TSTP Solution File: NUM490+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM490+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 11:40:49 EDT 2023
% Result : Theorem 89.25s 23.81s
% Output : Refutation 89.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 65
% Syntax : Number of formulae : 645 ( 110 unt; 18 typ; 0 def)
% Number of atoms : 2094 (1011 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 5613 ( 984 ~; 974 |; 178 &;3336 @)
% ( 5 <=>; 136 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 473 ( 0 ^; 465 !; 8 ?; 473 :)
% 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(xr_type,type,
xr: $i ).
thf(xm_type,type,
xm: $i ).
thf(xn_type,type,
xn: $i ).
thf(xp_type,type,
xp: $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 ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
thf(69,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
thf(134,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(136,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A
= ( sdtpldt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(138,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[136]) ).
thf(13,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(86,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)],[13]) ).
thf(87,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( doDivides0 @ ( sk2 @ A ) @ A )
| ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[86]) ).
thf(101,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( doDivides0 @ ( sk2 @ A ) @ A )
| ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(37,axiom,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1951) ).
thf(195,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(196,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(lifteq,[status(thm)],[195]) ).
thf(45,axiom,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
thf(221,plain,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(224,plain,
aNaturalNumber0 @ xn,
inference(cnf,[status(esa)],[221]) ).
thf(27,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
thf(151,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(152,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ A @ sz00 )
= sz00 ) ),
inference(cnf,[status(esa)],[151]) ).
thf(154,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(1509,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,154]) ).
thf(1510,plain,
( ( sdtasdt0 @ xn @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[1509:[bind(A,$thf( xn ))]]) ).
thf(1705,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) )
= sz00 )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xn @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[196,1510]) ).
thf(1755,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) )
= sz00 )
| ( xn != xn )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1705]) ).
thf(1767,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) )
= sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1755]) ).
thf(223,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[221]) ).
thf(12,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
thf(84,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(85,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sdtlseqdt0 @ A @ A ) ),
inference(cnf,[status(esa)],[84]) ).
thf(10864,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,85]) ).
thf(10865,plain,
sdtlseqdt0 @ xm @ xm,
inference(pattern_uni,[status(thm)],[10864:[bind(A,$thf( xm ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(43,axiom,
( ( isPrime0 @ xp )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
thf(213,plain,
( ( isPrime0 @ xp )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(215,plain,
isPrime0 @ xp,
inference(cnf,[status(esa)],[213]) ).
thf(89,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ( A != sz00 ) ),
inference(cnf,[status(esa)],[86]) ).
thf(97,plain,
! [A: $i] :
( ( A != sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(98,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( isPrime0 @ sz00 ) ),
inference(simp,[status(thm)],[97]) ).
thf(19,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(119,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(248,plain,
( ~ $true
| ~ ( isPrime0 @ sz00 ) ),
inference(rewrite,[status(thm)],[98,119]) ).
thf(249,plain,
~ ( isPrime0 @ sz00 ),
inference(simp,[status(thm)],[248]) ).
thf(250,plain,
( ( isPrime0 @ xp )
!= ( isPrime0 @ sz00 ) ),
inference(paramod_ordered,[status(thm)],[215,249]) ).
thf(252,plain,
xp != sz00,
inference(simp,[status(thm)],[250]) ).
thf(4106,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ B @ A )
| ( B != sz00 )
| ( A != xp ) ),
inference(paramod_ordered,[status(thm)],[66,252]) ).
thf(4107,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ A )
| ~ ( sdtlseqdt0 @ xp @ A )
| ~ ( sdtlseqdt0 @ A @ xp )
| ( A != sz00 ) ),
inference(pattern_uni,[status(thm)],[4106:[bind(A,$thf( xp ))]]) ).
thf(4478,plain,
( ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( sdtlseqdt0 @ xp @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ xp ) ),
inference(simp,[status(thm)],[4107]) ).
thf(222,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[221]) ).
thf(15191,plain,
( ~ $true
| ~ $true
| ~ ( sdtlseqdt0 @ xp @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ xp ) ),
inference(rewrite,[status(thm)],[4478,119,222]) ).
thf(15192,plain,
( ~ ( sdtlseqdt0 @ xp @ sz00 )
| ~ ( sdtlseqdt0 @ sz00 @ xp ) ),
inference(simp,[status(thm)],[15191]) ).
thf(15193,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xp )
| ( ( sdtlseqdt0 @ xp @ sz00 )
!= ( sdtlseqdt0 @ xm @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[10865,15192]) ).
thf(15323,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xp )
| ( xp != xm )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[15193]) ).
thf(30759,plain,
( ( xp != xm )
| ( xm != sz00 )
| ( ( sdtlseqdt0 @ xm @ xm )
!= ( sdtlseqdt0 @ sz00 @ xp ) ) ),
inference(paramod_ordered,[status(thm)],[10865,15323]) ).
thf(30902,plain,
( ( xp != xm )
| ( xm != sz00 )
| ( xm != sz00 )
| ( xp != xm ) ),
inference(simp,[status(thm)],[30759]) ).
thf(30927,plain,
( ( xp != xm )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[30902]) ).
thf(3,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
thf(51,plain,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(53,plain,
aNaturalNumber0 @ sz10,
inference(cnf,[status(esa)],[51]) ).
thf(10854,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53,85]) ).
thf(10855,plain,
sdtlseqdt0 @ sz10 @ sz10,
inference(pattern_uni,[status(thm)],[10854:[bind(A,$thf( sz10 ))]]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
<=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) )
& ( ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) )
=> ( sdtlseqdt0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(10966,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz10 @ sz10 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10855,73]) ).
thf(10967,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[10966:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(11010,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(simp,[status(thm)],[10967]) ).
thf(14706,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) ) ),
inference(rewrite,[status(thm)],[11010,53]) ).
thf(14707,plain,
aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ),
inference(simp,[status(thm)],[14706]) ).
thf(32642,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14707,138]) ).
thf(32643,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ sz10 @ sz10 ) )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[32642:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(153,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[151]) ).
thf(155,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[153]) ).
thf(6142,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,155]) ).
thf(6143,plain,
( ( sdtasdt0 @ sz00 @ xm )
= sz00 ),
inference(pattern_uni,[status(thm)],[6142:[bind(A,$thf( xm ))]]) ).
thf(1,conjecture,
( ( sdtasdt0 @ xr @ xm )
= ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
( ( sdtasdt0 @ xr @ xm )
!= ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(49,plain,
( ( sdtasdt0 @ xr @ xm )
!= ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(50,plain,
( ( sdtasdt0 @ xr @ xm )
!= ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(6755,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz00 @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[6143,50]) ).
