TSTP Solution File: NUM483+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM483+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:40:48 EDT 2023
% Result : Theorem 87.55s 23.87s
% Output : Refutation 87.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 58
% Syntax : Number of formulae : 593 ( 116 unt; 16 typ; 0 def)
% Number of atoms : 2051 ( 689 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 5610 ( 921 ~; 907 |; 176 &;3465 @)
% ( 5 <=>; 136 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 569 ( 0 ^; 558 !; 11 ?; 569 :)
% 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(isPrime0_type,type,
isPrime0: $i > $o ).
thf(sz10_type,type,
sz10: $i ).
thf(xk_type,type,
xk: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(8,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(63,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)],[8]) ).
thf(65,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)],[63]) ).
thf(69,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)],[65]) ).
thf(37,axiom,
aNaturalNumber0 @ xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716) ).
thf(197,plain,
aNaturalNumber0 @ xk,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(26,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
thf(143,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(144,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sdtlseqdt0 @ A @ A ) ),
inference(cnf,[status(esa)],[143]) ).
thf(493,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,144]) ).
thf(494,plain,
sdtlseqdt0 @ xk @ xk,
inference(pattern_uni,[status(thm)],[493:[bind(A,$thf( xk ))]]) ).
thf(16,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(97,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)],[16]) ).
thf(98,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)],[97]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( C
!= ( sdtmndt0 @ B @ A ) )
| ( aNaturalNumber0 @ C ) ),
inference(cnf,[status(esa)],[98]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sdtmndt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(13246,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) )
| ( ( sdtlseqdt0 @ xk @ xk )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[494,105]) ).
thf(13247,plain,
( ~ ( aNaturalNumber0 @ xk )
| ~ ( aNaturalNumber0 @ xk )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) ) ),
inference(pattern_uni,[status(thm)],[13246:[bind(A,$thf( xk )),bind(B,$thf( xk ))]]) ).
thf(13362,plain,
( ~ ( aNaturalNumber0 @ xk )
| ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) ) ),
inference(simp,[status(thm)],[13247]) ).
thf(16033,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) ) ),
inference(rewrite,[status(thm)],[13362,197]) ).
thf(16034,plain,
aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ),
inference(simp,[status(thm)],[16033]) ).
thf(16136,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,144]) ).
thf(16137,plain,
sdtlseqdt0 @ ( sdtmndt0 @ xk @ xk ) @ ( sdtmndt0 @ xk @ xk ),
inference(pattern_uni,[status(thm)],[16136:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(7,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
thf(59,plain,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,plain,
aNaturalNumber0 @ sz10,
inference(cnf,[status(esa)],[59]) ).
thf(491,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[61,144]) ).
thf(492,plain,
sdtlseqdt0 @ sz10 @ sz10,
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( sz10 ))]]) ).
thf(12,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(83,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)],[12]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) ) ),
inference(cnf,[status(esa)],[83]) ).
thf(5634,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz10 @ sz10 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[492,85]) ).
thf(5635,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[5634:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(5735,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(simp,[status(thm)],[5635]) ).
thf(5789,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(rewrite,[status(thm)],[5735,61]) ).
thf(5790,plain,
aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ),
inference(simp,[status(thm)],[5789]) ).
thf(22,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
thf(128,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(129,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtpldt0 @ A @ sz00 )
= A ) ),
inference(cnf,[status(esa)],[128]) ).
thf(131,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(5917,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,131]) ).
thf(5918,plain,
( ( sdtpldt0 @ ( sk1 @ sz10 @ sz10 ) @ sz00 )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[5917:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
thf(138,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(5676,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ xk @ xk )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[494,85]) ).
thf(5677,plain,
( ~ ( aNaturalNumber0 @ xk )
| ~ ( aNaturalNumber0 @ xk )
| ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) ) ),
inference(pattern_uni,[status(thm)],[5676:[bind(A,$thf( xk )),bind(B,$thf( xk ))]]) ).
thf(5751,plain,
( ~ ( aNaturalNumber0 @ xk )
| ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) ) ),
inference(simp,[status(thm)],[5677]) ).
thf(10167,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) ) ),
inference(rewrite,[status(thm)],[5751,197]) ).
thf(10168,plain,
aNaturalNumber0 @ ( sk1 @ xk @ xk ),
inference(simp,[status(thm)],[10167]) ).
thf(10258,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,144]) ).
thf(10259,plain,
sdtlseqdt0 @ ( sk1 @ xk @ xk ) @ ( sk1 @ xk @ xk ),
inference(pattern_uni,[status(thm)],[10258:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(30,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(170,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)],[30]) ).
thf(41,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
thf(213,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(215,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A
= ( sdtasdt0 @ sz10 @ A ) ) ),
inference(cnf,[status(esa)],[213]) ).
thf(217,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(27,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( isPrime0 @ A )
<=> ( ( A != sz00 )
& ( A != sz10 )
& ! [B: $i] :
( ( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A ) )
=> ( ( B = sz10 )
| ( B = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
thf(145,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( isPrime0 @ A )
=> ( ( A != sz00 )
& ( A != sz10 )
& ! [B: $i] :
( ( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A ) )
=> ( ( B = sz10 )
| ( B = A ) ) ) ) )
& ( ( ( A != sz00 )
& ( A != sz10 )
& ! [B: $i] :
( ( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A ) )
=> ( ( B = sz10 )
| ( B = A ) ) ) )
=> ( isPrime0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(148,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[145]) ).
thf(158,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(288,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,158]) ).
thf(289,plain,
( ( xk = sz00 )
| ( xk = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ xk ) )
| ( isPrime0 @ xk ) ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( xk ))]]) ).
thf(4,axiom,
~ ( isPrime0 @ xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1725) ).
thf(51,plain,
~ ( isPrime0 @ xk ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(52,plain,
~ ( isPrime0 @ xk ),
inference(polarity_switch,[status(thm)],[51]) ).
thf(789,plain,
( ( xk = sz00 )
| ( xk = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ xk ) )
| $false ),
inference(rewrite,[status(thm)],[289,52]) ).
thf(790,plain,
( ( xk = sz00 )
| ( xk = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ xk ) ) ),
inference(simp,[status(thm)],[789]) ).
thf(10,axiom,
( ( xk != sz00 )
& ( xk != sz10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716_04) ).
thf(75,plain,
( ( xk != sz00 )
& ( xk != sz10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(76,plain,
xk != sz10,
inference(cnf,[status(esa)],[75]) ).
thf(78,plain,
xk != sz10,
inference(lifteq,[status(thm)],[76]) ).
thf(77,plain,
xk != sz00,
inference(cnf,[status(esa)],[75]) ).
thf(79,plain,
xk != sz00,
inference(lifteq,[status(thm)],[77]) ).
thf(791,plain,
aNaturalNumber0 @ ( sk2 @ xk ),
inference(simplifyReflect,[status(thm)],[790,78,79]) ).
thf(130,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A
= ( sdtpldt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[128]) ).
thf(132,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(2230,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,132]) ).
thf(2231,plain,
( ( sdtpldt0 @ sz00 @ ( sk2 @ xk ) )
= ( sk2 @ xk ) ),
inference(pattern_uni,[status(thm)],[2230:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
thf(46,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(48,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(50,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(5877,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,50]) ).
thf(5878,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ sz10 @ sz10 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[5877:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(35,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
thf(186,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(188,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A ) ),
inference(cnf,[status(esa)],[186]) ).
thf(191,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( sdtlseqdt0 @ sz10 @ A ) ),
inference(lifteq,[status(thm)],[188]) ).
thf(50039,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,191]) ).
thf(50040,plain,
( ( ( sk2 @ xk )
= sz00 )
| ( ( sk2 @ xk )
= sz10 )
| ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[50039:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(800,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,144]) ).
thf(801,plain,
sdtlseqdt0 @ ( sk2 @ xk ) @ ( sk2 @ xk ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(52030,plain,
( ( ( sk2 @ xk )
= sz00 )
| ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( ( sk2 @ xk )
!= ( sk2 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[50040,801]) ).
thf(52031,plain,
( ( ( sk2 @ xk )
= sz00 )
| ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[52030:[]]) ).
thf(5720,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ ( sk2 @ xk ) @ ( sk2 @ xk ) )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[801,85]) ).
