thf(2077,plain,
sdtlseqdt0 @ xl @ xl,
inference(pattern_uni,[status(thm)],[2076:[bind(A,$thf( xl ))]]) ).
thf(9,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(70,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)],[9]) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> ( ! [C: $i] :
( ( C
= ( sdtmndt0 @ B @ A ) )
=> ( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) )
& ! [C: $i] :
( ( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) )
=> ( C
= ( sdtmndt0 @ B @ A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[70]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( C
!= ( sdtmndt0 @ B @ A ) )
| ( aNaturalNumber0 @ C ) ),
inference(cnf,[status(esa)],[71]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sdtmndt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(5985,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) )
| ( ( sdtlseqdt0 @ xl @ xl )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2077,78]) ).
thf(5986,plain,
( ~ ( aNaturalNumber0 @ xl )
| ~ ( aNaturalNumber0 @ xl )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) ) ),
inference(pattern_uni,[status(thm)],[5985:[bind(A,$thf( xl )),bind(B,$thf( xl ))]]) ).
thf(6152,plain,
( ~ ( aNaturalNumber0 @ xl )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) ) ),
inference(simp,[status(thm)],[5986]) ).
thf(11407,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) ) ),
inference(rewrite,[status(thm)],[6152,180]) ).
thf(11408,plain,
aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ),
inference(simp,[status(thm)],[11407]) ).
thf(23,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
thf(120,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(122,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A
= ( sdtpldt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[120]) ).
thf(124,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(18278,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11408,124]) ).
thf(18279,plain,
( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ xl @ xl ) )
= ( sdtmndt0 @ xl @ xl ) ),
inference(pattern_uni,[status(thm)],[18278:[bind(A,$thf( sdtmndt0 @ xl @ xl ))]]) ).
thf(179,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[178]) ).
thf(21,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
thf(109,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(111,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A ) ),
inference(cnf,[status(esa)],[109]) ).
thf(114,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( sdtlseqdt0 @ sz10 @ A ) ),
inference(lifteq,[status(thm)],[111]) ).
thf(1443,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,114]) ).
thf(1444,plain,
( ( xm = sz00 )
| ( sz10 = xm )
| ( sdtlseqdt0 @ sz10 @ xm ) ),
inference(pattern_uni,[status(thm)],[1443:[bind(A,$thf( xm ))]]) ).
thf(3,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
thf(43,plain,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(45,plain,
aNaturalNumber0 @ sz10,
inference(cnf,[status(esa)],[43]) ).
thf(2074,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,91]) ).
thf(2075,plain,
sdtlseqdt0 @ sz10 @ sz10,
inference(pattern_uni,[status(thm)],[2074:[bind(A,$thf( sz10 ))]]) ).
thf(2807,plain,
( ( xm = sz00 )
| ( sdtlseqdt0 @ sz10 @ xm )
| ( sz10 != sz10 ) ),
inference(paramod_ordered,[status(thm)],[1444,2075]) ).
thf(2808,plain,
( ( xm = sz00 )
| ( sdtlseqdt0 @ sz10 @ xm ) ),
inference(pattern_uni,[status(thm)],[2807:[]]) ).
thf(26,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
thf(130,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(131,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ A @ sz00 )
= sz00 ) ),
inference(cnf,[status(esa)],[130]) ).
thf(133,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[131]) ).
thf(1,conjecture,
( ( sdtasdt0 @ ( sdtasdt0 @ xl @ xn ) @ ( sdtsldt0 @ xm @ xl ) )
= ( sdtasdt0 @ xl @ ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
( ( sdtasdt0 @ ( sdtasdt0 @ xl @ xn ) @ ( sdtsldt0 @ xm @ xl ) )
!= ( sdtasdt0 @ xl @ ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xl ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(41,plain,
( ( sdtasdt0 @ ( sdtasdt0 @ xl @ xn ) @ ( sdtsldt0 @ xm @ xl ) )
!= ( sdtasdt0 @ xl @ ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,plain,
( ( sdtasdt0 @ ( sdtasdt0 @ xl @ xn ) @ ( sdtsldt0 @ xm @ xl ) )
!= ( sdtasdt0 @ xl @ ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xl ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(199,plain,
( ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xl )
!= ( sdtsldt0 @ xm @ xl ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(200,plain,
( ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( ( sdtasdt0 @ xn @ xm )
!= xm )
| ( xl != xl ) ),
inference(simp,[status(thm)],[199]) ).
thf(201,plain,
( ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( ( sdtasdt0 @ xn @ xm )
!= xm ) ),
inference(simp,[status(thm)],[200]) ).
thf(251,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( xm != sz00 )
| ( ( sdtasdt0 @ A @ sz00 )
!= ( sdtasdt0 @ xn @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[133,201]) ).
thf(267,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( xm != sz00 )
| ( A != xn )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[251]) ).
thf(282,plain,
( ~ ( aNaturalNumber0 @ xn )
| ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[267]) ).
thf(31,axiom,
aNaturalNumber0 @ xn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1553) ).
thf(147,plain,
aNaturalNumber0 @ xn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(325,plain,
( ~ $true
| ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( xm != sz00 ) ),
inference(rewrite,[status(thm)],[282,147]) ).
thf(326,plain,
( ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[325]) ).
thf(3007,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,326]) ).
thf(3008,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ xl @ xn )
!= xl ) ),
inference(pattern_uni,[status(thm)],[3007:[]]) ).
thf(2070,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,91]) ).
thf(2071,plain,
sdtlseqdt0 @ xm @ xm,
inference(pattern_uni,[status(thm)],[2070:[bind(A,$thf( xm ))]]) ).
thf(5968,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) )
| ( ( sdtlseqdt0 @ xm @ xm )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2071,78]) ).
thf(5969,plain,
( ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xm )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) ) ),
inference(pattern_uni,[status(thm)],[5968:[bind(A,$thf( xm )),bind(B,$thf( xm ))]]) ).
thf(6143,plain,
( ~ ( aNaturalNumber0 @ xm )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) ) ),
inference(simp,[status(thm)],[5969]) ).
thf(10555,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) ) ),
inference(rewrite,[status(thm)],[6143,179]) ).
thf(10556,plain,
aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ),
inference(simp,[status(thm)],[10555]) ).
thf(10576,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ sz00 ) )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,10556]) ).
thf(10577,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[10576:[]]) ).
thf(2072,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,91]) ).
thf(2073,plain,
sdtlseqdt0 @ xn @ xn,
inference(pattern_uni,[status(thm)],[2072:[bind(A,$thf( xn ))]]) ).
thf(6003,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) )
| ( ( sdtlseqdt0 @ xn @ xn )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2073,78]) ).
thf(6004,plain,
( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xn )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) ) ),
inference(pattern_uni,[status(thm)],[6003:[bind(A,$thf( xn )),bind(B,$thf( xn ))]]) ).
thf(6159,plain,
( ~ ( aNaturalNumber0 @ xn )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) ) ),
inference(simp,[status(thm)],[6004]) ).
thf(12256,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) ) ),
inference(rewrite,[status(thm)],[6159,147]) ).
thf(12257,plain,
aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ),
inference(simp,[status(thm)],[12256]) ).
thf(132,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[130]) ).
thf(134,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[132]) ).
thf(12343,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12257,134]) ).
thf(12344,plain,
( ( sdtasdt0 @ sz00 @ ( sdtmndt0 @ xn @ xn ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[12343:[bind(A,$thf( sdtmndt0 @ xn @ xn ))]]) ).
thf(4,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(47,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)],[4]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(218,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45,52]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( A = sz10 )
| ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ B @ sz10 ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ sz10 )
| ~ ( aNaturalNumber0 @ B ) ),
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( A )),bind(B,$thf( sz10 ))]]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( A = sz10 )
| ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ B @ sz10 ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ sz10 )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[219]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) ) ),
inference(cnf,[status(esa)],[63]) ).