thf(6786,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xr != sz00 )
| ( xm != xm ) ),
inference(simp,[status(thm)],[6755]) ).
thf(6808,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xr != sz00 ) ),
inference(simp,[status(thm)],[6786]) ).
thf(32694,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ xp )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[222,138]) ).
thf(32695,plain,
( ( sdtpldt0 @ sz00 @ xp )
= xp ),
inference(pattern_uni,[status(thm)],[32694:[bind(A,$thf( xp ))]]) ).
thf(13255,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ xm @ xm )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10865,73]) ).
thf(13256,plain,
( ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xm )
| ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) ) ),
inference(pattern_uni,[status(thm)],[13255:[bind(A,$thf( xm )),bind(B,$thf( xm ))]]) ).
thf(13308,plain,
( ~ ( aNaturalNumber0 @ xm )
| ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) ) ),
inference(simp,[status(thm)],[13256]) ).
thf(17960,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) ) ),
inference(rewrite,[status(thm)],[13308,223]) ).
thf(17961,plain,
aNaturalNumber0 @ ( sk1 @ xm @ xm ),
inference(simp,[status(thm)],[17960]) ).
thf(35,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
thf(188,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(189,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ A @ sz10 )
= A ) ),
inference(cnf,[status(esa)],[188]) ).
thf(191,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(58977,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17961,191]) ).
thf(58978,plain,
( ( sdtasdt0 @ ( sk1 @ xm @ xm ) @ sz10 )
= ( sk1 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[58977:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(135,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtpldt0 @ A @ sz00 )
= A ) ),
inference(cnf,[status(esa)],[134]) ).
thf(137,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(31255,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14707,137]) ).
thf(31256,plain,
( ( sdtpldt0 @ ( sk1 @ sz10 @ sz10 ) @ sz00 )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[31255:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(10852,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,85]) ).
thf(10853,plain,
sdtlseqdt0 @ xn @ xn,
inference(pattern_uni,[status(thm)],[10852:[bind(A,$thf( xn ))]]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B ) ),
inference(cnf,[status(esa)],[71]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(10936,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ xn @ xn )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10853,75]) ).
thf(10937,plain,
( ( ( sdtpldt0 @ xn @ ( sk1 @ xn @ xn ) )
= xn )
| ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xn ) ),
inference(pattern_uni,[status(thm)],[10936:[bind(A,$thf( xn )),bind(B,$thf( xn ))]]) ).
thf(10949,plain,
( ( ( sdtpldt0 @ xn @ ( sk1 @ xn @ xn ) )
= xn )
| ~ ( aNaturalNumber0 @ xn ) ),
inference(simp,[status(thm)],[10937]) ).
thf(22758,plain,
( ( ( sdtpldt0 @ xn @ ( sk1 @ xn @ xn ) )
= xn )
| ~ $true ),
inference(rewrite,[status(thm)],[10949,224]) ).
thf(22759,plain,
( ( sdtpldt0 @ xn @ ( sk1 @ xn @ xn ) )
= xn ),
inference(simp,[status(thm)],[22758]) ).
thf(58990,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ xp )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[222,191]) ).
thf(58991,plain,
( ( sdtasdt0 @ xp @ sz10 )
= xp ),
inference(pattern_uni,[status(thm)],[58990:[bind(A,$thf( xp ))]]) ).
thf(41,axiom,
( xr
= ( sdtmndt0 @ xn @ xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
thf(209,plain,
( xr
= ( sdtmndt0 @ xn @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(210,plain,
( ( sdtmndt0 @ xn @ xp )
= xr ),
inference(lifteq,[status(thm)],[209]) ).
thf(439,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= xr )
| ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
!= ( sdtmndt0 @ xn @ xp ) ) ),
inference(paramod_ordered,[status(thm)],[210,50]) ).
thf(440,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= xr )
| ( ( sdtasdt0 @ xn @ xm )
!= xn )
| ( ( sdtasdt0 @ xp @ xm )
!= xp ) ),
inference(simp,[status(thm)],[439]) ).
thf(6705,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= xr )
| ( xn != sz00 )
| ( ( sdtasdt0 @ xp @ xm )
!= xp )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ sz00 @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[6143,440]) ).
thf(6793,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= xr )
| ( xn != sz00 )
| ( ( sdtasdt0 @ xp @ xm )
!= xp )
| ( xn != sz00 )
| ( xm != xm ) ),
inference(simp,[status(thm)],[6705]) ).
thf(6815,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= xr )
| ( xn != sz00 )
| ( ( sdtasdt0 @ xp @ xm )
!= xp ) ),
inference(simp,[status(thm)],[6793]) ).
thf(60705,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= xr )
| ( xn != sz00 )
| ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ sz10 ) ) ),
inference(paramod_ordered,[status(thm)],[58991,6815]) ).
thf(60945,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= xr )
| ( xn != sz00 )
| ( xp != xp )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[60705]) ).
thf(60977,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= xr )
| ( xn != sz00 )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[60945]) ).
thf(67789,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A != xr )
| ( xn != sz00 )
| ( xm != sz10 )
| ( ( sdtasdt0 @ A @ sz10 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[191,60977]) ).
thf(67984,plain,
( ~ ( aNaturalNumber0 @ xr )
| ( xn != sz00 )
| ( xm != sz10 )
| ( xr != xr )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[67789]) ).
thf(68045,plain,
( ~ ( aNaturalNumber0 @ xr )
| ( xn != sz00 )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[67984]) ).
thf(1514,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[119,154]) ).
thf(1515,plain,
( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[1514:[bind(A,$thf( sz00 ))]]) ).
thf(1522,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xp )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[222,154]) ).
thf(1523,plain,
( ( sdtasdt0 @ xp @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[1522:[bind(A,$thf( xp ))]]) ).
thf(2987,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) )
| ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1523,50]) ).
thf(3014,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) )
| ( xp != xp )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[2987]) ).
thf(3028,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3014]) ).
thf(5653,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz00 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1515,3028]) ).
thf(5811,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[5653]) ).
thf(5842,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz00 ) ),
inference(simp,[status(thm)],[5811]) ).
thf(31299,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ xp )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[222,137]) ).
thf(31300,plain,
( ( sdtpldt0 @ xp @ sz00 )
= xp ),
inference(pattern_uni,[status(thm)],[31299:[bind(A,$thf( xp ))]]) ).
thf(42,axiom,
( xn
= ( sdtpldt0 @ xp @ xr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1924) ).