thf(5721,plain,
( ~ ( aNaturalNumber0 @ ( sk2 @ xk ) )
| ~ ( aNaturalNumber0 @ ( sk2 @ xk ) )
| ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) ) ),
inference(pattern_uni,[status(thm)],[5720:[bind(A,$thf( sk2 @ xk )),bind(B,$thf( sk2 @ xk ))]]) ).
thf(5770,plain,
( ~ ( aNaturalNumber0 @ ( sk2 @ xk ) )
| ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) ) ),
inference(simp,[status(thm)],[5721]) ).
thf(62903,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) ) ),
inference(rewrite,[status(thm)],[5770,791]) ).
thf(62904,plain,
aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ),
inference(simp,[status(thm)],[62903]) ).
thf(63249,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ ( sk2 @ xk ) ) )
| ( ( sk2 @ xk )
!= ( sk2 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[52031,62904]) ).
thf(63250,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ ( sk2 @ xk ) ) ) ),
inference(pattern_uni,[status(thm)],[63249:[]]) ).
thf(13179,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz10 @ sz10 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[492,105]) ).
thf(13180,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[13179:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(13405,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) ) ),
inference(simp,[status(thm)],[13180]) ).
thf(18137,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) ) ),
inference(rewrite,[status(thm)],[13405,61]) ).
thf(18138,plain,
aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ),
inference(simp,[status(thm)],[18137]) ).
thf(18177,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,132]) ).
thf(18178,plain,
( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= ( sdtmndt0 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[18177:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(18264,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,50]) ).
thf(18265,plain,
( ( sdtasdt0 @ sz00 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[18264:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtasdt0 @ C @ ( sdtsldt0 @ B @ A ) )
= ( sdtsldt0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtasdt0 @ C @ ( sdtsldt0 @ B @ A ) )
= ( sdtsldt0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(812,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,158]) ).
thf(813,plain,
( ( ( sk2 @ xk )
= sz00 )
| ( ( sk2 @ xk )
= sz10 )
| ( aNaturalNumber0 @ ( sk2 @ ( sk2 @ xk ) ) )
| ( isPrime0 @ ( sk2 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[812:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(1,conjecture,
? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( doDivides0 @ A @ xk )
& ( isPrime0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( doDivides0 @ A @ xk )
& ( isPrime0 @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( doDivides0 @ A @ xk )
& ( isPrime0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( doDivides0 @ A @ xk )
| ~ ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[44]) ).
thf(794,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,45]) ).
thf(795,plain,
( ~ ( doDivides0 @ ( sk2 @ xk ) @ xk )
| ~ ( isPrime0 @ ( sk2 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[794:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(151,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( doDivides0 @ ( sk2 @ A ) @ A )
| ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[145]) ).
thf(160,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( doDivides0 @ ( sk2 @ A ) @ A )
| ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(32702,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( doDivides0 @ ( sk2 @ A ) @ A )
| ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,160]) ).
thf(32703,plain,
( ( xk = sz00 )
| ( xk = sz10 )
| ( doDivides0 @ ( sk2 @ xk ) @ xk )
| ( isPrime0 @ xk ) ),
inference(pattern_uni,[status(thm)],[32702:[bind(A,$thf( xk ))]]) ).
thf(33986,plain,
( ( xk = sz00 )
| ( xk = sz10 )
| ( doDivides0 @ ( sk2 @ xk ) @ xk )
| $false ),
inference(rewrite,[status(thm)],[32703,52]) ).
thf(33987,plain,
( ( xk = sz00 )
| ( xk = sz10 )
| ( doDivides0 @ ( sk2 @ xk ) @ xk ) ),
inference(simp,[status(thm)],[33986]) ).
thf(33988,plain,
doDivides0 @ ( sk2 @ xk ) @ xk,
inference(simplifyReflect,[status(thm)],[33987,78,79]) ).
thf(33989,plain,
( ~ $true
| ~ ( isPrime0 @ ( sk2 @ xk ) ) ),
inference(rewrite,[status(thm)],[795,33988]) ).
thf(33990,plain,
~ ( isPrime0 @ ( sk2 @ xk ) ),
inference(simp,[status(thm)],[33989]) ).
thf(34231,plain,
( ( ( sk2 @ xk )
= sz00 )
| ( ( sk2 @ xk )
= sz10 )
| ( aNaturalNumber0 @ ( sk2 @ ( sk2 @ xk ) ) )
| $false ),
inference(rewrite,[status(thm)],[813,33990]) ).
thf(34232,plain,
( ( ( sk2 @ xk )
= sz00 )
| ( ( sk2 @ xk )
= sz10 )
| ( aNaturalNumber0 @ ( sk2 @ ( sk2 @ xk ) ) ) ),
inference(simp,[status(thm)],[34231]) ).
thf(37694,plain,
( ( ( sk2 @ xk )
= sz00 )
| ( aNaturalNumber0 @ ( sk2 @ ( sk2 @ xk ) ) )
| ( doDivides0 @ sz10 @ xk )
| ( ( sk2 @ xk )
!= ( sk2 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[34232,33988]) ).
thf(37695,plain,
( ( ( sk2 @ xk )
= sz00 )
| ( aNaturalNumber0 @ ( sk2 @ ( sk2 @ xk ) ) )
| ( doDivides0 @ sz10 @ xk ) ),
inference(pattern_uni,[status(thm)],[37694:[]]) ).
thf(16116,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,45]) ).
thf(16117,plain,
( ~ ( doDivides0 @ ( sdtmndt0 @ xk @ xk ) @ xk )
| ~ ( isPrime0 @ ( sdtmndt0 @ xk @ xk ) ) ),
inference(pattern_uni,[status(thm)],[16116:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(34119,plain,
( ~ ( isPrime0 @ ( sdtmndt0 @ xk @ xk ) )
| ( ( doDivides0 @ ( sdtmndt0 @ xk @ xk ) @ xk )
!= ( doDivides0 @ ( sk2 @ xk ) @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[33988,16117]) ).
thf(34156,plain,
( ~ ( isPrime0 @ ( sdtmndt0 @ xk @ xk ) )
| ( ( sdtmndt0 @ xk @ xk )
!= ( sk2 @ xk ) )
| ( xk != xk ) ),
inference(simp,[status(thm)],[34119]) ).
thf(34208,plain,
( ~ ( isPrime0 @ ( sdtmndt0 @ xk @ xk ) )
| ( ( sdtmndt0 @ xk @ xk )
!= ( sk2 @ xk ) ) ),
inference(simp,[status(thm)],[34156]) ).
thf(13,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(90,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)],[13]) ).
thf(91,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)],[90]) ).
thf(528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( isPrime0 @ D )
| ( ( doDivides0 @ A @ C )
!= ( doDivides0 @ D @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[91,45]) ).
thf(529,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ xk )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ xk )
| ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A ) ),
inference(pattern_uni,[status(thm)],[528:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( xk )),bind(D,$thf( A ))]]) ).
thf(556,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ xk )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ xk )
| ~ ( isPrime0 @ A ) ),
inference(simp,[status(thm)],[529]) ).
thf(564,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ $true
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ xk )
| ~ ( isPrime0 @ A ) ),
inference(rewrite,[status(thm)],[556,197]) ).
thf(565,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ xk )
| ~ ( isPrime0 @ A ) ),
inference(simp,[status(thm)],[564]) ).
thf(568,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,565]) ).
thf(569,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( doDivides0 @ A @ sz10 )
| ~ ( doDivides0 @ sz10 @ xk )
| ~ ( isPrime0 @ A ) ),
inference(pattern_uni,[status(thm)],[568:[bind(A,$thf( A )),bind(B,$thf( sz10 ))]]) ).
thf(10169,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ sz10 )
| ~ ( doDivides0 @ sz10 @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,569]) ).
thf(10170,plain,
( ~ ( doDivides0 @ ( sk1 @ xk @ xk ) @ sz10 )
| ~ ( doDivides0 @ sz10 @ xk )
| ~ ( isPrime0 @ ( sk1 @ xk @ xk ) ) ),
inference(pattern_uni,[status(thm)],[10169:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(34,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(185,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(47,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ A @ sz00 )
= sz00 ) ),
inference(cnf,[status(esa)],[46]) ).
thf(49,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(235,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[185,49]) ).
thf(236,plain,
( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[235:[bind(A,$thf( sz00 ))]]) ).