thf(3609,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ xm @ xm )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2071,65]) ).
thf(3610,plain,
( ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xm )
| ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) ) ),
inference(pattern_uni,[status(thm)],[3609:[bind(A,$thf( xm )),bind(B,$thf( xm ))]]) ).
thf(3702,plain,
( ~ ( aNaturalNumber0 @ xm )
| ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) ) ),
inference(simp,[status(thm)],[3610]) ).
thf(4810,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) ) ),
inference(rewrite,[status(thm)],[3702,179]) ).
thf(4811,plain,
aNaturalNumber0 @ ( sk1 @ xm @ xm ),
inference(simp,[status(thm)],[4810]) ).
thf(4834,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4811,134]) ).
thf(4835,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ xm @ xm ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[4834:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(28,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(138,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)],[28]) ).
thf(36,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
thf(173,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(175,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A
= ( sdtasdt0 @ sz10 @ A ) ) ),
inference(cnf,[status(esa)],[173]) ).
thf(177,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(40675,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,177]) ).
thf(40676,plain,
( ( sdtasdt0 @ sz10 @ xn )
= xn ),
inference(pattern_uni,[status(thm)],[40675:[bind(A,$thf( xn ))]]) ).
thf(41448,plain,
( ( xn != xl )
| ( ( sdtasdt0 @ xn @ xm )
!= xm )
| ( ( sdtasdt0 @ sz10 @ xn )
!= ( sdtasdt0 @ xl @ xn ) ) ),
inference(paramod_ordered,[status(thm)],[40676,201]) ).
thf(41612,plain,
( ( xn != xl )
| ( ( sdtasdt0 @ xn @ xm )
!= xm )
| ( sz10 != xl )
| ( xn != xn ) ),
inference(simp,[status(thm)],[41448]) ).
thf(41726,plain,
( ( xn != xl )
| ( ( sdtasdt0 @ xn @ xm )
!= xm )
| ( sz10 != xl ) ),
inference(simp,[status(thm)],[41612]) ).
thf(248,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,133]) ).
thf(249,plain,
( ( sdtasdt0 @ xm @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( xm ))]]) ).
thf(22,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(115,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)],[22]) ).
thf(6060,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz10 @ sz10 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2075,78]) ).
thf(6061,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[6060:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(6120,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) ) ),
inference(simp,[status(thm)],[6061]) ).
thf(9105,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) ) ),
inference(rewrite,[status(thm)],[6120,45]) ).
thf(9106,plain,
aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ),
inference(simp,[status(thm)],[9105]) ).
thf(174,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ A @ sz10 )
= A ) ),
inference(cnf,[status(esa)],[173]) ).
thf(176,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(38804,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9106,176]) ).
thf(38805,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ sz10 )
= ( sdtmndt0 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[38804:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(38712,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11408,176]) ).
thf(38713,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ xl @ xl ) @ sz10 )
= ( sdtmndt0 @ xl @ xl ) ),
inference(pattern_uni,[status(thm)],[38712:[bind(A,$thf( sdtmndt0 @ xl @ xl ))]]) ).
thf(9134,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9106,133]) ).
thf(9135,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[9134:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(20,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(108,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2078,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[108,91]) ).
thf(2079,plain,
sdtlseqdt0 @ sz00 @ sz00,
inference(pattern_uni,[status(thm)],[2078:[bind(A,$thf( sz00 ))]]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B ) ),
inference(cnf,[status(esa)],[63]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(4060,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ sz00 @ sz00 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2079,67]) ).
thf(4061,plain,
( ( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[4060:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(4163,plain,
( ( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= sz00 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference(simp,[status(thm)],[4061]) ).
thf(3605,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz00 @ sz00 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2079,65]) ).
thf(3606,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[3605:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(3701,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) ) ),
inference(simp,[status(thm)],[3606]) ).
thf(3845,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[3701,108]) ).
thf(3846,plain,
aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ),
inference(simp,[status(thm)],[3845]) ).
thf(18306,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3846,124]) ).
thf(18307,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= ( sk1 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[18306:[bind(A,$thf( sk1 @ sz00 @ sz00 ))]]) ).
thf(35160,plain,
( ( ( sk1 @ sz00 @ sz00 )
= sz00 )
| ~ $true ),
inference(rewrite,[status(thm)],[4163,18307,108]) ).
thf(35161,plain,
( ( sk1 @ sz00 @ sz00 )
= sz00 ),
inference(simp,[status(thm)],[35160]) ).
thf(5,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(56,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)],[5]) ).
thf(6043,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz00 @ sz00 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2079,78]) ).
thf(6044,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[6043:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(6114,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) ) ),
inference(simp,[status(thm)],[6044]) ).
thf(8297,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[6114,108]) ).
thf(8298,plain,
aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ),
inference(simp,[status(thm)],[8297]) ).
thf(40641,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8298,177]) ).
thf(40642,plain,
( ( sdtasdt0 @ sz10 @ ( sdtmndt0 @ sz00 @ sz00 ) )
= ( sdtmndt0 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[40641:[bind(A,$thf( sdtmndt0 @ sz00 @ sz00 ))]]) ).
thf(4869,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ xm ) )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,4811]) ).
thf(4870,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ xm ) ) ),
inference(pattern_uni,[status(thm)],[4869:[]]) ).
thf(3641,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ xn @ xn )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2073,65]) ).
thf(3642,plain,
( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) ) ),
inference(pattern_uni,[status(thm)],[3641:[bind(A,$thf( xn )),bind(B,$thf( xn ))]]) ).
thf(3714,plain,
( ~ ( aNaturalNumber0 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) ) ),
inference(simp,[status(thm)],[3642]) ).
thf(6616,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) ) ),
inference(rewrite,[status(thm)],[3714,147]) ).
thf(6617,plain,
aNaturalNumber0 @ ( sk1 @ xn @ xn ),
inference(simp,[status(thm)],[6616]) ).
thf(6679,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6617,133]) ).
thf(6680,plain,
( ( sdtasdt0 @ ( sk1 @ xn @ xn ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[6679:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(121,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtpldt0 @ A @ sz00 )
= A ) ),
inference(cnf,[status(esa)],[120]) ).
thf(123,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[121]) ).
thf(17112,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6617,123]) ).
thf(17113,plain,
( ( sdtpldt0 @ ( sk1 @ xn @ xn ) @ sz00 )
= ( sk1 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[17112:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(18264,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12257,124]) ).
thf(18265,plain,
( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ xn @ xn ) )
= ( sdtmndt0 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[18264:[bind(A,$thf( sdtmndt0 @ xn @ xn ))]]) ).
thf(38778,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,176]) ).
thf(38779,plain,
( ( sdtasdt0 @ sz10 @ sz10 )
= sz10 ),
inference(pattern_uni,[status(thm)],[38778:[bind(A,$thf( sz10 ))]]) ).
thf(39,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(183,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)],[39]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( aNaturalNumber0 @ ( sk2 @ B @ A ) ) ),
inference(cnf,[status(esa)],[183]) ).
thf(10598,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10556,133]) ).
thf(10599,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ xm @ xm ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[10598:[bind(A,$thf( sdtmndt0 @ xm @ xm ))]]) ).
thf(3673,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz10 @ sz10 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2075,65]) ).
thf(3674,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[3673:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(3725,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(simp,[status(thm)],[3674]) ).
thf(7443,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(rewrite,[status(thm)],[3725,45]) ).
thf(7444,plain,
aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ),
inference(simp,[status(thm)],[7443]) ).
thf(18320,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7444,124]) ).
thf(18321,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ sz10 @ sz10 ) )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[18320:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(17110,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[180,123]) ).
thf(17111,plain,
( ( sdtpldt0 @ xl @ sz00 )
= xl ),
inference(pattern_uni,[status(thm)],[17110:[bind(A,$thf( xl ))]]) ).