thf(211,plain,
( xn
= ( sdtpldt0 @ xp @ xr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(212,plain,
( ( sdtpldt0 @ xp @ xr )
= xn ),
inference(lifteq,[status(thm)],[211]) ).
thf(32347,plain,
( ( xp = xn )
| ( ( sdtpldt0 @ xp @ xr )
!= ( sdtpldt0 @ xp @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[31300,212]) ).
thf(32446,plain,
( ( xp = xn )
| ( xp != xp )
| ( xr != sz00 ) ),
inference(simp,[status(thm)],[32347]) ).
thf(32497,plain,
( ( xp = xn )
| ( xr != sz00 ) ),
inference(simp,[status(thm)],[32446]) ).
thf(33,axiom,
( ( xr != xn )
& ( sdtlseqdt0 @ xr @ xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1894) ).
thf(179,plain,
( ( xr != xn )
& ( sdtlseqdt0 @ xr @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(180,plain,
sdtlseqdt0 @ xr @ xn,
inference(cnf,[status(esa)],[179]) ).
thf(15228,plain,
( ~ ( sdtlseqdt0 @ xp @ sz00 )
| ( ( sdtlseqdt0 @ xr @ xn )
!= ( sdtlseqdt0 @ sz00 @ xp ) ) ),
inference(paramod_ordered,[status(thm)],[180,15192]) ).
thf(15315,plain,
( ~ ( sdtlseqdt0 @ xp @ sz00 )
| ( xr != sz00 )
| ( xp != xn ) ),
inference(simp,[status(thm)],[15228]) ).
thf(43527,plain,
( ( xr != sz00 )
| ~ ( sdtlseqdt0 @ xp @ sz00 )
| ( xp != xp ) ),
inference(paramod_ordered,[status(thm)],[32497,15315]) ).
thf(43528,plain,
( ( xr != sz00 )
| ~ ( sdtlseqdt0 @ xp @ sz00 ) ),
inference(pattern_uni,[status(thm)],[43527:[]]) ).
thf(44298,plain,
( ( xr != sz00 )
| ~ ( sdtlseqdt0 @ xn @ sz00 )
| ( xp != xp ) ),
inference(paramod_ordered,[status(thm)],[32497,43528]) ).
thf(44299,plain,
( ( xr != sz00 )
| ~ ( sdtlseqdt0 @ xn @ sz00 ) ),
inference(pattern_uni,[status(thm)],[44298:[]]) ).
thf(20,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
thf(120,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(93,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ( A != sz10 ) ),
inference(cnf,[status(esa)],[86]) ).
thf(95,plain,
! [A: $i] :
( ( A != sz10 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(96,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( isPrime0 @ sz10 ) ),
inference(simp,[status(thm)],[95]) ).
thf(246,plain,
( ~ $true
| ~ ( isPrime0 @ sz10 ) ),
inference(rewrite,[status(thm)],[96,53]) ).
thf(247,plain,
~ ( isPrime0 @ sz10 ),
inference(simp,[status(thm)],[246]) ).
thf(1735,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xn @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1510,50]) ).
thf(1756,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( xn != xn )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1735]) ).
thf(1768,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1756]) ).
thf(2983,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xp @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[1523,1768]) ).
thf(3005,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( xp != xr )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[2983]) ).
thf(3044,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( xp != xr ) ),
inference(simp,[status(thm)],[3005]) ).
thf(13287,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ xm @ xm )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10865,75]) ).
thf(13288,plain,
( ( ( sdtpldt0 @ xm @ ( sk1 @ xm @ xm ) )
= xm )
| ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xm ) ),
inference(pattern_uni,[status(thm)],[13287:[bind(A,$thf( xm )),bind(B,$thf( xm ))]]) ).
thf(13309,plain,
( ( ( sdtpldt0 @ xm @ ( sk1 @ xm @ xm ) )
= xm )
| ~ ( aNaturalNumber0 @ xm ) ),
inference(simp,[status(thm)],[13288]) ).
thf(23250,plain,
( ( ( sdtpldt0 @ xm @ ( sk1 @ xm @ xm ) )
= xm )
| ~ $true ),
inference(rewrite,[status(thm)],[13309,223]) ).
thf(23251,plain,
( ( sdtpldt0 @ xm @ ( sk1 @ xm @ xm ) )
= xm ),
inference(simp,[status(thm)],[23250]) ).
thf(10878,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ xp )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[222,85]) ).
thf(10879,plain,
sdtlseqdt0 @ xp @ xp,
inference(pattern_uni,[status(thm)],[10878:[bind(A,$thf( xp ))]]) ).
thf(13399,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ xp @ xp )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10879,73]) ).
thf(13400,plain,
( ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ xp )
| ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) ) ),
inference(pattern_uni,[status(thm)],[13399:[bind(A,$thf( xp )),bind(B,$thf( xp ))]]) ).
thf(13453,plain,
( ~ ( aNaturalNumber0 @ xp )
| ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) ) ),
inference(simp,[status(thm)],[13400]) ).
thf(20947,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) ) ),
inference(rewrite,[status(thm)],[13453,222]) ).
thf(20948,plain,
aNaturalNumber0 @ ( sk1 @ xp @ xp ),
inference(simp,[status(thm)],[20947]) ).
thf(20985,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20948,85]) ).
thf(20986,plain,
sdtlseqdt0 @ ( sk1 @ xp @ xp ) @ ( sk1 @ xp @ xp ),
inference(pattern_uni,[status(thm)],[20985:[bind(A,$thf( sk1 @ xp @ xp ))]]) ).
thf(190,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A
= ( sdtasdt0 @ sz10 @ A ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(192,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[190]) ).
thf(61778,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,192]) ).
thf(61779,plain,
( ( sdtasdt0 @ sz10 @ xn )
= xn ),
inference(pattern_uni,[status(thm)],[61778:[bind(A,$thf( xn ))]]) ).
thf(4761,plain,
( ( xm != sz00 )
| ( ( sdtasdt0 @ xn @ xm )
= sz00 )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) ) ),
inference(paramod_ordered,[status(thm)],[1767,196]) ).
thf(4762,plain,
( ( xm != sz00 )
| ( ( sdtasdt0 @ xn @ xm )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[4761:[]]) ).
thf(58900,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20948,191]) ).
thf(58901,plain,
( ( sdtasdt0 @ ( sk1 @ xp @ xp ) @ sz10 )
= ( sk1 @ xp @ xp ) ),
inference(pattern_uni,[status(thm)],[58900:[bind(A,$thf( sk1 @ xp @ xp ))]]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtsldt0 @ B @ A ) )
<=> ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
thf(168,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtsldt0 @ B @ A ) )
=> ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) )
& ( ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) )
=> ( C
= ( sdtsldt0 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(169,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)],[168]) ).