thf(29,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(163,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)],[29]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( B
!= ( sdtasdt0 @ A @ C ) )
| ( doDivides0 @ A @ B ) ),
inference(cnf,[status(esa)],[163]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sdtasdt0 @ A @ C ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( doDivides0 @ A @ B ) ),
inference(lifteq,[status(thm)],[166]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ( doDivides0 @ A @ ( sdtasdt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(39674,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ B )
| ( doDivides0 @ A @ ( sdtasdt0 @ A @ B ) )
| ( ( sdtasdt0 @ sz00 @ sz00 )
!= ( sdtasdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[236,169]) ).
thf(39675,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ( doDivides0 @ sz00 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[39674:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(39991,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ( doDivides0 @ sz00 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ),
inference(simp,[status(thm)],[39675]) ).
thf(43912,plain,
( ~ $true
| ( doDivides0 @ sz00 @ sz00 ) ),
inference(rewrite,[status(thm)],[39991,185,236]) ).
thf(43913,plain,
doDivides0 @ sz00 @ sz00,
inference(simp,[status(thm)],[43912]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( aNaturalNumber0 @ ( sk3 @ B @ A ) ) ),
inference(cnf,[status(esa)],[163]) ).
thf(43970,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk3 @ B @ A ) )
| ( ( doDivides0 @ sz00 @ sz00 )
!= ( doDivides0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[43913,165]) ).
thf(43971,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[43970:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(44080,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) ) ),
inference(simp,[status(thm)],[43971]) ).
thf(44089,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[44080,185]) ).
thf(44090,plain,
aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ),
inference(simp,[status(thm)],[44089]) ).
thf(44163,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44090,132]) ).
thf(44164,plain,
( ( sdtpldt0 @ sz00 @ ( sk3 @ sz00 @ sz00 ) )
= ( sk3 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[44163:[bind(A,$thf( sk3 @ sz00 @ sz00 ))]]) ).
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(140,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(141,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( iLess0 @ A @ B ) ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( iLess0 @ A @ B ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( A = sz00 ) ),
inference(cnf,[status(esa)],[170]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[172]) ).
thf(416,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[61,50]) ).
thf(417,plain,
( ( sdtasdt0 @ sz00 @ sz10 )
= sz00 ),
inference(pattern_uni,[status(thm)],[416:[bind(A,$thf( sz10 ))]]) ).
thf(497,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[185,144]) ).
thf(498,plain,
sdtlseqdt0 @ sz00 @ sz00,
inference(pattern_uni,[status(thm)],[497:[bind(A,$thf( sz00 ))]]) ).
thf(101,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)],[98]) ).
thf(106,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)],[101]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sdtmndt0 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(simp,[status(thm)],[106]) ).
thf(14440,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sdtmndt0 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ sz00 @ sz00 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[498,107]) ).
thf(14441,plain,
( ( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ sz00 @ sz00 ) )
= sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[14440:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(14573,plain,
( ( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ sz00 @ sz00 ) )
= sz00 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference(simp,[status(thm)],[14441]) ).
thf(13242,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtmndt0 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz00 @ sz00 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[498,105]) ).
thf(13243,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[13242:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(13360,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) ) ),
inference(simp,[status(thm)],[13243]) ).
thf(13408,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[13360,185]) ).
thf(13409,plain,
aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ),
inference(simp,[status(thm)],[13408]) ).
thf(13446,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13409,132]) ).
thf(13447,plain,
( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ sz00 @ sz00 ) )
= ( sdtmndt0 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[13446:[bind(A,$thf( sdtmndt0 @ sz00 @ sz00 ))]]) ).
thf(33774,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
= sz00 )
| ~ $true ),
inference(rewrite,[status(thm)],[14573,13447,185]) ).
thf(33775,plain,
( ( sdtmndt0 @ sz00 @ sz00 )
= sz00 ),
inference(simp,[status(thm)],[33774]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
thf(183,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[183]) ).
thf(17,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(108,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)],[17]) ).
thf(109,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)],[108]) ).
thf(110,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)],[109]) ).
thf(2216,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,132]) ).
thf(2217,plain,
( ( sdtpldt0 @ sz00 @ xk )
= xk ),
inference(pattern_uni,[status(thm)],[2216:[bind(A,$thf( xk ))]]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtsldt0 @ B @ A ) )
<=> ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
thf(117,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtsldt0 @ B @ A ) )
=> ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) )
& ( ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) )
=> ( C
= ( sdtsldt0 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(118,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)],[117]) ).
thf(120,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)],[118]) ).
thf(124,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)],[120]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( aNaturalNumber0 @ ( sdtsldt0 @ B @ A ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(9,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(72,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)],[9]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(4359,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A )
| ( B != sz10 )
| ( A != xk ) ),
inference(paramod_ordered,[status(thm)],[74,78]) ).
thf(4360,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ xk )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ xk @ A )
| ~ ( sdtlseqdt0 @ A @ xk )
| ( A != sz10 ) ),
inference(pattern_uni,[status(thm)],[4359:[bind(A,$thf( xk ))]]) ).
thf(5068,plain,
( ~ ( aNaturalNumber0 @ xk )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( sdtlseqdt0 @ xk @ sz10 )
| ~ ( sdtlseqdt0 @ sz10 @ xk ) ),
inference(simp,[status(thm)],[4360]) ).
thf(5182,plain,
( ~ $true
| ~ $true
| ~ ( sdtlseqdt0 @ xk @ sz10 )
| ~ ( sdtlseqdt0 @ sz10 @ xk ) ),
inference(rewrite,[status(thm)],[5068,197,61]) ).
thf(5183,plain,
( ~ ( sdtlseqdt0 @ xk @ sz10 )
| ~ ( sdtlseqdt0 @ sz10 @ xk ) ),
inference(simp,[status(thm)],[5182]) ).
thf(5270,plain,
( ~ ( sdtlseqdt0 @ sz10 @ xk )
| ( ( sdtlseqdt0 @ xk @ sz10 )
!= ( sdtlseqdt0 @ sz10 @ xk ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5183]) ).
thf(5279,plain,
( ~ ( sdtlseqdt0 @ sz10 @ xk )
| ( ( sdtlseqdt0 @ xk @ sz10 )
!= ( sdtlseqdt0 @ sz10 @ xk ) ) ),
inference(simp,[status(thm)],[5270]) ).
thf(49447,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,191]) ).
thf(49448,plain,
( ( xk = sz00 )
| ( xk = sz10 )
| ( sdtlseqdt0 @ sz10 @ xk ) ),
inference(pattern_uni,[status(thm)],[49447:[bind(A,$thf( xk ))]]) ).
thf(50494,plain,
sdtlseqdt0 @ sz10 @ xk,
inference(simplifyReflect,[status(thm)],[49448,78,79]) ).
thf(50495,plain,
( ~ $true
| ~ ( sdtlseqdt0 @ xk @ sz10 ) ),
inference(rewrite,[status(thm)],[5279,50494]) ).
thf(50496,plain,
~ ( sdtlseqdt0 @ xk @ sz10 ),
inference(simp,[status(thm)],[50495]) ).
thf(36,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(192,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)],[36]) ).
thf(194,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)],[192]) ).
thf(196,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)],[194]) ).
thf(150,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( ( sk2 @ A )
!= sz10 )
| ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[145]) ).
thf(157,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( ( sk2 @ A )
!= sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(44319,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44090,50]) ).
thf(44320,plain,
( ( sdtasdt0 @ sz00 @ ( sk3 @ sz00 @ sz00 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[44319:[bind(A,$thf( sk3 @ sz00 @ sz00 ))]]) ).
thf(5867,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,49]) ).
thf(5868,plain,
( ( sdtasdt0 @ ( sk1 @ sz10 @ sz10 ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[5867:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(5865,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,144]) ).
thf(5866,plain,
sdtlseqdt0 @ ( sk1 @ sz10 @ sz10 ) @ ( sk1 @ sz10 @ sz10 ),
inference(pattern_uni,[status(thm)],[5865:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(68258,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,217]) ).
thf(68259,plain,
( ( sdtasdt0 @ sz10 @ ( sdtmndt0 @ xk @ xk ) )
= ( sdtmndt0 @ xk @ xk ) ),
inference(pattern_uni,[status(thm)],[68258:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(51666,plain,
( ( sdtlseqdt0 @ ( sk1 @ sz10 @ sz10 ) @ ( sk1 @ sz10 @ sz10 ) )
!= ( sdtlseqdt0 @ xk @ sz10 ) ),
inference(paramod_ordered,[status(thm)],[5866,50496]) ).