thf(256,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,133]) ).
thf(257,plain,
( ( sdtasdt0 @ xn @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( xn ))]]) ).
thf(1450,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,114]) ).
thf(1451,plain,
( ( xn = sz00 )
| ( sz10 = xn )
| ( sdtlseqdt0 @ sz10 @ xn ) ),
inference(pattern_uni,[status(thm)],[1450:[bind(A,$thf( xn ))]]) ).
thf(3526,plain,
( ( xn = sz00 )
| ( sdtlseqdt0 @ sz10 @ xn )
| ( sz10 != sz10 ) ),
inference(paramod_ordered,[status(thm)],[1451,2075]) ).
thf(3527,plain,
( ( xn = sz00 )
| ( sdtlseqdt0 @ sz10 @ xn ) ),
inference(pattern_uni,[status(thm)],[3526:[]]) ).
thf(12285,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ xn ) )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[3527,12257]) ).
thf(12286,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ xn ) ) ),
inference(pattern_uni,[status(thm)],[12285:[]]) ).
thf(8356,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8298,134]) ).
thf(8357,plain,
( ( sdtasdt0 @ sz00 @ ( sdtmndt0 @ sz00 @ sz00 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[8356:[bind(A,$thf( sdtmndt0 @ sz00 @ sz00 ))]]) ).
thf(38854,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4811,176]) ).
thf(38855,plain,
( ( sdtasdt0 @ ( sk1 @ xm @ xm ) @ sz10 )
= ( sk1 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[38854:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(24,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(125,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)],[24]) ).
thf(6675,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ xn ) )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[3527,6617]) ).
thf(6676,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ xn ) ) ),
inference(pattern_uni,[status(thm)],[6675:[]]) ).
thf(40671,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,177]) ).
thf(40672,plain,
( ( sdtasdt0 @ sz10 @ xm )
= xm ),
inference(pattern_uni,[status(thm)],[40671:[bind(A,$thf( xm ))]]) ).
thf(38780,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[180,176]) ).
thf(38781,plain,
( ( sdtasdt0 @ xl @ sz10 )
= xl ),
inference(pattern_uni,[status(thm)],[38780:[bind(A,$thf( xl ))]]) ).
thf(40107,plain,
( ( ( sdtasdt0 @ xn @ xm )
!= xm )
| ( ( sdtasdt0 @ xl @ sz10 )
!= ( sdtasdt0 @ xl @ xn ) ) ),
inference(paramod_ordered,[status(thm)],[38781,201]) ).
thf(40256,plain,
( ( ( sdtasdt0 @ xn @ xm )
!= xm )
| ( xl != xl )
| ( sz10 != xn ) ),
inference(simp,[status(thm)],[40107]) ).
thf(40358,plain,
( ( ( sdtasdt0 @ xn @ xm )
!= xm )
| ( sz10 != xn ) ),
inference(simp,[status(thm)],[40256]) ).
thf(47336,plain,
( ( sz10 != xn )
| ( ( sdtasdt0 @ sz10 @ xm )
!= ( sdtasdt0 @ xn @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[40672,40358]) ).
thf(47414,plain,
( ( sz10 != xn )
| ( sz10 != xn )
| ( xm != xm ) ),
inference(simp,[status(thm)],[47336]) ).
thf(47471,plain,
sz10 != xn,
inference(simp,[status(thm)],[47414]) ).
thf(948,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,134]) ).
thf(949,plain,
( ( sdtasdt0 @ sz00 @ xn )
= sz00 ),
inference(pattern_uni,[status(thm)],[948:[bind(A,$thf( xn ))]]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( B
!= ( sdtasdt0 @ A @ C ) )
| ( doDivides0 @ A @ B ) ),
inference(cnf,[status(esa)],[183]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sdtasdt0 @ A @ C ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( doDivides0 @ A @ B ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ( doDivides0 @ A @ ( sdtasdt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(17048,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8298,123]) ).
thf(17049,plain,
( ( sdtpldt0 @ ( sdtmndt0 @ sz00 @ sz00 ) @ sz00 )
= ( sdtmndt0 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[17048:[bind(A,$thf( sdtmndt0 @ sz00 @ sz00 ))]]) ).
thf(44,plain,
sz10 != sz00,
inference(cnf,[status(esa)],[43]) ).
thf(46,plain,
sz10 != sz00,
inference(lifteq,[status(thm)],[44]) ).
thf(16,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(93,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)],[16]) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[108,52]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ B @ sz00 ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ sz00 )
| ~ ( aNaturalNumber0 @ B ) ),
inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( A )),bind(B,$thf( sz00 ))]]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ B @ sz00 ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ sz00 )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[225]) ).
thf(11494,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11408,91]) ).
thf(11495,plain,
sdtlseqdt0 @ ( sdtmndt0 @ xl @ xl ) @ ( sdtmndt0 @ xl @ xl ),
inference(pattern_uni,[status(thm)],[11494:[bind(A,$thf( sdtmndt0 @ xl @ xl ))]]) ).
thf(260,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[180,133]) ).
thf(261,plain,
( ( sdtasdt0 @ xl @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( xl ))]]) ).
thf(34,axiom,
( ( xl != sz00 )
& ( doDivides0 @ xl @ xm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524_04) ).
thf(164,plain,
( ( xl != sz00 )
& ( doDivides0 @ xl @ xm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(17128,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9106,123]) ).
thf(17129,plain,
( ( sdtpldt0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ sz00 )
= ( sdtmndt0 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[17128:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(50329,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ B )
| ( doDivides0 @ A @ ( sdtasdt0 @ A @ B ) )
| ( ( sdtasdt0 @ sz10 @ sz10 )
!= ( sdtasdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38779,189]) ).
thf(50330,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ( doDivides0 @ sz10 @ ( sdtasdt0 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[50329:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(50779,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ( doDivides0 @ sz10 @ ( sdtasdt0 @ sz10 @ sz10 ) ) ),
inference(simp,[status(thm)],[50330]) ).
thf(82556,plain,
( ~ $true
| ( doDivides0 @ sz10 @ sz10 ) ),
inference(rewrite,[status(thm)],[50779,38779,45]) ).
thf(82557,plain,
doDivides0 @ sz10 @ sz10,
inference(simp,[status(thm)],[82556]) ).
thf(82558,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk2 @ B @ A ) )
| ( ( doDivides0 @ sz10 @ sz10 )
!= ( doDivides0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[82557,185]) ).
thf(82559,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk2 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[82558:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(82691,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk2 @ sz10 @ sz10 ) ) ),
inference(simp,[status(thm)],[82559]) ).
thf(82692,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk2 @ sz10 @ sz10 ) ) ),
inference(rewrite,[status(thm)],[82691,45]) ).
thf(82693,plain,
aNaturalNumber0 @ ( sk2 @ sz10 @ sz10 ),
inference(simp,[status(thm)],[82692]) ).
thf(82848,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk2 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82693,176]) ).
thf(82849,plain,
( ( sdtasdt0 @ ( sk2 @ sz10 @ sz10 ) @ sz10 )
= ( sk2 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[82848:[bind(A,$thf( sk2 @ sz10 @ sz10 ))]]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) )
=> ( doDivides0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
thf(84,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) )
=> ( doDivides0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(2356,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A )
| ( B != sz00 )
| ( A != sz10 ) ),
inference(paramod_ordered,[status(thm)],[58,46]) ).
thf(2357,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ sz10 @ A )
| ~ ( sdtlseqdt0 @ A @ sz10 )
| ( A != sz00 ) ),
inference(pattern_uni,[status(thm)],[2356:[bind(A,$thf( sz10 ))]]) ).
thf(2546,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( sdtlseqdt0 @ sz10 @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ sz10 ) ),
inference(simp,[status(thm)],[2357]) ).