thf(170,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)],[169]) ).
thf(173,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)],[170]) ).
thf(174,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)],[173]) ).
thf(61855,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,192]) ).
thf(61856,plain,
( ( sdtasdt0 @ sz10 @ xm )
= xm ),
inference(pattern_uni,[status(thm)],[61855:[bind(A,$thf( xm ))]]) ).
thf(43565,plain,
( ( xr != sz00 )
| ( isPrime0 @ xn )
| ( xp != xp ) ),
inference(paramod_ordered,[status(thm)],[32497,215]) ).
thf(43566,plain,
( ( xr != sz00 )
| ( isPrime0 @ xn ) ),
inference(pattern_uni,[status(thm)],[43565:[]]) ).
thf(32677,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17961,138]) ).
thf(32678,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ xm @ xm ) )
= ( sk1 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[32677:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(2982,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= ( sdtmndt0 @ sz00 @ sz00 ) )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1523,1768]) ).
thf(3007,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= ( sdtmndt0 @ sz00 @ sz00 ) )
| ( xm != sz00 )
| ( xp != xp )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[2982]) ).
thf(3046,plain,
( ( ( sdtasdt0 @ xr @ xm )
!= ( sdtmndt0 @ sz00 @ sz00 ) )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3007]) ).
thf(16,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(109,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)],[16]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ),
inference(cnf,[status(esa)],[109]) ).
thf(122,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A ) ),
inference(cnf,[status(esa)],[120]) ).
thf(125,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( sdtlseqdt0 @ sz10 @ A ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(26678,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,125]) ).
thf(26679,plain,
( ( xn = sz00 )
| ( xn = sz10 )
| ( sdtlseqdt0 @ sz10 @ xn ) ),
inference(pattern_uni,[status(thm)],[26678:[bind(A,$thf( xn ))]]) ).
thf(27775,plain,
( ( xn = sz00 )
| ( sdtlseqdt0 @ sz10 @ xn )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[26679,10853]) ).
thf(27776,plain,
( ( xn = sz00 )
| ( sdtlseqdt0 @ sz10 @ xn ) ),
inference(pattern_uni,[status(thm)],[27775:[]]) ).
thf(181,plain,
xr != xn,
inference(cnf,[status(esa)],[179]) ).
thf(182,plain,
xn != xr,
inference(lifteq,[status(thm)],[181]) ).
thf(28814,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( xr != sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,182]) ).
thf(28815,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( xr != sz00 ) ),
inference(pattern_uni,[status(thm)],[28814:[]]) ).
thf(58797,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,191]) ).
thf(58798,plain,
( ( sdtasdt0 @ xn @ sz10 )
= xn ),
inference(pattern_uni,[status(thm)],[58797:[bind(A,$thf( xn ))]]) ).
thf(6704,plain,
( ( xr != sz00 )
| ( ( sdtasdt0 @ xn @ xm )
!= xn )
| ( ( sdtasdt0 @ xp @ xm )
!= xp )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz00 @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[6143,440]) ).
thf(6795,plain,
( ( xr != sz00 )
| ( ( sdtasdt0 @ xn @ xm )
!= xn )
| ( ( sdtasdt0 @ xp @ xm )
!= xp )
| ( xr != sz00 )
| ( xm != xm ) ),
inference(simp,[status(thm)],[6704]) ).
thf(6817,plain,
( ( xr != sz00 )
| ( ( sdtasdt0 @ xn @ xm )
!= xn )
| ( ( sdtasdt0 @ xp @ xm )
!= xp ) ),
inference(simp,[status(thm)],[6795]) ).
thf(59392,plain,
( ( xr != sz00 )
| ( ( sdtasdt0 @ xp @ xm )
!= xp )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xn @ sz10 ) ) ),
inference(paramod_ordered,[status(thm)],[58798,6817]) ).
thf(59609,plain,
( ( xr != sz00 )
| ( ( sdtasdt0 @ xp @ xm )
!= xp )
| ( xn != xn )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[59392]) ).
thf(59688,plain,
( ( xr != sz00 )
| ( ( sdtasdt0 @ xp @ xm )
!= xp )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[59609]) ).
thf(61259,plain,
( ( xr != sz00 )
| ( xm != sz10 )
| ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ sz10 ) ) ),
inference(paramod_ordered,[status(thm)],[58991,59688]) ).
thf(61526,plain,
( ( xr != sz00 )
| ( xm != sz10 )
| ( xp != xp )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[61259]) ).
thf(61560,plain,
( ( xr != sz00 )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[61526]) ).
thf(10904,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ xn @ xn )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10853,73]) ).
thf(10905,plain,
( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) ) ),
inference(pattern_uni,[status(thm)],[10904:[bind(A,$thf( xn )),bind(B,$thf( xn ))]]) ).
thf(10948,plain,
( ~ ( aNaturalNumber0 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) ) ),
inference(simp,[status(thm)],[10905]) ).
thf(13455,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) ) ),
inference(rewrite,[status(thm)],[10948,224]) ).
thf(13456,plain,
aNaturalNumber0 @ ( sk1 @ xn @ xn ),
inference(simp,[status(thm)],[13455]) ).
thf(31288,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17961,137]) ).
thf(31289,plain,
( ( sdtpldt0 @ ( sk1 @ xm @ xm ) @ sz00 )
= ( sk1 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[31288:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(9,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(78,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)],[9]) ).
thf(1494,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53,154]) ).
thf(1495,plain,
( ( sdtasdt0 @ sz10 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[1494:[bind(A,$thf( sz10 ))]]) ).
thf(1839,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz10 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1495,1768]) ).
thf(1850,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz10 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1839]) ).
thf(1875,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz10 ) ),
inference(simp,[status(thm)],[1850]) ).
thf(15877,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( doDivides0 @ ( sk2 @ A ) @ A )
| ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,101]) ).
thf(15878,plain,
( ( xn = sz00 )
| ( xn = sz10 )
| ( doDivides0 @ ( sk2 @ xn ) @ xn )
| ( isPrime0 @ xn ) ),
inference(pattern_uni,[status(thm)],[15877:[bind(A,$thf( xn ))]]) ).
thf(30,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(162,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)],[30]) ).
thf(163,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)],[162]) ).
thf(164,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)],[163]) ).
thf(21023,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20948,155]) ).
thf(21024,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ xp @ xp ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[21023:[bind(A,$thf( sk1 @ xp @ xp ))]]) ).
thf(5798,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz10 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1495,3028]) ).
thf(5805,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz10 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[5798]) ).