thf(51757,plain,
( ( ( sk1 @ sz10 @ sz10 )
!= xk )
| ( ( sk1 @ sz10 @ sz10 )
!= sz10 ) ),
inference(simp,[status(thm)],[51666]) ).
thf(14,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(92,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)],[14]) ).
thf(93,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)],[92]) ).
thf(10205,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,132]) ).
thf(10206,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ xk @ xk ) )
= ( sk1 @ xk @ xk ) ),
inference(pattern_uni,[status(thm)],[10205:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(44285,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44090,144]) ).
thf(44286,plain,
sdtlseqdt0 @ ( sk3 @ sz00 @ sz00 ) @ ( sk3 @ sz00 @ sz00 ),
inference(pattern_uni,[status(thm)],[44285:[bind(A,$thf( sk3 @ sz00 @ sz00 ))]]) ).
thf(51690,plain,
( ( sdtlseqdt0 @ ( sk3 @ sz00 @ sz00 ) @ ( sk3 @ sz00 @ sz00 ) )
!= ( sdtlseqdt0 @ xk @ sz10 ) ),
inference(paramod_ordered,[status(thm)],[44286,50496]) ).
thf(51747,plain,
( ( ( sk3 @ sz00 @ sz00 )
!= xk )
| ( ( sk3 @ sz00 @ sz00 )
!= sz10 ) ),
inference(simp,[status(thm)],[51690]) ).
thf(214,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ A @ sz10 )
= A ) ),
inference(cnf,[status(esa)],[213]) ).
thf(216,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[214]) ).
thf(40,axiom,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 )
& ( A != sz10 ) )
=> ( ( iLess0 @ A @ xk )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A )
& ( isPrime0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1700) ).
thf(206,plain,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 )
& ( A != sz10 ) )
=> ( ( iLess0 @ A @ xk )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A )
& ( isPrime0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(208,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ~ ( iLess0 @ A @ xk )
| ( doDivides0 @ ( sk4 @ A ) @ A ) ),
inference(cnf,[status(esa)],[206]) ).
thf(211,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( iLess0 @ A @ xk )
| ( doDivides0 @ ( sk4 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[208]) ).
thf(63205,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62904,144]) ).
thf(63206,plain,
sdtlseqdt0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ),
inference(pattern_uni,[status(thm)],[63205:[bind(A,$thf( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ))]]) ).
thf(237,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[61,49]) ).
thf(238,plain,
( ( sdtasdt0 @ sz10 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( sz10 ))]]) ).
thf(63005,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62904,216]) ).
thf(63006,plain,
( ( sdtasdt0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) @ sz10 )
= ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[63005:[bind(A,$thf( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ))]]) ).
thf(10270,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,50]) ).
thf(10271,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ xk @ xk ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[10270:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(18240,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,144]) ).
thf(18241,plain,
sdtlseqdt0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ ( sdtmndt0 @ sz10 @ sz10 ),
inference(pattern_uni,[status(thm)],[18240:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(5845,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,45]) ).
thf(5846,plain,
( ~ ( doDivides0 @ ( sk1 @ sz10 @ sz10 ) @ xk )
| ~ ( isPrime0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[5845:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(20,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(114,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)],[20]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( B = sz00 )
| ( sdtlseqdt0 @ A @ B ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( B = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(5823,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,132]) ).
thf(5824,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ sz10 @ sz10 ) )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[5823:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(10302,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,131]) ).
thf(10303,plain,
( ( sdtpldt0 @ ( sk1 @ xk @ xk ) @ sz00 )
= ( sk1 @ xk @ xk ) ),
inference(pattern_uni,[status(thm)],[10302:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtpldt0 @ A @ C )
!= B )
| ( sdtlseqdt0 @ A @ B ) ),
inference(cnf,[status(esa)],[83]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ C )
!= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ( sdtlseqdt0 @ A @ ( sdtpldt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(2717,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[61,216]) ).
thf(2718,plain,
( ( sdtasdt0 @ sz10 @ sz10 )
= sz10 ),
inference(pattern_uni,[status(thm)],[2717:[bind(A,$thf( sz10 ))]]) ).
thf(14444,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sdtmndt0 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ xk @ xk )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[494,107]) ).
thf(14445,plain,
( ( ( sdtpldt0 @ xk @ ( sdtmndt0 @ xk @ xk ) )
= xk )
| ~ ( aNaturalNumber0 @ xk )
| ~ ( aNaturalNumber0 @ xk ) ),
inference(pattern_uni,[status(thm)],[14444:[bind(A,$thf( xk )),bind(B,$thf( xk ))]]) ).
thf(14574,plain,
( ( ( sdtpldt0 @ xk @ ( sdtmndt0 @ xk @ xk ) )
= xk )
| ~ ( aNaturalNumber0 @ xk ) ),
inference(simp,[status(thm)],[14445]) ).
thf(38839,plain,
( ( ( sdtpldt0 @ xk @ ( sdtmndt0 @ xk @ xk ) )
= xk )
| ~ $true ),
inference(rewrite,[status(thm)],[14574,197]) ).
thf(38840,plain,
( ( sdtpldt0 @ xk @ ( sdtmndt0 @ xk @ xk ) )
= xk ),
inference(simp,[status(thm)],[38839]) ).
thf(16154,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,50]) ).
thf(16155,plain,
( ( sdtasdt0 @ sz00 @ ( sdtmndt0 @ xk @ xk ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[16154:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(18139,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ sz10 )
| ~ ( doDivides0 @ sz10 @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,569]) ).
thf(18140,plain,
( ~ ( doDivides0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ sz10 )
| ~ ( doDivides0 @ sz10 @ xk )
| ~ ( isPrime0 @ ( sdtmndt0 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[18139:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(43,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(220,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)],[43]) ).
thf(39,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(201,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)],[39]) ).
thf(63239,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62904,50]) ).
thf(63240,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[63239:[bind(A,$thf( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ))]]) ).
thf(63207,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62904,49]) ).
thf(63208,plain,
( ( sdtasdt0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[63207:[bind(A,$thf( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ))]]) ).
thf(135,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)],[133]) ).
thf(137,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)],[135]) ).
thf(16194,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,131]) ).
thf(16195,plain,
( ( sdtpldt0 @ ( sdtmndt0 @ xk @ xk ) @ sz00 )
= ( sdtmndt0 @ xk @ xk ) ),
inference(pattern_uni,[status(thm)],[16194:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(16071,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,216]) ).
thf(16072,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ xk @ xk ) @ sz10 )
= ( sdtmndt0 @ xk @ xk ) ),
inference(pattern_uni,[status(thm)],[16071:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(51670,plain,
( ( sdtlseqdt0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( sdtlseqdt0 @ xk @ sz10 ) ),
inference(paramod_ordered,[status(thm)],[18241,50496]) ).
thf(51756,plain,
( ( ( sdtmndt0 @ sz10 @ sz10 )
!= xk )
| ( ( sdtmndt0 @ sz10 @ sz10 )
!= sz10 ) ),
inference(simp,[status(thm)],[51670]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B ) ),
inference(cnf,[status(esa)],[83]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(7073,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ sz10 @ sz10 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[492,87]) ).
thf(7074,plain,
( ( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[7073:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(7190,plain,
( ( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(simp,[status(thm)],[7074]) ).
thf(25878,plain,
( ( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 )
| ~ $true ),
inference(rewrite,[status(thm)],[7190,61]) ).
thf(25879,plain,
( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 ),
inference(simp,[status(thm)],[25878]) ).
thf(221,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)],[220]) ).
thf(225,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)],[221]) ).
thf(209,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ~ ( iLess0 @ A @ xk )
| ( aNaturalNumber0 @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[206]) ).
thf(212,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( iLess0 @ A @ xk )
| ( aNaturalNumber0 @ ( sk4 @ A ) ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(15,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(94,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)],[15]) ).
thf(95,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)],[94]) ).
thf(96,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)],[95]) ).
thf(4887,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A )
| ( B != sz00 )
| ( A != xk ) ),
inference(paramod_ordered,[status(thm)],[74,79]) ).
thf(4888,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ xk )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ xk @ A )
| ~ ( sdtlseqdt0 @ A @ xk )
| ( A != sz00 ) ),
inference(pattern_uni,[status(thm)],[4887:[bind(A,$thf( xk ))]]) ).
thf(5079,plain,
( ~ ( aNaturalNumber0 @ xk )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( sdtlseqdt0 @ xk @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ xk ) ),
inference(simp,[status(thm)],[4888]) ).