thf(16464,plain,
( ~ $true
| ~ $true
| ~ ( sdtlseqdt0 @ sz10 @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ sz10 ) ),
inference(rewrite,[status(thm)],[2546,108,45]) ).
thf(16465,plain,
( ~ ( sdtlseqdt0 @ sz10 @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ sz10 ) ),
inference(simp,[status(thm)],[16464]) ).
thf(16555,plain,
( ~ ( sdtlseqdt0 @ sz10 @ sz00 )
| ( ( sdtlseqdt0 @ xm @ xm )
!= ( sdtlseqdt0 @ sz00 @ sz10 ) ) ),
inference(paramod_ordered,[status(thm)],[2071,16465]) ).
thf(16622,plain,
( ~ ( sdtlseqdt0 @ sz10 @ sz00 )
| ( xm != sz00 )
| ( sz10 != xm ) ),
inference(simp,[status(thm)],[16555]) ).
thf(17896,plain,
( ( xm != sz00 )
| ( sz10 != xm )
| ( ( sdtlseqdt0 @ sz10 @ sz00 )
!= ( sdtlseqdt0 @ xm @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[2071,16622]) ).
thf(17974,plain,
( ( xm != sz00 )
| ( sz10 != xm )
| ( sz10 != xm )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[17896]) ).
thf(18003,plain,
( ( xm != sz00 )
| ( sz10 != xm ) ),
inference(simp,[status(thm)],[17974]) ).
thf(18025,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sz10 != xm )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,18003]) ).
thf(18026,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sz10 != xm ) ),
inference(pattern_uni,[status(thm)],[18025:[]]) ).
thf(252,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[108,133]) ).
thf(253,plain,
( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( sz00 ))]]) ).
thf(38684,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12257,176]) ).
thf(38685,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ xn @ xn ) @ sz10 )
= ( sdtmndt0 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[38684:[bind(A,$thf( sdtmndt0 @ xn @ xn ))]]) ).
thf(7,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(61,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)],[7]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[45,52]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ sz10 @ A )
!= ( sdtpldt0 @ sz10 @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sz10 ))]]) ).
thf(4995,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ sz00 @ ( sk1 @ xm @ sz00 ) )
= sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,4835]) ).
thf(4996,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ sz00 @ ( sk1 @ xm @ sz00 ) )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[4995:[]]) ).
thf(38674,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8298,176]) ).
thf(38675,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ sz00 @ sz00 ) @ sz10 )
= ( sdtmndt0 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[38674:[bind(A,$thf( sdtmndt0 @ sz00 @ sz00 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( doDivides0 @ A @ B )
& ( B != sz00 ) )
=> ( sdtlseqdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( doDivides0 @ A @ B )
& ( B != sz00 ) )
=> ( sdtlseqdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( B = sz00 )
| ( sdtlseqdt0 @ A @ B ) ),
inference(cnf,[status(esa)],[87]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( B = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(18328,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[180,124]) ).
thf(18329,plain,
( ( sdtpldt0 @ sz00 @ xl )
= xl ),
inference(pattern_uni,[status(thm)],[18328:[bind(A,$thf( xl ))]]) ).
thf(2953,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ xm @ sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,2071]) ).
thf(2954,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ xm @ sz00 ) ),
inference(pattern_uni,[status(thm)],[2953:[]]) ).
thf(216,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,52]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( sz10 = A )
| ( ( sdtpldt0 @ B @ sz10 )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ sz10 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( sz10 ))]]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( sz10 = A )
| ( ( sdtpldt0 @ B @ sz10 )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ sz10 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[217]) ).
thf(4879,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4811,133]) ).
thf(4880,plain,
( ( sdtasdt0 @ ( sk1 @ xm @ xm ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[4879:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(5156,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ ( sk1 @ xm @ sz00 ) @ sz00 )
= sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,4880]) ).
thf(5157,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ ( sk1 @ xm @ sz00 ) @ sz00 )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[5156:[]]) ).
thf(4887,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4811,91]) ).
thf(4888,plain,
sdtlseqdt0 @ ( sk1 @ xm @ xm ) @ ( sk1 @ xm @ xm ),
inference(pattern_uni,[status(thm)],[4887:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(82820,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk2 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82693,124]) ).
thf(82821,plain,
( ( sdtpldt0 @ sz00 @ ( sk2 @ sz10 @ sz10 ) )
= ( sk2 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[82820:[bind(A,$thf( sk2 @ sz10 @ sz10 ))]]) ).
thf(12299,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12257,133]) ).
thf(12300,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ xn @ xn ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[12299:[bind(A,$thf( sdtmndt0 @ xn @ xn ))]]) ).
thf(6,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(59,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)],[6]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ( doDivides0 @ A @ C ) ),
inference(cnf,[status(esa)],[59]) ).
thf(3627,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ xl @ xl )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2077,65]) ).
thf(3628,plain,
( ~ ( aNaturalNumber0 @ xl )
| ~ ( aNaturalNumber0 @ xl )
| ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) ) ),
inference(pattern_uni,[status(thm)],[3627:[bind(A,$thf( xl )),bind(B,$thf( xl ))]]) ).
thf(3709,plain,
( ~ ( aNaturalNumber0 @ xl )
| ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) ) ),
inference(simp,[status(thm)],[3628]) ).
thf(5802,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) ) ),
inference(rewrite,[status(thm)],[3709,180]) ).
thf(5803,plain,
aNaturalNumber0 @ ( sk1 @ xl @ xl ),
inference(simp,[status(thm)],[5802]) ).
thf(5874,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5803,91]) ).
thf(5875,plain,
sdtlseqdt0 @ ( sk1 @ xl @ xl ) @ ( sk1 @ xl @ xl ),
inference(pattern_uni,[status(thm)],[5874:[bind(A,$thf( sk1 @ xl @ xl ))]]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) )
| ( doDivides0 @ A @ C ) ),
inference(cnf,[status(esa)],[84]) ).
thf(8364,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8298,91]) ).
thf(8365,plain,
sdtlseqdt0 @ ( sdtmndt0 @ sz00 @ sz00 ) @ ( sdtmndt0 @ sz00 @ sz00 ),
inference(pattern_uni,[status(thm)],[8364:[bind(A,$thf( sdtmndt0 @ sz00 @ sz00 ))]]) ).
thf(17060,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,123]) ).
thf(17061,plain,
( ( sdtpldt0 @ xn @ sz00 )
= xn ),
inference(pattern_uni,[status(thm)],[17060:[bind(A,$thf( xn ))]]) ).
thf(956,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[180,134]) ).
thf(957,plain,
( ( sdtasdt0 @ sz00 @ xl )
= sz00 ),
inference(pattern_uni,[status(thm)],[956:[bind(A,$thf( xl ))]]) ).
thf(6696,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6617,91]) ).
thf(6697,plain,
sdtlseqdt0 @ ( sk1 @ xn @ xn ) @ ( sk1 @ xn @ xn ),
inference(pattern_uni,[status(thm)],[6696:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(35286,plain,
( ( sdtlseqdt0 @ ( sk1 @ xn @ xn ) @ sz00 )
| ( ( sk1 @ xn @ xn )
!= ( sk1 @ sz00 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[35161,6697]) ).
thf(35290,plain,
( ( sdtlseqdt0 @ ( sk1 @ xn @ xn ) @ sz00 )
| ( xn != sz00 )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[35286]) ).
thf(35344,plain,
( ( sdtlseqdt0 @ ( sk1 @ xn @ xn ) @ sz00 )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[35290]) ).
thf(37126,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ ( sk1 @ xn @ xn ) @ sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[3527,35344]) ).
thf(37127,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ ( sk1 @ xn @ xn ) @ sz00 ) ),
inference(pattern_uni,[status(thm)],[37126:[]]) ).
thf(37827,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ ( sk1 @ xn @ sz00 ) @ sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[3527,37127]) ).