thf(5834,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz10 ) ),
inference(simp,[status(thm)],[5805]) ).
thf(6080,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53,155]) ).
thf(6081,plain,
( ( sdtasdt0 @ sz00 @ sz10 )
= sz00 ),
inference(pattern_uni,[status(thm)],[6080:[bind(A,$thf( sz10 ))]]) ).
thf(44,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(216,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)],[44]) ).
thf(32539,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13456,138]) ).
thf(32540,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ xn @ xn ) )
= ( sk1 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[32539:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(39396,plain,
( ( ( sk1 @ xn @ xn )
= xn )
| ( ( sdtpldt0 @ xn @ ( sk1 @ xn @ xn ) )
!= ( sdtpldt0 @ sz00 @ ( sk1 @ xn @ xn ) ) ) ),
inference(paramod_ordered,[status(thm)],[32540,22759]) ).
thf(39656,plain,
( ( ( sk1 @ xn @ xn )
= xn )
| ( xn != sz00 )
| ( ( sk1 @ xn @ xn )
!= ( sk1 @ xn @ xn ) ) ),
inference(simp,[status(thm)],[39396]) ).
thf(39753,plain,
( ( ( sk1 @ xn @ xn )
= xn )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[39656]) ).
thf(251,plain,
( ( isPrime0 @ xp )
!= ( isPrime0 @ sz10 ) ),
inference(paramod_ordered,[status(thm)],[215,247]) ).
thf(253,plain,
xp != sz10,
inference(simp,[status(thm)],[251]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ C ) )
=> ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
thf(146,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ C ) )
=> ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(147,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)],[146]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ C @ A ) @ ( sdtpldt0 @ C @ B ) )
& ( ( sdtpldt0 @ A @ C )
!= ( sdtpldt0 @ B @ C ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ C @ A ) @ ( sdtpldt0 @ C @ B ) )
& ( ( sdtpldt0 @ A @ C )
!= ( sdtpldt0 @ B @ C ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(57,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)],[55]) ).
thf(61,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)],[57]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ A @ C ) )
| ( ( sdtpldt0 @ B @ A )
= ( sdtpldt0 @ C @ A ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ A @ C ) )
| ( ( sdtpldt0 @ B @ A )
= ( sdtpldt0 @ C @ A ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(130,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)],[129]) ).
thf(132,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)],[130]) ).
thf(131,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)],[129]) ).
thf(133,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)],[131]) ).
thf(28746,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ xr @ sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,180]) ).
thf(28747,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ xr @ sz00 ) ),
inference(pattern_uni,[status(thm)],[28746:[]]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(13427,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ xp @ xp )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10879,75]) ).
thf(13428,plain,
( ( ( sdtpldt0 @ xp @ ( sk1 @ xp @ xp ) )
= xp )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ xp ) ),
inference(pattern_uni,[status(thm)],[13427:[bind(A,$thf( xp )),bind(B,$thf( xp ))]]) ).
thf(13452,plain,
( ( ( sdtpldt0 @ xp @ ( sk1 @ xp @ xp ) )
= xp )
| ~ ( aNaturalNumber0 @ xp ) ),
inference(simp,[status(thm)],[13428]) ).
thf(24670,plain,
( ( ( sdtpldt0 @ xp @ ( sk1 @ xp @ xp ) )
= xp )
| ~ $true ),
inference(rewrite,[status(thm)],[13452,222]) ).
thf(24671,plain,
( ( sdtpldt0 @ xp @ ( sk1 @ xp @ xp ) )
= xp ),
inference(simp,[status(thm)],[24670]) ).
thf(24729,plain,
( ( xp = xn )
| ( ( sdtpldt0 @ xp @ ( sk1 @ xp @ xp ) )
!= ( sdtpldt0 @ xp @ xr ) ) ),
inference(paramod_ordered,[status(thm)],[212,24671]) ).
thf(24875,plain,
( ( xp = xn )
| ( xp != xp )
| ( ( sk1 @ xp @ xp )
!= xr ) ),
inference(simp,[status(thm)],[24729]) ).
thf(24881,plain,
( ( xp = xn )
| ( ( sk1 @ xp @ xp )
!= xr ) ),
inference(simp,[status(thm)],[24875]) ).
thf(39,axiom,
sdtlseqdt0 @ xp @ xn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
thf(199,plain,
sdtlseqdt0 @ xp @ xn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(15265,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xp )
| ( ( sdtlseqdt0 @ xp @ xn )
!= ( sdtlseqdt0 @ xp @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[199,15192]) ).
thf(15328,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xp )
| ( xp != xp )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[15265]) ).
thf(15360,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xp )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[15328]) ).
thf(3143,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xp @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[1523,3046]) ).
thf(3150,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xp != xr )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3143]) ).
thf(3157,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xp != xr ) ),
inference(simp,[status(thm)],[3150]) ).
thf(92,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[86]) ).
thf(99,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(1125,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,99]) ).
thf(1126,plain,
( ( xm = sz00 )
| ( xm = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ xm ) )
| ( isPrime0 @ xm ) ),
inference(pattern_uni,[status(thm)],[1125:[bind(A,$thf( xm ))]]) ).
thf(13285,plain,
( ( xm = sz00 )
| ( aNaturalNumber0 @ ( sk2 @ xm ) )
| ( isPrime0 @ xm )
| ( sdtlseqdt0 @ xm @ sz10 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[1126,10865]) ).
thf(13286,plain,
( ( xm = sz00 )
| ( aNaturalNumber0 @ ( sk2 @ xm ) )
| ( isPrime0 @ xm )
| ( sdtlseqdt0 @ xm @ sz10 ) ),
inference(pattern_uni,[status(thm)],[13285:[]]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
thf(117,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10874,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[119,85]) ).
thf(10875,plain,
sdtlseqdt0 @ sz00 @ sz00,
inference(pattern_uni,[status(thm)],[10874:[bind(A,$thf( sz00 ))]]) ).
thf(28699,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ~ ( sdtlseqdt0 @ sz00 @ xp )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,15360]) ).
thf(28700,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ~ ( sdtlseqdt0 @ sz00 @ xp ) ),
inference(pattern_uni,[status(thm)],[28699:[]]) ).
thf(13331,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sk1 @ B @ A ) )
| ( ( sdtlseqdt0 @ sz00 @ sz00 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10875,73]) ).
thf(13332,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[13331:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(13382,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) ) ),
inference(simp,[status(thm)],[13332]) ).
thf(19592,plain,
( ~ $true
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[13382,119]) ).
thf(19593,plain,
aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ),
inference(simp,[status(thm)],[19592]) ).