thf(21614,plain,
( ~ $true
| ~ $true
| ~ ( sdtlseqdt0 @ xk @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ xk ) ),
inference(rewrite,[status(thm)],[5079,197,185]) ).
thf(21615,plain,
( ~ ( sdtlseqdt0 @ xk @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ xk ) ),
inference(simp,[status(thm)],[21614]) ).
thf(34031,plain,
( ~ ( isPrime0 @ ( sk1 @ sz10 @ sz10 ) )
| ( ( doDivides0 @ ( sk1 @ sz10 @ sz10 ) @ xk )
!= ( doDivides0 @ ( sk2 @ xk ) @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[33988,5846]) ).
thf(34161,plain,
( ~ ( isPrime0 @ ( sk1 @ sz10 @ sz10 ) )
| ( ( sk1 @ sz10 @ sz10 )
!= ( sk2 @ xk ) )
| ( xk != xk ) ),
inference(simp,[status(thm)],[34031]) ).
thf(34212,plain,
( ~ ( isPrime0 @ ( sk1 @ sz10 @ sz10 ) )
| ( ( sk1 @ sz10 @ sz10 )
!= ( sk2 @ xk ) ) ),
inference(simp,[status(thm)],[34161]) ).
thf(10238,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,45]) ).
thf(10239,plain,
( ~ ( doDivides0 @ ( sk1 @ xk @ xk ) @ xk )
| ~ ( isPrime0 @ ( sk1 @ xk @ xk ) ) ),
inference(pattern_uni,[status(thm)],[10238:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(34064,plain,
( ~ ( isPrime0 @ ( sk1 @ xk @ xk ) )
| ( ( doDivides0 @ ( sk1 @ xk @ xk ) @ xk )
!= ( doDivides0 @ ( sk2 @ xk ) @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[33988,10239]) ).
thf(34158,plain,
( ~ ( isPrime0 @ ( sk1 @ xk @ xk ) )
| ( ( sk1 @ xk @ xk )
!= ( sk2 @ xk ) )
| ( xk != xk ) ),
inference(simp,[status(thm)],[34064]) ).
thf(34210,plain,
( ~ ( isPrime0 @ ( sk1 @ xk @ xk ) )
| ( ( sk1 @ xk @ xk )
!= ( sk2 @ xk ) ) ),
inference(simp,[status(thm)],[34158]) ).
thf(16035,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ sz10 )
| ~ ( doDivides0 @ sz10 @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,569]) ).
thf(16036,plain,
( ~ ( doDivides0 @ ( sdtmndt0 @ xk @ xk ) @ sz10 )
| ~ ( doDivides0 @ sz10 @ xk )
| ~ ( isPrime0 @ ( sdtmndt0 @ xk @ xk ) ) ),
inference(pattern_uni,[status(thm)],[16035:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(18175,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,216]) ).
thf(18176,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ sz10 )
= ( sdtmndt0 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[18175:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( B = sz00 ) ),
inference(cnf,[status(esa)],[170]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( B = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(588,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[185,565]) ).
thf(589,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( doDivides0 @ A @ sz00 )
| ~ ( doDivides0 @ sz00 @ xk )
| ~ ( isPrime0 @ A ) ),
inference(pattern_uni,[status(thm)],[588:[bind(A,$thf( A )),bind(B,$thf( sz00 ))]]) ).
thf(18256,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ sz00 )
| ~ ( doDivides0 @ sz00 @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,589]) ).
thf(18257,plain,
( ~ ( doDivides0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ sz00 )
| ~ ( doDivides0 @ sz00 @ xk )
| ~ ( isPrime0 @ ( sdtmndt0 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[18256:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(203,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)],[201]) ).
thf(205,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)],[203]) ).
thf(68122,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62904,217]) ).
thf(68123,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
= ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[68122:[bind(A,$thf( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ))]]) ).
thf(44247,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44090,45]) ).
thf(44248,plain,
( ~ ( doDivides0 @ ( sk3 @ sz00 @ sz00 ) @ xk )
| ~ ( isPrime0 @ ( sk3 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[44247:[bind(A,$thf( sk3 @ sz00 @ sz00 ))]]) ).
thf(48647,plain,
( ~ ( isPrime0 @ ( sk3 @ sz00 @ sz00 ) )
| ( ( doDivides0 @ ( sk3 @ sz00 @ sz00 ) @ xk )
!= ( doDivides0 @ ( sk2 @ xk ) @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[33988,44248]) ).
thf(48802,plain,
( ~ ( isPrime0 @ ( sk3 @ sz00 @ sz00 ) )
| ( ( sk3 @ sz00 @ sz00 )
!= ( sk2 @ xk ) )
| ( xk != xk ) ),
inference(simp,[status(thm)],[48647]) ).
thf(48834,plain,
( ~ ( isPrime0 @ ( sk3 @ sz00 @ sz00 ) )
| ( ( sk3 @ sz00 @ sz00 )
!= ( sk2 @ xk ) ) ),
inference(simp,[status(thm)],[48802]) ).
thf(63328,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62904,131]) ).
thf(63329,plain,
( ( sdtpldt0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) @ sz00 )
= ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[63328:[bind(A,$thf( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ))]]) ).
thf(1277,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[61,131]) ).
thf(1278,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= sz10 ),
inference(pattern_uni,[status(thm)],[1277:[bind(A,$thf( sz10 ))]]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ B @ A )
| ( B = sz10 )
| ( B = A ) ),
inference(cnf,[status(esa)],[145]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( B = sz10 )
| ( B = A )
| ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ B @ A ) ),
inference(lifteq,[status(thm)],[146]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
thf(180,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(31,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(175,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)],[31]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ),
inference(cnf,[status(esa)],[175]) ).
thf(5875,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ sz00 )
| ~ ( doDivides0 @ sz00 @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,589]) ).
thf(5876,plain,
( ~ ( doDivides0 @ ( sk1 @ sz10 @ sz10 ) @ sz00 )
| ~ ( doDivides0 @ sz00 @ xk )
| ~ ( isPrime0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[5875:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(202,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)],[201]) ).
thf(204,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)],[202]) ).
thf(5257,plain,
( ~ ( sdtlseqdt0 @ xk @ sz10 )
| ( ( sdtlseqdt0 @ ( sk2 @ xk ) @ ( sk2 @ xk ) )
!= ( sdtlseqdt0 @ sz10 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[801,5183]) ).
thf(5271,plain,
( ~ ( sdtlseqdt0 @ xk @ sz10 )
| ( ( sk2 @ xk )
!= sz10 )
| ( ( sk2 @ xk )
!= xk ) ),
inference(simp,[status(thm)],[5257]) ).
thf(8016,plain,
( ( ( sk2 @ xk )
!= sz10 )
| ( ( sk2 @ xk )
!= xk )
| ( ( sdtlseqdt0 @ ( sk2 @ xk ) @ ( sk2 @ xk ) )
!= ( sdtlseqdt0 @ xk @ sz10 ) ) ),
inference(paramod_ordered,[status(thm)],[801,5271]) ).
thf(8036,plain,
( ( ( sk2 @ xk )
!= sz10 )
| ( ( sk2 @ xk )
!= xk )
| ( ( sk2 @ xk )
!= xk )
| ( ( sk2 @ xk )
!= sz10 ) ),
inference(simp,[status(thm)],[8016]) ).
thf(8064,plain,
( ( ( sk2 @ xk )
!= sz10 )
| ( ( sk2 @ xk )
!= xk ) ),
inference(simp,[status(thm)],[8036]) ).
thf(67,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)],[63]) ).
thf(71,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)],[67]) ).
thf(39588,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ B )
| ( doDivides0 @ A @ ( sdtasdt0 @ A @ B ) )
| ( ( sdtasdt0 @ sz10 @ sz10 )
!= ( sdtasdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2718,169]) ).
thf(39589,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ( doDivides0 @ sz10 @ ( sdtasdt0 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[39588:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(39952,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ( doDivides0 @ sz10 @ ( sdtasdt0 @ sz10 @ sz10 ) ) ),
inference(simp,[status(thm)],[39589]) ).
thf(39994,plain,
( ~ $true
| ( doDivides0 @ sz10 @ sz10 ) ),
inference(rewrite,[status(thm)],[39952,61,2718]) ).
thf(39995,plain,
doDivides0 @ sz10 @ sz10,
inference(simp,[status(thm)],[39994]) ).