thf(37828,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ ( sk1 @ xn @ sz00 ) @ sz00 ) ),
inference(pattern_uni,[status(thm)],[37827:[]]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[135]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[136]) ).
thf(165,plain,
doDivides0 @ xl @ xm,
inference(cnf,[status(esa)],[164]) ).
thf(15,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(92,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(204,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,52]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( xm = A )
| ( ( sdtpldt0 @ B @ xm )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ xm @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( xm ))]]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( xm = A )
| ( ( sdtpldt0 @ B @ xm )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ xm @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[205]) ).
thf(40,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(190,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)],[40]) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( A = sz00 )
| ( B = C )
| ~ ( sdtlseqdt0 @ B @ C )
| ( sdtlseqdt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) ),
inference(cnf,[status(esa)],[190]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( A = sz00 )
| ( B = C )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( sdtlseqdt0 @ B @ C )
| ( sdtlseqdt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(1468,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[180,114]) ).
thf(1469,plain,
( ( xl = sz00 )
| ( sz10 = xl )
| ( sdtlseqdt0 @ sz10 @ xl ) ),
inference(pattern_uni,[status(thm)],[1468:[bind(A,$thf( xl ))]]) ).
thf(166,plain,
xl != sz00,
inference(cnf,[status(esa)],[164]) ).
thf(167,plain,
xl != sz00,
inference(lifteq,[status(thm)],[166]) ).
thf(5400,plain,
( ( sz10 = xl )
| ( sdtlseqdt0 @ sz10 @ xl ) ),
inference(simplifyReflect,[status(thm)],[1469,167]) ).
thf(5464,plain,
( ( sdtlseqdt0 @ sz10 @ xl )
| ( sz10 != sz10 ) ),
inference(paramod_ordered,[status(thm)],[5400,2075]) ).
thf(5465,plain,
sdtlseqdt0 @ sz10 @ xl,
inference(pattern_uni,[status(thm)],[5464:[]]) ).
thf(4993,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ sz00 @ ( sk1 @ sz00 @ xm ) )
= sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,4835]) ).
thf(4994,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ sz00 @ ( sk1 @ sz00 @ xm ) )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[4993:[]]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( A = sz00 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(5857,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5803,133]) ).
thf(5858,plain,
( ( sdtasdt0 @ ( sk1 @ xl @ xl ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[5857:[bind(A,$thf( sk1 @ xl @ xl ))]]) ).
thf(41407,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( xn != xl )
| ( ( sdtasdt0 @ sz10 @ xn )
!= ( sdtasdt0 @ xl @ xn ) ) ),
inference(paramod_ordered,[status(thm)],[40676,3008]) ).
thf(41653,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( xn != xl )
| ( sz10 != xl )
| ( xn != xn ) ),
inference(simp,[status(thm)],[41407]) ).
thf(41741,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( xn != xl )
| ( sz10 != xl ) ),
inference(simp,[status(thm)],[41653]) ).
thf(7500,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7444,133]) ).
thf(7501,plain,
( ( sdtasdt0 @ ( sk1 @ sz10 @ sz10 ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[7500:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(32,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(148,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)],[32]) ).
thf(149,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 ) ) ) )
& ! [C: $i] :
( ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) )
=> ( C
= ( sdtsldt0 @ B @ A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[148]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = sz00 )
| ~ ( doDivides0 @ A @ B )
| ( C
!= ( sdtsldt0 @ B @ A ) )
| ( aNaturalNumber0 @ C ) ),
inference(cnf,[status(esa)],[149]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( A = sz00 )
| ( C
!= ( sdtsldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( aNaturalNumber0 @ ( sdtsldt0 @ B @ A ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( sdtlseqdt0 @ ( sdtpldt0 @ C @ A ) @ ( sdtpldt0 @ C @ B ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( sdtlseqdt0 @ ( sdtpldt0 @ C @ A ) @ ( sdtpldt0 @ C @ B ) ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(7512,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7444,134]) ).
thf(7513,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ sz10 @ sz10 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[7512:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(29,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(141,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)],[29]) ).
thf(35184,plain,
( ( sdtlseqdt0 @ sz00 @ ( sk1 @ xm @ xm ) )
| ( ( sk1 @ xm @ xm )
!= ( sk1 @ sz00 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[35161,4888]) ).
thf(35296,plain,
( ( sdtlseqdt0 @ sz00 @ ( sk1 @ xm @ xm ) )
| ( xm != sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[35184]) ).
thf(35350,plain,
( ( sdtlseqdt0 @ sz00 @ ( sk1 @ xm @ xm ) )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[35296]) ).
thf(76839,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ ( sk1 @ xm @ xm ) )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,35350]) ).
thf(76840,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ ( sk1 @ xm @ xm ) ) ),
inference(pattern_uni,[status(thm)],[76839:[]]) ).
thf(77199,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ ( sk1 @ xm @ sz00 ) )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,76840]) ).
thf(77200,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ ( sk1 @ xm @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[77199:[]]) ).
thf(82881,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk2 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82693,91]) ).
thf(82882,plain,
sdtlseqdt0 @ ( sk2 @ sz10 @ sz10 ) @ ( sk2 @ sz10 @ sz10 ),
inference(pattern_uni,[status(thm)],[82881:[bind(A,$thf( sk2 @ sz10 @ sz10 ))]]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( B = sz00 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( B = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(10574,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ xm ) )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,10556]) ).
thf(10575,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ xm ) ) ),
inference(pattern_uni,[status(thm)],[10574:[]]) ).
thf(38774,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10556,176]) ).
thf(38775,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ xm @ xm ) @ sz10 )
= ( sdtmndt0 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[38774:[bind(A,$thf( sdtmndt0 @ xm @ xm ))]]) ).
thf(41255,plain,
( ( xm != xl )
| ( xm != sz00 )
| ( ( sdtasdt0 @ sz10 @ xm )
!= ( sdtasdt0 @ xl @ xn ) ) ),
inference(paramod_ordered,[status(thm)],[40672,326]) ).
thf(41342,plain,
( ( xm != xl )
| ( xm != sz00 )
| ( sz10 != xl )
| ( xm != xn ) ),
inference(simp,[status(thm)],[41255]) ).
thf(82842,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk2 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82693,134]) ).
thf(82843,plain,
( ( sdtasdt0 @ sz00 @ ( sk2 @ sz10 @ sz10 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[82842:[bind(A,$thf( sk2 @ sz10 @ sz10 ))]]) ).
thf(25,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(127,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)],[25]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( iLess0 @ A @ B ) ),
inference(cnf,[status(esa)],[127]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( iLess0 @ A @ B ) ),
inference(lifteq,[status(thm)],[128]) ).
thf(5822,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5803,134]) ).
thf(5823,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ xl @ xl ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[5822:[bind(A,$thf( sk1 @ xl @ xl ))]]) ).
thf(35285,plain,
( ( sdtlseqdt0 @ sz00 @ ( sk1 @ xn @ xn ) )
| ( ( sk1 @ xn @ xn )
!= ( sk1 @ sz00 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[35161,6697]) ).
thf(35299,plain,
( ( sdtlseqdt0 @ sz00 @ ( sk1 @ xn @ xn ) )
| ( xn != sz00 )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[35285]) ).
thf(35353,plain,
( ( sdtlseqdt0 @ sz00 @ ( sk1 @ xn @ xn ) )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[35299]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(10634,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10556,134]) ).
thf(10635,plain,
( ( sdtasdt0 @ sz00 @ ( sdtmndt0 @ xm @ xm ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[10634:[bind(A,$thf( sdtmndt0 @ xm @ xm ))]]) ).
thf(9170,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9106,134]) ).
thf(9171,plain,
( ( sdtasdt0 @ sz00 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[9170:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(6636,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6617,134]) ).
thf(6637,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ xn @ xn ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[6636:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(38770,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7444,176]) ).