thf(32656,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz00 @ sz00 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19593,138]) ).
thf(32657,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= ( sk1 @ sz00 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[32656:[bind(A,$thf( sk1 @ sz00 @ sz00 ))]]) ).
thf(13357,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ sz00 @ sz00 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10875,75]) ).
thf(13358,plain,
( ( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[13357:[bind(A,$thf( sz00 )),bind(B,$thf( sz00 ))]]) ).
thf(13381,plain,
( ( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= sz00 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference(simp,[status(thm)],[13358]) ).
thf(23489,plain,
( ( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= sz00 )
| ~ $true ),
inference(rewrite,[status(thm)],[13381,119]) ).
thf(23490,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ sz00 @ sz00 ) )
= sz00 ),
inference(simp,[status(thm)],[23489]) ).
thf(42740,plain,
( ( sk1 @ sz00 @ sz00 )
= sz00 ),
inference(rewrite,[status(thm)],[32657,23490]) ).
thf(28806,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ xp @ sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,199]) ).
thf(28807,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ xp @ sz00 ) ),
inference(pattern_uni,[status(thm)],[28806:[]]) ).
thf(90,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( ( sk2 @ A )
!= sz10 )
| ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[86]) ).
thf(102,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( ( sk2 @ A )
!= sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(1173,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ A ) )
| ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,99]) ).
thf(1174,plain,
( ( xn = sz00 )
| ( xn = sz10 )
| ( aNaturalNumber0 @ ( sk2 @ xn ) )
| ( isPrime0 @ xn ) ),
inference(pattern_uni,[status(thm)],[1173:[bind(A,$thf( xn ))]]) ).
thf(70,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)],[69]) ).
thf(61883,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20948,192]) ).
thf(61884,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ xp @ xp ) )
= ( sk1 @ xp @ xp ) ),
inference(pattern_uni,[status(thm)],[61883:[bind(A,$thf( sk1 @ xp @ xp ))]]) ).
thf(31,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(165,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)],[31]) ).
thf(1499,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,154]) ).
thf(1500,plain,
( ( sdtasdt0 @ xm @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[1499:[bind(A,$thf( xm ))]]) ).
thf(5800,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xm @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[1500,3028]) ).
thf(5812,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xm != xr )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[5800]) ).
thf(5843,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xm != xr ) ),
inference(simp,[status(thm)],[5812]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
thf(197,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(6708,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) )
= sz00 )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ sz00 @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[6143,196]) ).
thf(6789,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) )
= sz00 )
| ( xn != sz00 )
| ( xm != xm ) ),
inference(simp,[status(thm)],[6708]) ).
thf(6811,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) )
= sz00 )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[6789]) ).
thf(8030,plain,
( ( xn != sz00 )
| ( ( sdtasdt0 @ xn @ xm )
= sz00 )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) ) ),
inference(paramod_ordered,[status(thm)],[6811,196]) ).
thf(8031,plain,
( ( xn != sz00 )
| ( ( sdtasdt0 @ xn @ xm )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[8030:[]]) ).
thf(43421,plain,
( ( xr != sz00 )
| ( sdtlseqdt0 @ xn @ xp )
| ( xp != xp ) ),
inference(paramod_ordered,[status(thm)],[32497,10879]) ).
thf(43422,plain,
( ( xr != sz00 )
| ( sdtlseqdt0 @ xn @ xp ) ),
inference(pattern_uni,[status(thm)],[43421:[]]) ).
thf(6167,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xp )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[222,155]) ).
thf(6168,plain,
( ( sdtasdt0 @ sz00 @ xp )
= sz00 ),
inference(pattern_uni,[status(thm)],[6167:[bind(A,$thf( xp ))]]) ).
thf(16776,plain,
( ( xn != sz00 )
| ( ( sdtlseqdt0 @ xn @ xn )
!= ( sdtlseqdt0 @ sz00 @ xp ) ) ),
inference(paramod_ordered,[status(thm)],[10853,15360]) ).
thf(16804,plain,
( ( xn != sz00 )
| ( xn != sz00 )
| ( xp != xn ) ),
inference(simp,[status(thm)],[16776]) ).
thf(16818,plain,
( ( xn != sz00 )
| ( xp != xn ) ),
inference(simp,[status(thm)],[16804]) ).
thf(1912,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz00 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1515,1768]) ).
thf(1948,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1912]) ).
thf(1953,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz00 ) ),
inference(simp,[status(thm)],[1948]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(16143,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( doDivides0 @ ( sk2 @ A ) @ A )
| ( isPrime0 @ A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,101]) ).
thf(16144,plain,
( ( xm = sz00 )
| ( xm = sz10 )
| ( doDivides0 @ ( sk2 @ xm ) @ xm )
| ( isPrime0 @ xm ) ),
inference(pattern_uni,[status(thm)],[16143:[bind(A,$thf( xm ))]]) ).
thf(27024,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,125]) ).
thf(27025,plain,
( ( xm = sz00 )
| ( xm = sz10 )
| ( sdtlseqdt0 @ sz10 @ xm ) ),
inference(pattern_uni,[status(thm)],[27024:[bind(A,$thf( xm ))]]) ).
thf(36786,plain,
( ( xm = sz00 )
| ( sdtlseqdt0 @ sz10 @ xm )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[27025,10865]) ).
thf(36787,plain,
( ( xm = sz00 )
| ( sdtlseqdt0 @ sz10 @ xm ) ),
inference(pattern_uni,[status(thm)],[36786:[]]) ).
thf(28671,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ xn @ sz00 ) )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,13456]) ).
thf(28672,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ xn @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[28671:[]]) ).
thf(214,plain,
doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ),
inference(cnf,[status(esa)],[213]) ).
thf(1736,plain,
( ( doDivides0 @ xp @ sz00 )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xn @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1510,214]) ).
thf(1757,plain,
( ( doDivides0 @ xp @ sz00 )
| ( xn != xn )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1736]) ).
thf(1769,plain,
( ( doDivides0 @ xp @ sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1757]) ).
thf(40901,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( doDivides0 @ xp @ sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,1769]) ).
thf(40902,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( doDivides0 @ xp @ sz00 ) ),
inference(pattern_uni,[status(thm)],[40901:[]]) ).
thf(27448,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( sdtlseqdt0 @ sz10 @ A )
| ( ( aNaturalNumber0 @ xp )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[222,125]) ).
thf(27449,plain,
( ( xp = sz00 )
| ( xp = sz10 )
| ( sdtlseqdt0 @ sz10 @ xp ) ),
inference(pattern_uni,[status(thm)],[27448:[bind(A,$thf( xp ))]]) ).