thf(18220,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,45]) ).
thf(18221,plain,
( ~ ( doDivides0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ xk )
| ~ ( isPrime0 @ ( sdtmndt0 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[18220:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(34120,plain,
( ~ ( isPrime0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
| ( ( doDivides0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ xk )
!= ( doDivides0 @ ( sk2 @ xk ) @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[33988,18221]) ).
thf(34147,plain,
( ~ ( isPrime0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
| ( ( sdtmndt0 @ sz10 @ sz10 )
!= ( sk2 @ xk ) )
| ( xk != xk ) ),
inference(simp,[status(thm)],[34120]) ).
thf(34198,plain,
( ~ ( isPrime0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
| ( ( sdtmndt0 @ sz10 @ sz10 )
!= ( sk2 @ xk ) ) ),
inference(simp,[status(thm)],[34147]) ).
thf(149,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( ( sk2 @ A )
!= A )
| ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[145]) ).
thf(159,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( ( sk2 @ A )
!= A )
| ~ ( aNaturalNumber0 @ A )
| ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[149]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(113,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(51653,plain,
( ( sdtlseqdt0 @ ( sk1 @ xk @ xk ) @ ( sk1 @ xk @ xk ) )
!= ( sdtlseqdt0 @ xk @ sz10 ) ),
inference(paramod_ordered,[status(thm)],[10259,50496]) ).
thf(51755,plain,
( ( ( sk1 @ xk @ xk )
!= xk )
| ( ( sk1 @ xk @ xk )
!= sz10 ) ),
inference(simp,[status(thm)],[51653]) ).
thf(10203,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,216]) ).
thf(10204,plain,
( ( sdtasdt0 @ ( sk1 @ xk @ xk ) @ sz10 )
= ( sk1 @ xk @ xk ) ),
inference(pattern_uni,[status(thm)],[10203:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(418,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,50]) ).
thf(419,plain,
( ( sdtasdt0 @ sz00 @ xk )
= sz00 ),
inference(pattern_uni,[status(thm)],[418:[bind(A,$thf( xk ))]]) ).
thf(44161,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44090,216]) ).
thf(44162,plain,
( ( sdtasdt0 @ ( sk3 @ sz00 @ sz00 ) @ sz10 )
= ( sk3 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[44161:[bind(A,$thf( sk3 @ sz00 @ sz00 ))]]) ).
thf(152,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ( A != sz10 ) ),
inference(cnf,[status(esa)],[145]) ).
thf(153,plain,
! [A: $i] :
( ( A != sz10 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(154,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( isPrime0 @ sz10 ) ),
inference(simp,[status(thm)],[153]) ).
thf(229,plain,
( ~ $true
| ~ ( isPrime0 @ sz10 ) ),
inference(rewrite,[status(thm)],[154,61]) ).
thf(230,plain,
~ ( isPrime0 @ sz10 ),
inference(simp,[status(thm)],[229]) ).
thf(1281,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[185,131]) ).
thf(1282,plain,
( ( sdtpldt0 @ sz00 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[1281:[bind(A,$thf( sz00 ))]]) ).
thf(42,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(218,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)],[42]) ).
thf(219,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)],[218]) ).
thf(810,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,50]) ).
thf(811,plain,
( ( sdtasdt0 @ sz00 @ ( sk2 @ xk ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[810:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(5815,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ sz10 )
| ~ ( doDivides0 @ sz10 @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,569]) ).
thf(5816,plain,
( ~ ( doDivides0 @ ( sk1 @ sz10 @ sz10 ) @ sz10 )
| ~ ( doDivides0 @ sz10 @ xk )
| ~ ( isPrime0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[5815:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(16138,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,49]) ).
thf(16139,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ xk @ xk ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[16138:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(99,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)],[98]) ).
thf(102,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)],[99]) ).
thf(103,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)],[102]) ).
thf(38,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(198,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(18242,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,49]) ).
thf(18243,plain,
( ( sdtasdt0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[18242:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(68296,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,217]) ).
thf(68297,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ xk @ xk ) )
= ( sk1 @ xk @ xk ) ),
inference(pattern_uni,[status(thm)],[68296:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(11,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(80,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)],[11]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( B
= ( sdtasdt0 @ A @ ( sk3 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[163]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ ( sk3 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B ) ),
inference(lifteq,[status(thm)],[164]) ).
thf(21716,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xk )
| ( ( sdtlseqdt0 @ ( sk2 @ xk ) @ ( sk2 @ xk ) )
!= ( sdtlseqdt0 @ xk @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[801,21615]) ).
thf(21728,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xk )
| ( ( sk2 @ xk )
!= xk )
| ( ( sk2 @ xk )
!= sz00 ) ),
inference(simp,[status(thm)],[21716]) ).
thf(26304,plain,
( ( ( sk2 @ xk )
!= xk )
| ( ( sk2 @ xk )
!= sz00 )
| ( ( sdtlseqdt0 @ ( sk2 @ xk ) @ ( sk2 @ xk ) )
!= ( sdtlseqdt0 @ sz00 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[801,21728]) ).
thf(26320,plain,
( ( ( sk2 @ xk )
!= xk )
| ( ( sk2 @ xk )
!= sz00 )
| ( ( sk2 @ xk )
!= sz00 )
| ( ( sk2 @ xk )
!= xk ) ),
inference(simp,[status(thm)],[26304]) ).
thf(26360,plain,
( ( ( sk2 @ xk )
!= xk )
| ( ( sk2 @ xk )
!= sz00 ) ),
inference(simp,[status(thm)],[26320]) ).
thf(44369,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44090,131]) ).
thf(44370,plain,
( ( sdtpldt0 @ ( sk3 @ sz00 @ sz00 ) @ sz00 )
= ( sk3 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[44369:[bind(A,$thf( sk3 @ sz00 @ sz00 ))]]) ).
thf(28,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(162,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10268,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ sz00 )
| ~ ( doDivides0 @ sz00 @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,589]) ).
thf(10269,plain,
( ~ ( doDivides0 @ ( sk1 @ xk @ xk ) @ sz00 )
| ~ ( doDivides0 @ sz00 @ xk )
| ~ ( isPrime0 @ ( sk1 @ xk @ xk ) ) ),
inference(pattern_uni,[status(thm)],[10268:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(18,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(111,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)],[18]) ).
thf(112,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)],[111]) ).
thf(119,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)],[118]) ).
thf(122,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)],[119]) ).
thf(123,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)],[122]) ).
thf(68220,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44090,217]) ).
thf(68221,plain,
( ( sdtasdt0 @ sz10 @ ( sk3 @ sz00 @ sz00 ) )
= ( sk3 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[68220:[bind(A,$thf( sk3 @ sz00 @ sz00 ))]]) ).
thf(5821,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,216]) ).
thf(5822,plain,
( ( sdtasdt0 @ ( sk1 @ sz10 @ sz10 ) @ sz10 )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[5821:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(21724,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xk )
| ( ( sdtlseqdt0 @ xk @ sz00 )
!= ( sdtlseqdt0 @ sz00 @ xk ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21615]) ).
thf(21743,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xk )
| ( ( sdtlseqdt0 @ xk @ sz00 )
!= ( sdtlseqdt0 @ sz00 @ xk ) ) ),
inference(simp,[status(thm)],[21724]) ).
thf(14376,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sdtmndt0 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ sz10 @ sz10 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[492,107]) ).
thf(14377,plain,
( ( ( sdtpldt0 @ sz10 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[14376:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(14549,plain,
( ( ( sdtpldt0 @ sz10 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(simp,[status(thm)],[14377]) ).
thf(31739,plain,
( ( ( sdtpldt0 @ sz10 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= sz10 )
| ~ $true ),
inference(rewrite,[status(thm)],[14549,61]) ).
thf(31740,plain,
( ( sdtpldt0 @ sz10 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= sz10 ),
inference(simp,[status(thm)],[31739]) ).
thf(2731,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,216]) ).
thf(2732,plain,
( ( sdtasdt0 @ ( sk2 @ xk ) @ sz10 )
= ( sk2 @ xk ) ),
inference(pattern_uni,[status(thm)],[2731:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(60,plain,
sz10 != sz00,
inference(cnf,[status(esa)],[59]) ).
thf(62,plain,
sz10 != sz00,
inference(lifteq,[status(thm)],[60]) ).