thf(38771,plain,
( ( sdtasdt0 @ ( sk1 @ sz10 @ sz10 ) @ sz10 )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[38770:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(40854,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5803,177]) ).
thf(40855,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ xl @ xl ) )
= ( sk1 @ xl @ xl ) ),
inference(pattern_uni,[status(thm)],[40854:[bind(A,$thf( sk1 @ xl @ xl ))]]) ).
thf(4871,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( aNaturalNumber0 @ ( sk1 @ xm @ sz00 ) )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,4811]) ).
thf(4872,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( aNaturalNumber0 @ ( sk1 @ xm @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[4871:[]]) ).
thf(3791,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ xn @ sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[3527,2073]) ).
thf(3792,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ xn @ sz00 ) ),
inference(pattern_uni,[status(thm)],[3791:[]]) ).
thf(38700,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,176]) ).
thf(38701,plain,
( ( sdtasdt0 @ xm @ sz10 )
= xm ),
inference(pattern_uni,[status(thm)],[38700:[bind(A,$thf( xm ))]]) ).
thf(40685,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11408,177]) ).
thf(40686,plain,
( ( sdtasdt0 @ sz10 @ ( sdtmndt0 @ xl @ xl ) )
= ( sdtmndt0 @ xl @ xl ) ),
inference(pattern_uni,[status(thm)],[40685:[bind(A,$thf( sdtmndt0 @ xl @ xl ))]]) ).
thf(258,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,133]) ).
thf(259,plain,
( ( sdtasdt0 @ sz10 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( sz10 ))]]) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ C @ A ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[115]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ C @ A ) )
| ( B = C )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(17108,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,123]) ).
thf(17109,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= sz10 ),
inference(pattern_uni,[status(thm)],[17108:[bind(A,$thf( sz10 ))]]) ).
thf(30,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(144,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39115,plain,
( ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( ( sdtasdt0 @ xm @ sz10 )
!= ( sdtasdt0 @ xn @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[38701,201]) ).
thf(39295,plain,
( ( ( sdtasdt0 @ xl @ xn )
!= xl )
| ( xm != xn )
| ( sz10 != xm ) ),
inference(simp,[status(thm)],[39115]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(86,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,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(159,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)],[33]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( B
= ( sdtasdt0 @ A @ ( sk2 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[183]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ ( sk2 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B ) ),
inference(lifteq,[status(thm)],[184]) ).
thf(35,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(168,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)],[35]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtasdt0 @ A @ B )
!= ( sdtasdt0 @ A @ C ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[168]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( A = sz00 )
| ( ( sdtasdt0 @ A @ B )
!= ( sdtasdt0 @ A @ C ) )
| ( B = C )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(10,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(81,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)],[10]) ).
thf(18330,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6617,124]) ).
thf(18331,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ xn @ xn ) )
= ( sk1 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[18330:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[179,52]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( A = xm )
| ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ B @ xm ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ xm )
| ~ ( aNaturalNumber0 @ B ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( A )),bind(B,$thf( xm ))]]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( A = xm )
| ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ B @ xm ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ xm )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[207]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtpldt0 @ A @ C )
!= B )
| ( C
= ( sdtmndt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ C )
!= B )
| ( C
= ( sdtmndt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( ( sdtmndt0 @ ( sdtpldt0 @ A @ B ) @ A )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) )
| ~ ( sdtlseqdt0 @ A @ ( sdtpldt0 @ A @ B ) )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[75]) ).
thf(17,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(98,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)],[17]) ).
thf(82734,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk2 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82693,133]) ).
thf(82735,plain,
( ( sdtasdt0 @ ( sk2 @ sz10 @ sz10 ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[82734:[bind(A,$thf( sk2 @ sz10 @ sz10 ))]]) ).
thf(38873,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5803,176]) ).
thf(38874,plain,
( ( sdtasdt0 @ ( sk1 @ xl @ xl ) @ sz10 )
= ( sk1 @ xl @ xl ) ),
inference(pattern_uni,[status(thm)],[38873:[bind(A,$thf( sk1 @ xl @ xl ))]]) ).
thf(11486,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11408,134]) ).
thf(11487,plain,
( ( sdtasdt0 @ sz00 @ ( sdtmndt0 @ xl @ xl ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[11486:[bind(A,$thf( sdtmndt0 @ xl @ xl ))]]) ).
thf(18276,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,124]) ).
thf(18277,plain,
( ( sdtpldt0 @ sz00 @ xn )
= xn ),
inference(pattern_uni,[status(thm)],[18276:[bind(A,$thf( xn ))]]) ).
thf(40743,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7444,177]) ).
thf(40744,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[40743:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[139]) ).
thf(6677,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ xn @ sz00 ) )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[3527,6617]) ).
thf(6678,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ xn @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[6677:[]]) ).
thf(942,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,134]) ).
thf(943,plain,
( ( sdtasdt0 @ sz00 @ xm )
= sz00 ),
inference(pattern_uni,[status(thm)],[942:[bind(A,$thf( xm ))]]) ).
thf(77197,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ ( sk1 @ sz00 @ xm ) )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,76840]) ).
thf(77198,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ ( sk1 @ sz00 @ xm ) ) ),
inference(pattern_uni,[status(thm)],[77197:[]]) ).
thf(2951,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ xm )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,2071]) ).
thf(2952,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ xm ) ),
inference(pattern_uni,[status(thm)],[2951:[]]) ).
thf(3072,plain,
( ( sdtlseqdt0 @ sz00 @ xm )
| ( ( sdtlseqdt0 @ sz10 @ xm )
!= ( sdtlseqdt0 @ sz00 @ xm ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2952]) ).
thf(3073,plain,
( ( sdtlseqdt0 @ sz00 @ xm )
| ( ( sdtlseqdt0 @ sz10 @ xm )
!= ( sdtlseqdt0 @ sz00 @ xm ) ) ),
inference(simp,[status(thm)],[3072]) ).
thf(17050,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12257,123]) ).
thf(17051,plain,
( ( sdtpldt0 @ ( sdtmndt0 @ xn @ xn ) @ sz00 )
= ( sdtmndt0 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[17050:[bind(A,$thf( sdtmndt0 @ xn @ xn ))]]) ).
thf(2983,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( doDivides0 @ xl @ sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,165]) ).
thf(2984,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( doDivides0 @ xl @ sz00 ) ),
inference(pattern_uni,[status(thm)],[2983:[]]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[180,52]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ xl @ A )
!= ( sdtpldt0 @ xl @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( xl ))]]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( C
!= ( sdtmndt0 @ B @ A ) )
| ( ( sdtpldt0 @ A @ C )
= B ) ),
inference(cnf,[status(esa)],[71]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sdtmndt0 @ B @ A ) )
| ( ( sdtpldt0 @ A @ C )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sdtmndt0 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(simp,[status(thm)],[79]) ).
thf(10642,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10556,91]) ).
thf(10643,plain,
sdtlseqdt0 @ ( sdtmndt0 @ xm @ xm ) @ ( sdtmndt0 @ xm @ xm ),
inference(pattern_uni,[status(thm)],[10642:[bind(A,$thf( sdtmndt0 @ xm @ xm ))]]) ).
thf(18274,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,124]) ).
thf(18275,plain,
( ( sdtpldt0 @ sz00 @ xm )
= xm ),
inference(pattern_uni,[status(thm)],[18274:[bind(A,$thf( xm ))]]) ).
thf(40761,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6617,177]) ).
thf(40762,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ xn @ xn ) )
= ( sk1 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[40761:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(4114,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ sz10 @ sz10 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2075,67]) ).
thf(4115,plain,
( ( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[4114:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(4140,plain,
( ( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(simp,[status(thm)],[4115]) ).
thf(16284,plain,
( ( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 )
| ~ $true ),
inference(rewrite,[status(thm)],[4140,45]) ).