thf(51415,plain,
sdtlseqdt0 @ sz10 @ xp,
inference(simplifyReflect,[status(thm)],[27449,252,253]) ).
thf(46,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(225,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)],[46]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( ( sdtpldt0 @ A @ C )
!= B )
| ( sdtlseqdt0 @ A @ B ) ),
inference(cnf,[status(esa)],[71]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ C )
!= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) )
| ~ ( aNaturalNumber0 @ B )
| ( sdtlseqdt0 @ A @ ( sdtpldt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(40590,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ xm @ sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,10865]) ).
thf(40591,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ xm @ sz00 ) ),
inference(pattern_uni,[status(thm)],[40590:[]]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( isPrime0 @ C )
& ( doDivides0 @ C @ ( sdtasdt0 @ A @ B ) ) )
=> ( ( iLess0 @ ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
=> ( ( doDivides0 @ C @ A )
| ( doDivides0 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
thf(193,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( isPrime0 @ C )
& ( doDivides0 @ C @ ( sdtasdt0 @ A @ B ) ) )
=> ( ( iLess0 @ ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
=> ( ( doDivides0 @ C @ A )
| ( doDivides0 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(3134,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ A @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[154,3046]) ).
thf(3148,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( A != xr )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3134]) ).
thf(3155,plain,
( ~ ( aNaturalNumber0 @ xr )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3148]) ).
thf(40742,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ~ ( aNaturalNumber0 @ xr )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,3155]) ).
thf(40743,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ~ ( aNaturalNumber0 @ xr )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 ) ),
inference(pattern_uni,[status(thm)],[40742:[]]) ).
thf(2939,plain,
( ( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ xr @ xm ) ) )
| ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1523,196]) ).
thf(3018,plain,
( ( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ xr @ xm ) ) )
| ( xp != xp )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[2939]) ).
thf(3032,plain,
( ( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ xr @ xm ) ) )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3018]) ).
thf(28847,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ xn @ sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,10853]) ).
thf(28848,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ xn @ sz00 ) ),
inference(pattern_uni,[status(thm)],[28847:[]]) ).
thf(6128,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,155]) ).
thf(6129,plain,
( ( sdtasdt0 @ sz00 @ xn )
= sz00 ),
inference(pattern_uni,[status(thm)],[6128:[bind(A,$thf( xn ))]]) ).
thf(61985,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ xp )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[222,192]) ).
thf(61986,plain,
( ( sdtasdt0 @ sz10 @ xp )
= xp ),
inference(pattern_uni,[status(thm)],[61985:[bind(A,$thf( xp ))]]) ).
thf(1841,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xm @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[1500,1768]) ).
thf(1849,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( xm != xr )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1841]) ).
thf(1874,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( xm != xr ) ),
inference(simp,[status(thm)],[1849]) ).
thf(4760,plain,
( ( ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ xr @ xm ) )
= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1523,1767]) ).
thf(4847,plain,
( ( ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ xr @ xm ) )
= sz00 )
| ( xm != sz00 )
| ( xp != xp )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[4760]) ).
thf(4902,plain,
( ( ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ xr @ xm ) )
= sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[4847]) ).
thf(21,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(126,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)],[21]) ).
thf(127,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)],[126]) ).
thf(128,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)],[127]) ).
thf(3147,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xm @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[1500,3046]) ).
thf(3151,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xm != xr )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3147]) ).
thf(3158,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xm != xr ) ),
inference(simp,[status(thm)],[3151]) ).
thf(40710,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != xr )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,3158]) ).
thf(40711,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != xr ) ),
inference(pattern_uni,[status(thm)],[40710:[]]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( A != sz00 )
& ( B != C )
& ( sdtlseqdt0 @ B @ C ) )
=> ( ( ( sdtasdt0 @ A @ B )
!= ( sdtasdt0 @ A @ C ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) )
& ( ( sdtasdt0 @ B @ A )
!= ( sdtasdt0 @ C @ A ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
thf(200,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( A != sz00 )
& ( B != C )
& ( sdtlseqdt0 @ B @ C ) )
=> ( ( ( sdtasdt0 @ A @ B )
!= ( sdtasdt0 @ A @ C ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) )
& ( ( sdtasdt0 @ B @ A )
!= ( sdtasdt0 @ C @ A ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(201,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)],[200]) ).
thf(205,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)],[201]) ).
thf(5729,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xp @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[1523,3028]) ).
thf(5804,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xp != xr )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[5729]) ).
thf(5833,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xp != xr ) ),
inference(simp,[status(thm)],[5804]) ).
thf(6709,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ sz00 )
= ( sdtasdt0 @ xn @ xm ) )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz00 @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[6143,196]) ).
thf(6790,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ sz00 )
= ( sdtasdt0 @ xn @ xm ) )
| ( xr != sz00 )
| ( xm != xm ) ),
inference(simp,[status(thm)],[6709]) ).
thf(6812,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ sz00 )
= ( sdtasdt0 @ xn @ xm ) )
| ( xr != sz00 ) ),
inference(simp,[status(thm)],[6790]) ).
thf(61893,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14707,192]) ).
thf(61894,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[61893:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(6765,plain,
( ( doDivides0 @ xp @ sz00 )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ sz00 @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[6143,214]) ).
thf(6804,plain,
( ( doDivides0 @ xp @ sz00 )
| ( xn != sz00 )
| ( xm != xm ) ),
inference(simp,[status(thm)],[6765]) ).
thf(6826,plain,
( ( doDivides0 @ xp @ sz00 )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[6804]) ).
thf(28802,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( doDivides0 @ xp @ sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,6826]) ).
thf(28803,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( doDivides0 @ xp @ sz00 ) ),
inference(pattern_uni,[status(thm)],[28802:[]]) ).
thf(31196,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53,137]) ).
thf(31197,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= sz10 ),
inference(pattern_uni,[status(thm)],[31196:[bind(A,$thf( sz10 ))]]) ).
thf(40586,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtmndt0 @ sz00 @ sz00 ) )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,3046]) ).
thf(40587,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtmndt0 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[40586:[]]) ).
thf(26,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(148,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)],[26]) ).
thf(13465,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13456,154]) ).
thf(13466,plain,
( ( sdtasdt0 @ ( sk1 @ xn @ xn ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[13465:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(40554,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( xp != xm )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,30927]) ).
thf(40555,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( xp != xm ) ),
inference(pattern_uni,[status(thm)],[40554:[]]) ).
thf(43357,plain,
( ( xr != sz00 )
| ( xn != xm )
| ( xm != sz00 )
| ( xp != xp ) ),
inference(paramod_ordered,[status(thm)],[32497,30927]) ).