thf(4939,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A )
| ( B != sz00 )
| ( A != sz10 ) ),
inference(paramod_ordered,[status(thm)],[74,62]) ).
thf(4940,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ sz10 @ A )
| ~ ( sdtlseqdt0 @ A @ sz10 )
| ( A != sz00 ) ),
inference(pattern_uni,[status(thm)],[4939:[bind(A,$thf( sz10 ))]]) ).
thf(5115,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( sdtlseqdt0 @ sz10 @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ sz10 ) ),
inference(simp,[status(thm)],[4940]) ).
thf(80414,plain,
( ~ $true
| ~ $true
| ~ ( sdtlseqdt0 @ sz10 @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ sz10 ) ),
inference(rewrite,[status(thm)],[5115,185,61]) ).
thf(80415,plain,
( ~ ( sdtlseqdt0 @ sz10 @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ sz10 ) ),
inference(simp,[status(thm)],[80414]) ).
thf(121,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)],[118]) ).
thf(126,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)],[121]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ( ( sdtasdt0 @ A @ ( sdtsldt0 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B ) ),
inference(simp,[status(thm)],[126]) ).
thf(40050,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk3 @ B @ A ) )
| ( ( doDivides0 @ sz10 @ sz10 )
!= ( doDivides0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39995,165]) ).
thf(40051,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk3 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[40050:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(40193,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk3 @ sz10 @ sz10 ) ) ),
inference(simp,[status(thm)],[40051]) ).
thf(40194,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk3 @ sz10 @ sz10 ) ) ),
inference(rewrite,[status(thm)],[40193,61]) ).
thf(40195,plain,
aNaturalNumber0 @ ( sk3 @ sz10 @ sz10 ),
inference(simp,[status(thm)],[40194]) ).
thf(68228,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk3 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40195,217]) ).
thf(68229,plain,
( ( sdtasdt0 @ sz10 @ ( sk3 @ sz10 @ sz10 ) )
= ( sk3 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[68228:[bind(A,$thf( sk3 @ sz10 @ sz10 ))]]) ).
thf(40093,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ ( sk3 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( doDivides0 @ sz10 @ sz10 )
!= ( doDivides0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39995,167]) ).
thf(40094,plain,
( ( ( sdtasdt0 @ sz10 @ ( sk3 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[40093:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(40161,plain,
( ( ( sdtasdt0 @ sz10 @ ( sk3 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(simp,[status(thm)],[40094]) ).
thf(57222,plain,
( ( ( sdtasdt0 @ sz10 @ ( sk3 @ sz10 @ sz10 ) )
= sz10 )
| ~ $true ),
inference(rewrite,[status(thm)],[40161,61]) ).
thf(57223,plain,
( ( sdtasdt0 @ sz10 @ ( sk3 @ sz10 @ sz10 ) )
= sz10 ),
inference(simp,[status(thm)],[57222]) ).
thf(69883,plain,
( ( sk3 @ sz10 @ sz10 )
= sz10 ),
inference(rewrite,[status(thm)],[68229,57223]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[180]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[181]) ).
thf(1283,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,131]) ).
thf(1284,plain,
( ( sdtpldt0 @ ( sk2 @ xk ) @ sz00 )
= ( sk2 @ xk ) ),
inference(pattern_uni,[status(thm)],[1283:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(63023,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62904,132]) ).
thf(63024,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) )
= ( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[63023:[bind(A,$thf( sk1 @ ( sk2 @ xk ) @ ( sk2 @ xk ) ))]]) ).
thf(39244,plain,
( ( aNaturalNumber0 @ ( sk2 @ ( sk2 @ xk ) ) )
| ( doDivides0 @ sz10 @ xk )
| ( doDivides0 @ sz00 @ xk )
| ( ( sk2 @ xk )
!= ( sk2 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[37695,33988]) ).
thf(39245,plain,
( ( aNaturalNumber0 @ ( sk2 @ ( sk2 @ xk ) ) )
| ( doDivides0 @ sz10 @ xk )
| ( doDivides0 @ sz00 @ xk ) ),
inference(pattern_uni,[status(thm)],[39244:[]]) ).
thf(52824,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( sdtlseqdt0 @ ( sk2 @ xk ) @ sz00 )
| ( ( sk2 @ xk )
!= ( sk2 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[52031,801]) ).
thf(52825,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( sdtlseqdt0 @ ( sk2 @ xk ) @ sz00 ) ),
inference(pattern_uni,[status(thm)],[52824:[]]) ).
thf(52792,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( ( sk2 @ xk )
!= xk )
| ( ( sk2 @ xk )
!= ( sk2 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[52031,26360]) ).
thf(52793,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( ( sk2 @ xk )
!= xk ) ),
inference(pattern_uni,[status(thm)],[52792:[]]) ).
thf(51652,plain,
( ( sdtlseqdt0 @ ( sdtmndt0 @ xk @ xk ) @ ( sdtmndt0 @ xk @ xk ) )
!= ( sdtlseqdt0 @ xk @ sz10 ) ),
inference(paramod_ordered,[status(thm)],[16137,50496]) ).
thf(51752,plain,
( ( ( sdtmndt0 @ xk @ xk )
!= xk )
| ( ( sdtmndt0 @ xk @ xk )
!= sz10 ) ),
inference(simp,[status(thm)],[51652]) ).
thf(52646,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( doDivides0 @ sz00 @ xk )
| ( ( sk2 @ xk )
!= ( sk2 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[52031,33988]) ).
thf(52647,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( doDivides0 @ sz00 @ xk ) ),
inference(pattern_uni,[status(thm)],[52646:[]]) ).
thf(10260,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10168,49]) ).
thf(10261,plain,
( ( sdtasdt0 @ ( sk1 @ xk @ xk ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[10260:[bind(A,$thf( sk1 @ xk @ xk ))]]) ).
thf(16152,plain,
! [A: $i] :
( ~ ( doDivides0 @ A @ sz00 )
| ~ ( doDivides0 @ sz00 @ xk )
| ~ ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,589]) ).
thf(16153,plain,
( ~ ( doDivides0 @ ( sdtmndt0 @ xk @ xk ) @ sz00 )
| ~ ( doDivides0 @ sz00 @ xk )
| ~ ( isPrime0 @ ( sdtmndt0 @ xk @ xk ) ) ),
inference(pattern_uni,[status(thm)],[16152:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(68254,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,217]) ).
thf(68255,plain,
( ( sdtasdt0 @ sz10 @ ( sk2 @ xk ) )
= ( sk2 @ xk ) ),
inference(pattern_uni,[status(thm)],[68254:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(44287,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk3 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44090,49]) ).
thf(44288,plain,
( ( sdtasdt0 @ ( sk3 @ sz00 @ sz00 ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[44287:[bind(A,$thf( sk3 @ sz00 @ sz00 ))]]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(7113,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ sz00 @ sz00 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[498,87]) ).
thf(7114,plain,
( ( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[7113:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(7208,plain,
( ( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= sz00 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference(simp,[status(thm)],[7114]) ).
thf(5672,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz00 @ sz00 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[498,85]) ).
thf(5673,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[5672:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(5749,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) ) ),
inference(simp,[status(thm)],[5673]) ).
thf(7601,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[5749,185]) ).
thf(7602,plain,
aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ),
inference(simp,[status(thm)],[7601]) ).
thf(7639,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7602,132]) ).
thf(7640,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= ( sk1 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[7639:[bind(A,$thf( sk1 @ sz00 @ sz00 ))]]) ).
thf(26977,plain,
( ( ( sk1 @ sz00 @ sz00 )
= sz00 )
| ~ $true ),
inference(rewrite,[status(thm)],[7208,7640,185]) ).
thf(26978,plain,
( ( sk1 @ sz00 @ sz00 )
= sz00 ),
inference(simp,[status(thm)],[26977]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(68286,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,217]) ).
thf(68287,plain,
( ( sdtasdt0 @ sz10 @ ( sdtmndt0 @ sz10 @ sz10 ) )
= ( sdtmndt0 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[68286:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = sz00 )
| ~ ( doDivides0 @ A @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtasdt0 @ C @ ( sdtsldt0 @ B @ A ) )
= ( sdtsldt0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( A = sz00 )
| ( ( sdtsldt0 @ ( sdtasdt0 @ C @ B ) @ A )
= ( sdtasdt0 @ C @ ( sdtsldt0 @ B @ A ) ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ~ ( aNaturalNumber0 @ C ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(16073,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ xk @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16034,132]) ).