thf(16285,plain,
( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 ),
inference(simp,[status(thm)],[16284]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) ) ),
inference(cnf,[status(esa)],[159]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[160]) ).
thf(12287,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ sz00 ) )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[3527,12257]) ).
thf(12288,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[12287:[]]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[179,52]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ xm @ A )
!= ( sdtpldt0 @ xm @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( xm ))]]) ).
thf(38704,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,176]) ).
thf(38705,plain,
( ( sdtasdt0 @ xn @ sz10 )
= xn ),
inference(pattern_uni,[status(thm)],[38704:[bind(A,$thf( xn ))]]) ).
thf(17104,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10556,123]) ).
thf(17105,plain,
( ( sdtpldt0 @ ( sdtmndt0 @ xm @ xm ) @ sz00 )
= ( sdtmndt0 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[17104:[bind(A,$thf( sdtmndt0 @ xm @ xm ))]]) ).
thf(17165,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4811,123]) ).
thf(17166,plain,
( ( sdtpldt0 @ ( sk1 @ xm @ xm ) @ sz00 )
= ( sk1 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[17165:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(8326,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8298,133]) ).
thf(8327,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ sz00 @ sz00 ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[8326:[bind(A,$thf( sdtmndt0 @ sz00 @ sz00 ))]]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[181]) ).
thf(18326,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,124]) ).
thf(18327,plain,
( ( sdtpldt0 @ sz00 @ sz10 )
= sz10 ),
inference(pattern_uni,[status(thm)],[18326:[bind(A,$thf( sz10 ))]]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = sz00 )
| ~ ( doDivides0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( B
!= ( sdtasdt0 @ A @ C ) )
| ( C
= ( sdtsldt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( A = sz00 )
| ( B
!= ( sdtasdt0 @ A @ C ) )
| ( C
= ( sdtsldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ( ( sdtsldt0 @ ( sdtasdt0 @ A @ B ) @ A )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) )
| ~ ( doDivides0 @ A @ ( sdtasdt0 @ A @ B ) )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[153]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtasdt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ( B = sz00 ) ),
inference(cnf,[status(esa)],[141]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ( B = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,52]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( xn = A )
| ( ( sdtpldt0 @ B @ xn )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ xn @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( xn ))]]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( xn = A )
| ( ( sdtpldt0 @ B @ xn )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ xn @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[211]) ).
thf(40753,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[180,177]) ).
thf(40754,plain,
( ( sdtasdt0 @ sz10 @ xl )
= xl ),
inference(pattern_uni,[status(thm)],[40753:[bind(A,$thf( xl ))]]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ),
inference(cnf,[status(esa)],[98]) ).
thf(17126,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[108,123]) ).
thf(17127,plain,
( ( sdtpldt0 @ sz00 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[17126:[bind(A,$thf( sz00 ))]]) ).
thf(18397,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4811,124]) ).
thf(18398,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ xm @ xm ) )
= ( sk1 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[18397:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(41597,plain,
( ( xn != xl )
| ( xm != sz00 )
| ( ( sdtasdt0 @ sz10 @ xn )
!= ( sdtasdt0 @ xl @ xn ) ) ),
inference(paramod_ordered,[status(thm)],[40676,326]) ).
thf(41631,plain,
( ( xn != xl )
| ( xm != sz00 )
| ( sz10 != xl )
| ( xn != xn ) ),
inference(simp,[status(thm)],[41597]) ).
thf(41732,plain,
( ( xn != xl )
| ( xm != sz00 )
| ( sz10 != xl ) ),
inference(simp,[status(thm)],[41631]) ).
thf(38782,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6617,176]) ).
thf(38783,plain,
( ( sdtasdt0 @ ( sk1 @ xn @ xn ) @ sz10 )
= ( sk1 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[38782:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(40783,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9106,177]) ).
thf(40784,plain,
( ( sdtasdt0 @ sz10 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= ( sdtmndt0 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[40783:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = sz00 )
| ~ ( doDivides0 @ A @ B )
| ( C
!= ( sdtsldt0 @ B @ A ) )
| ( B
= ( sdtasdt0 @ A @ C ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( A = sz00 )
| ( C
!= ( sdtsldt0 @ B @ A ) )
| ( B
= ( sdtasdt0 @ A @ C ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ( ( sdtasdt0 @ A @ ( sdtsldt0 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B ) ),
inference(simp,[status(thm)],[157]) ).
thf(18348,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9106,124]) ).
thf(18349,plain,
( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= ( sdtmndt0 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[18348:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtasdt0 @ B @ A )
!= ( sdtasdt0 @ C @ A ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[168]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( A = sz00 )
| ( ( sdtasdt0 @ B @ A )
!= ( sdtasdt0 @ C @ A ) )
| ( B = C )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(9178,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9106,91]) ).
thf(9179,plain,
sdtlseqdt0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ ( sdtmndt0 @ sz10 @ sz10 ),
inference(pattern_uni,[status(thm)],[9178:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(37825,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ ( sk1 @ sz00 @ xn ) @ sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[3527,37127]) ).
thf(37826,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ ( sk1 @ sz00 @ xn ) @ sz00 ) ),
inference(pattern_uni,[status(thm)],[37825:[]]) ).
thf(17062,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11408,123]) ).
thf(17063,plain,
( ( sdtpldt0 @ ( sdtmndt0 @ xl @ xl ) @ sz00 )
= ( sdtmndt0 @ xl @ xl ) ),
inference(pattern_uni,[status(thm)],[17062:[bind(A,$thf( sdtmndt0 @ xl @ xl ))]]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ C ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ C ) ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[108,52]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( sz00 = A )
| ( ( sdtpldt0 @ B @ sz00 )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ sz00 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( sz00 ))]]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( sz00 = A )
| ( ( sdtpldt0 @ B @ sz00 )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ sz00 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[223]) ).
thf(7519,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7444,91]) ).
thf(7520,plain,
sdtlseqdt0 @ ( sk1 @ sz10 @ sz10 ) @ ( sk1 @ sz10 @ sz10 ),
inference(pattern_uni,[status(thm)],[7519:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(18262,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8298,124]) ).
thf(18263,plain,
( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ sz00 @ sz00 ) )
= ( sdtmndt0 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[18262:[bind(A,$thf( sdtmndt0 @ sz00 @ sz00 ))]]) ).
thf(117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtpldt0 @ A @ B )
!= ( sdtpldt0 @ A @ C ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[115]) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
!= ( sdtpldt0 @ A @ C ) )
| ( B = C )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[117]) ).
thf(11446,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11408,133]) ).
thf(11447,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ xl @ xl ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[11446:[bind(A,$thf( sdtmndt0 @ xl @ xl ))]]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = sz00 )
| ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[144]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(40655,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12257,177]) ).
thf(40656,plain,
( ( sdtasdt0 @ sz10 @ ( sdtmndt0 @ xn @ xn ) )
= ( sdtmndt0 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[40655:[bind(A,$thf( sdtmndt0 @ xn @ xn ))]]) ).
thf(17058,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,123]) ).
thf(17059,plain,
( ( sdtpldt0 @ xm @ sz00 )
= xm ),
inference(pattern_uni,[status(thm)],[17058:[bind(A,$thf( xm ))]]) ).
thf(3789,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ sz00 @ xn )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[3527,2073]) ).
thf(3790,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ sz00 @ xn ) ),
inference(pattern_uni,[status(thm)],[3789:[]]) ).
thf(236,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[180,52]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( xl = A )
| ( ( sdtpldt0 @ B @ xl )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ xl @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( xl ))]]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( xl = A )
| ( ( sdtpldt0 @ B @ xl )
!= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ xl @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[237]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ A @ C )
| ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) ),
inference(cnf,[status(esa)],[125]) ).
thf(40747,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10556,177]) ).
thf(40748,plain,
( ( sdtasdt0 @ sz10 @ ( sdtmndt0 @ xm @ xm ) )
= ( sdtmndt0 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[40747:[bind(A,$thf( sdtmndt0 @ xm @ xm ))]]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( A = sz00 )
| ( B = C )
| ~ ( sdtlseqdt0 @ B @ C )
| ( sdtlseqdt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ),
inference(cnf,[status(esa)],[190]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ( A = sz00 )
| ( B = C )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( sdtlseqdt0 @ B @ C )
| ( sdtlseqdt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(12351,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12257,91]) ).
thf(12352,plain,
sdtlseqdt0 @ ( sdtmndt0 @ xn @ xn ) @ ( sdtmndt0 @ xn @ xn ),
inference(pattern_uni,[status(thm)],[12351:[bind(A,$thf( sdtmndt0 @ xn @ xn ))]]) ).
thf(954,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,134]) ).
thf(955,plain,
( ( sdtasdt0 @ sz00 @ sz10 )
= sz00 ),
inference(pattern_uni,[status(thm)],[954:[bind(A,$thf( sz10 ))]]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[106]) ).
thf(17102,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7444,123]) ).
thf(17103,plain,
( ( sdtpldt0 @ ( sk1 @ sz10 @ sz10 ) @ sz00 )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[17102:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(18405,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5803,124]) ).
thf(18406,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ xl @ xl ) )
= ( sk1 @ xl @ xl ) ),
inference(pattern_uni,[status(thm)],[18405:[bind(A,$thf( sk1 @ xl @ xl ))]]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ),
inference(cnf,[status(esa)],[159]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(17171,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xl @ xl ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5803,123]) ).
thf(17172,plain,
( ( sdtpldt0 @ ( sk1 @ xl @ xl ) @ sz00 )
= ( sk1 @ xl @ xl ) ),
inference(pattern_uni,[status(thm)],[17171:[bind(A,$thf( sk1 @ xl @ xl ))]]) ).
thf(18322,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10556,124]) ).
thf(18323,plain,
( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ xm @ xm ) )
= ( sdtmndt0 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[18322:[bind(A,$thf( sdtmndt0 @ xm @ xm ))]]) ).
thf(40839,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4811,177]) ).
thf(40840,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ xm @ xm ) )
= ( sk1 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[40839:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ C )
| ( sdtlseqdt0 @ A @ C ) ),
inference(cnf,[status(esa)],[61]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[108,52]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ sz00 @ A )
!= ( sdtpldt0 @ sz00 @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sz00 ))]]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[147,52]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ xn @ A )
!= ( sdtpldt0 @ xn @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( xn ))]]) ).
thf(16617,plain,
( ~ ( sdtlseqdt0 @ sz00 @ sz10 )
| ( ( sdtlseqdt0 @ sz10 @ sz00 )
!= ( sdtlseqdt0 @ sz00 @ sz10 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16465]) ).
thf(16654,plain,
( ~ ( sdtlseqdt0 @ sz00 @ sz10 )
| ( ( sdtlseqdt0 @ sz10 @ sz00 )
!= ( sdtlseqdt0 @ sz00 @ sz10 ) ) ),
inference(simp,[status(thm)],[16617]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[147,52]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( A = xn )
| ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ B @ xn ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ xn )
| ~ ( aNaturalNumber0 @ B ) ),
inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( A )),bind(B,$thf( xn ))]]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( A = xn )
| ( ( sdtpldt0 @ B @ A )
!= ( sdtpldt0 @ B @ xn ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ A @ xn )
| ~ ( aNaturalNumber0 @ B ) ),
inference(simp,[status(thm)],[213]) ).
thf(5154,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ ( sk1 @ sz00 @ xm ) @ sz00 )
= sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[2808,4880]) ).
thf(5155,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ ( sk1 @ sz00 @ xm ) @ sz00 )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[5154:[]]) ).
thf(35185,plain,
( ( sdtlseqdt0 @ ( sk1 @ xm @ xm ) @ sz00 )
| ( ( sk1 @ xm @ xm )
!= ( sk1 @ sz00 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[35161,4888]) ).
thf(35297,plain,
( ( sdtlseqdt0 @ ( sk1 @ xm @ xm ) @ sz00 )
| ( xm != sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[35185]) ).
thf(35351,plain,
( ( sdtlseqdt0 @ ( sk1 @ xm @ xm ) @ sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[35297]) ).
thf(109054,plain,
$false,
inference(cvc4,[status(thm)],[69,18279,3008,10577,12344,234,4835,138,41726,249,2077,115,38805,2808,38713,120,9135,35161,56,40642,4870,8298,6680,17113,18265,38779,185,42,10599,18321,12257,17111,257,12286,8357,38855,125,6676,47471,949,189,17049,46,93,228,78,11495,261,164,179,17129,106,82849,84,18026,2073,3527,253,147,38685,61,221,4996,38675,89,133,18329,11408,2954,233,5157,4888,82821,12300,38781,60,5875,85,201,8365,17061,957,37828,16465,70,137,165,92,229,197,65,5465,4994,97,5858,41741,7501,156,40676,53,7513,141,109,124,77200,82882,96,10575,38775,41342,82843,173,129,5823,41,134,35353,105,82693,10635,9171,7444,6637,10556,38771,40855,4872,148,45,3792,180,38701,176,6617,40686,76840,259,59,118,17109,144,39295,181,18003,86,159,2079,187,172,81,18331,230,76,98,82735,38874,11487,18277,40744,103,140,91,6678,943,108,77198,3073,2075,130,135,9106,17051,167,2984,40672,241,80,10643,18275,2952,40762,16285,123,35344,162,12288,209,38705,63,17105,67,199,17166,127,8327,177,182,82557,18327,154,143,43,231,40754,99,17127,87,18398,41732,2071,38783,40784,158,18349,171,9179,37826,17063,55,114,235,35350,7520,18263,119,58,4880,11447,37127,146,40656,190,17059,168,4811,3790,183,242,126,40748,195,12352,955,326,107,17103,47,18406,163,178,5803,17172,18323,6697,40840,62,90,227,83,215,16654,232,5155,35351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM479+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n006.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 17:06:07 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 (129ms).
% 1.39/0.97 % [INFO] Running in sequential loop mode.
% 1.74/1.16 % [INFO] eprover registered as external prover.
% 1.74/1.16 % [INFO] cvc4 registered as external prover.
% 1.74/1.16 % [INFO] Scanning for conjecture ...
% 1.82/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.82/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.82/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.82/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.99/1.24 % [INFO] Found a conjecture and 38 axioms. Running axiom selection ...
% 2.05/1.28 % [INFO] Axiom selection finished. Selected 38 axioms (removed 0 axioms).
% 2.05/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.34/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.34/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 2.34/1.34 % [INFO] Type checking passed.
% 2.34/1.34 % [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 ...
% 83.79/22.26 % External prover 'cvc4' found a proof!
% 83.79/22.26 % [INFO] Killing All external provers ...
% 83.79/22.26 % Time passed: 21745ms (effective reasoning time: 21284ms)
% 83.79/22.26 % 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)>
% 83.79/22.26 % Axioms used in derivation (38): mSortsC, mAddComm, m_MulUnit, m_MulZero, mZeroMul, mZeroAdd, mLENTr, mIH_03, mDivMin, mDefQuot, mAMDistr, mLETotal, mMonAdd, mLEAsym, mAddCanc, mDivSum, mDivTrans, mSortsC_01, mMulCanc, mLETran, mDefDiff, mMonMul2, mAddAsso, mIH, mMulAsso, mDefDiv, mDefLE, m__1553, mMonMul, mSortsB_02, m_AddZero, m__1524_04, mSortsB, mNatSort, mMulComm, m__1524, mDivLE, mLERefl
% 83.79/22.26 % No. of inferences in proof: 608
% 83.79/22.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21745 ms resp. 21284 ms w/o parsing
% 83.79/22.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 83.79/22.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------