thf(16074,plain,
( ( sdtpldt0 @ sz00 @ ( sdtmndt0 @ xk @ xk ) )
= ( sdtmndt0 @ xk @ xk ) ),
inference(pattern_uni,[status(thm)],[16073:[bind(A,$thf( sdtmndt0 @ xk @ xk ))]]) ).
thf(52822,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( sdtlseqdt0 @ sz00 @ ( sk2 @ xk ) )
| ( ( sk2 @ xk )
!= ( sk2 @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[52031,801]) ).
thf(52823,plain,
( ( sdtlseqdt0 @ sz10 @ ( sk2 @ xk ) )
| ( sdtlseqdt0 @ sz00 @ ( sk2 @ xk ) ) ),
inference(pattern_uni,[status(thm)],[52822:[]]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtasdt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ( B = sz00 ) ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ( B = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(7117,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ xk @ xk )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[494,87]) ).
thf(7118,plain,
( ( ( sdtpldt0 @ xk @ ( sk1 @ xk @ xk ) )
= xk )
| ~ ( aNaturalNumber0 @ xk )
| ~ ( aNaturalNumber0 @ xk ) ),
inference(pattern_uni,[status(thm)],[7117:[bind(A,$thf( xk )),bind(B,$thf( xk ))]]) ).
thf(7209,plain,
( ( ( sdtpldt0 @ xk @ ( sk1 @ xk @ xk ) )
= xk )
| ~ ( aNaturalNumber0 @ xk ) ),
inference(simp,[status(thm)],[7118]) ).
thf(31193,plain,
( ( ( sdtpldt0 @ xk @ ( sk1 @ xk @ xk ) )
= xk )
| ~ $true ),
inference(rewrite,[status(thm)],[7209,197]) ).
thf(31194,plain,
( ( sdtpldt0 @ xk @ ( sk1 @ xk @ xk ) )
= xk ),
inference(simp,[status(thm)],[31193]) ).
thf(1279,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,131]) ).
thf(1280,plain,
( ( sdtpldt0 @ xk @ sz00 )
= xk ),
inference(pattern_uni,[status(thm)],[1279:[bind(A,$thf( xk ))]]) ).
thf(147,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ( A != sz00 ) ),
inference(cnf,[status(esa)],[145]) ).
thf(155,plain,
! [A: $i] :
( ( A != sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[147]) ).
thf(156,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( isPrime0 @ sz00 ) ),
inference(simp,[status(thm)],[155]) ).
thf(261,plain,
( ~ $true
| ~ ( isPrime0 @ sz00 ) ),
inference(rewrite,[status(thm)],[156,185]) ).
thf(262,plain,
~ ( isPrime0 @ sz00 ),
inference(simp,[status(thm)],[261]) ).
thf(68162,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,217]) ).
thf(68163,plain,
( ( sdtasdt0 @ sz10 @ xk )
= xk ),
inference(pattern_uni,[status(thm)],[68162:[bind(A,$thf( xk ))]]) ).
thf(207,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ~ ( iLess0 @ A @ xk )
| ( isPrime0 @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[206]) ).
thf(210,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( iLess0 @ A @ xk )
| ( isPrime0 @ ( sk4 @ A ) ) ),
inference(lifteq,[status(thm)],[207]) ).
thf(241,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,49]) ).
thf(242,plain,
( ( sdtasdt0 @ xk @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( xk ))]]) ).
thf(193,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)],[192]) ).
thf(195,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)],[193]) ).
thf(2703,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[197,216]) ).
thf(2704,plain,
( ( sdtasdt0 @ xk @ sz10 )
= xk ),
inference(pattern_uni,[status(thm)],[2703:[bind(A,$thf( xk ))]]) ).
thf(2222,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[61,132]) ).
thf(2223,plain,
( ( sdtpldt0 @ sz00 @ sz10 )
= sz10 ),
inference(pattern_uni,[status(thm)],[2222:[bind(A,$thf( sz10 ))]]) ).
thf(134,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)],[133]) ).
thf(136,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)],[134]) ).
thf(68246,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5790,217]) ).
thf(68247,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[68246:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ B @ xk )
| ( ( isPrime0 @ A )
!= ( isPrime0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[158,45]) ).
thf(295,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( doDivides0 @ A @ xk ) ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(332,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ~ ( doDivides0 @ A @ xk ) ),
inference(simp,[status(thm)],[295]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = sz00 )
| ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(802,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk2 @ xk ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[791,49]) ).
thf(803,plain,
( ( sdtasdt0 @ ( sk2 @ xk ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[802:[bind(A,$thf( sk2 @ xk ))]]) ).
thf(18312,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sdtmndt0 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18138,131]) ).
thf(18313,plain,
( ( sdtpldt0 @ ( sdtmndt0 @ sz10 @ sz10 ) @ sz00 )
= ( sdtmndt0 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[18312:[bind(A,$thf( sdtmndt0 @ sz10 @ sz10 ))]]) ).
thf(105869,plain,
$false,
inference(cvc4,[status(thm)],[69,16137,5918,138,10259,170,217,2231,5878,63250,18178,18265,56,37695,34208,10170,44164,142,174,185,417,33775,565,52,184,110,2217,125,50496,196,157,44320,5868,5866,68259,51757,46,93,10206,78,51747,216,492,33988,211,63206,238,63006,10271,34232,62904,18241,132,5846,116,5824,206,10303,61,89,133,74,2718,38840,16155,117,18140,220,85,201,63240,160,192,63208,137,165,197,97,16195,16072,92,43913,169,50494,51756,44286,53,25879,225,212,96,21615,34212,34210,16036,10239,18176,173,569,18257,128,105,205,68123,48834,63329,1278,45,161,180,176,191,44,5876,59,204,8064,71,39995,144,498,49,34198,236,159,113,51755,10204,419,44090,44162,230,1282,219,811,5816,494,16139,103,33990,140,213,91,198,108,18243,68297,80,167,26360,44370,589,162,10269,112,123,68221,145,5822,21743,63,31740,44248,2732,80415,5790,50,127,69883,791,182,1284,63024,72,175,52031,143,39245,52825,52793,51752,87,52647,10261,16153,218,16034,68255,158,44288,186,139,26978,55,114,68287,75,58,16074,16117,18138,52823,82,31194,1280,262,51,183,68163,18221,210,107,242,10168,79,195,2704,2223,94,801,136,68247,332,131,62,163,200,803,83,18313,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM483+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 16:06:16 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.93/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.09 % [INFO] Parsing done (161ms).
% 1.49/1.11 % [INFO] Running in sequential loop mode.
% 2.05/1.39 % [INFO] eprover registered as external prover.
% 2.05/1.39 % [INFO] cvc4 registered as external prover.
% 2.05/1.40 % [INFO] Scanning for conjecture ...
% 2.27/1.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.50 % [INFO] Found a conjecture and 41 axioms. Running axiom selection ...
% 2.50/1.56 % [INFO] Axiom selection finished. Selected 41 axioms (removed 0 axioms).
% 2.50/1.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.50/1.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/1.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/1.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/1.60 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/1.61 % [INFO] Problem is first-order (TPTP FOF).
% 2.69/1.62 % [INFO] Type checking passed.
% 2.69/1.62 % [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 ...
% 87.55/23.86 % External prover 'cvc4' found a proof!
% 87.55/23.86 % [INFO] Killing All external provers ...
% 87.55/23.86 % Time passed: 23318ms (effective reasoning time: 22750ms)
% 87.55/23.86 % 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)>
% 87.55/23.86 % Axioms used in derivation (41): mSortsC, mAddComm, m_MulZero, mZeroMul, mZeroAdd, mDivAsso, mLENTr, mMonMul, mIH_03, mDivMin, mDefQuot, m__1700, mAMDistr, mLETotal, mMonAdd, m__1716, mLEAsym, mAddCanc, mDivSum, mDivTrans, m_MulUnit, mDefPrime, mSortsC_01, mMulCanc, mLETran, mDefDiff, mMonMul2, mAddAsso, mIH, m__1716_04, mDefDiv, mDefLE, mMulAsso, m__1725, mSortsB_02, m_AddZero, mSortsB, mNatSort, mMulComm, mDivLE, mLERefl
% 87.55/23.86 % No. of inferences in proof: 577
% 87.55/23.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23318 ms resp. 22750 ms w/o parsing
% 87.98/23.97 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 87.98/23.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------