thf(43358,plain,
( ( xr != sz00 )
| ( xn != xm )
| ( xm != sz00 ) ),
inference(pattern_uni,[status(thm)],[43357:[]]) ).
thf(29,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(159,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)],[29]) ).
thf(160,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)],[159]) ).
thf(161,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)],[160]) ).
thf(28851,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( ( sdtmndt0 @ sz00 @ xp )
= xr )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,210]) ).
thf(28852,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( ( sdtmndt0 @ sz00 @ xp )
= xr ) ),
inference(pattern_uni,[status(thm)],[28851:[]]) ).
thf(61966,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17961,192]) ).
thf(61967,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ xm @ xm ) )
= ( sk1 @ xm @ xm ) ),
inference(pattern_uni,[status(thm)],[61966:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(171,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)],[169]) ).
thf(175,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)],[171]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( aNaturalNumber0 @ ( sdtsldt0 @ B @ A ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(5727,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ A @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[154,3028]) ).
thf(5802,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( A != xr )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[5727]) ).
thf(5831,plain,
( ~ ( aNaturalNumber0 @ xr )
| ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ sz00 )
!= sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[5802]) ).
thf(799,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xn @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[196,50]) ).
thf(808,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( xp != xn )
| ( xm != xm ) ),
inference(simp,[status(thm)],[799]) ).
thf(826,plain,
( ( ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( xp != xn ) ),
inference(simp,[status(thm)],[808]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(13491,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13456,85]) ).
thf(13492,plain,
sdtlseqdt0 @ ( sk1 @ xn @ xn ) @ ( sk1 @ xn @ xn ),
inference(pattern_uni,[status(thm)],[13491:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(31162,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13456,137]) ).
thf(31163,plain,
( ( sdtpldt0 @ ( sk1 @ xn @ xn ) @ sz00 )
= ( sk1 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[31162:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(14742,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14707,85]) ).
thf(14743,plain,
sdtlseqdt0 @ ( sk1 @ sz10 @ sz10 ) @ ( sk1 @ sz10 @ sz10 ),
inference(pattern_uni,[status(thm)],[14742:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(52,plain,
sz10 != sz00,
inference(cnf,[status(esa)],[51]) ).
thf(54,plain,
sz10 != sz00,
inference(lifteq,[status(thm)],[52]) ).
thf(24,axiom,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 )
& ( A != sz10 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A )
& ( isPrime0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
thf(139,plain,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 )
& ( A != sz10 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A )
& ( isPrime0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(141,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( doDivides0 @ ( sk3 @ A ) @ A ) ),
inference(cnf,[status(esa)],[139]) ).
thf(144,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( doDivides0 @ ( sk3 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(47,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(236,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(58764,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13456,191]) ).
thf(58765,plain,
( ( sdtasdt0 @ ( sk1 @ xn @ xn ) @ sz10 )
= ( sk1 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[58764:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(13530,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13456,155]) ).
thf(13531,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ xn @ xn ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[13530:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(18002,plain,
! [A: $i] :
( ( sdtlseqdt0 @ A @ A )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17961,85]) ).
thf(18003,plain,
sdtlseqdt0 @ ( sk1 @ xm @ xm ) @ ( sk1 @ xm @ xm ),
inference(pattern_uni,[status(thm)],[18002:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(31253,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20948,137]) ).
thf(31254,plain,
( ( sdtpldt0 @ ( sk1 @ xp @ xp ) @ sz00 )
= ( sk1 @ xp @ xp ) ),
inference(pattern_uni,[status(thm)],[31253:[bind(A,$thf( sk1 @ xp @ xp ))]]) ).
thf(34,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(183,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)],[34]) ).
thf(185,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)],[183]) ).
thf(187,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)],[185]) ).
thf(67710,plain,
( ( xp != xr )
| ( xn != sz00 )
| ( xm != sz10 )
| ( ( sdtasdt0 @ xp @ sz10 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[58991,60977]) ).
thf(67966,plain,
( ( xp != xr )
| ( xn != sz00 )
| ( xm != sz10 )
| ( xp != xr )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[67710]) ).
thf(68036,plain,
( ( xp != xr )
| ( xn != sz00 )
| ( xm != sz10 ) ),
inference(simp,[status(thm)],[67966]) ).
thf(3117,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz00 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1515,3046]) ).
thf(3153,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3117]) ).
thf(3160,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz00 ) ),
inference(simp,[status(thm)],[3153]) ).
thf(11,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(81,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)],[11]) ).
thf(1817,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ A @ sz00 )
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[154,1768]) ).
thf(1851,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 )
| ( A != xr )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1817]) ).
thf(1877,plain,
( ~ ( aNaturalNumber0 @ xr )
| ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= sz00 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[1851]) ).
thf(14,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(103,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,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(104,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)],[15]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( A = sz00 ) ),
inference(cnf,[status(esa)],[104]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[197]) ).
thf(32640,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20948,138]) ).
thf(32641,plain,
( ( sdtpldt0 @ sz00 @ ( sk1 @ xp @ xp ) )
= ( sk1 @ xp @ xp ) ),
inference(pattern_uni,[status(thm)],[32640:[bind(A,$thf( sk1 @ xp @ xp ))]]) ).
thf(58872,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,191]) ).
thf(58873,plain,
( ( sdtasdt0 @ xm @ sz10 )
= xm ),
inference(pattern_uni,[status(thm)],[58872:[bind(A,$thf( xm ))]]) ).
thf(3146,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz10 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1495,3046]) ).
thf(3152,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz10 )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3146]) ).
thf(3159,plain,
( ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xm != sz00 )
| ( xr != sz10 ) ),
inference(simp,[status(thm)],[3152]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(80,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtasdt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ( B = sz00 ) ),
inference(cnf,[status(esa)],[165]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ( B = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[166]) ).
thf(18040,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17961,155]) ).
thf(18041,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ xm @ xm ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[18040:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(32575,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,138]) ).
thf(32576,plain,
( ( sdtpldt0 @ sz00 @ xn )
= xn ),
inference(pattern_uni,[status(thm)],[32575:[bind(A,$thf( xn ))]]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ B @ C ) )
=> ( doDivides0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
thf(67,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ B @ C ) )
=> ( doDivides0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(68,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)],[67]) ).
thf(314,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( aNaturalNumber0 @ E )
| ~ ( aNaturalNumber0 @ F )
| ~ ( doDivides0 @ E @ F )
| ( doDivides0 @ D @ F )
| ( ( doDivides0 @ A @ C )
!= ( doDivides0 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[68,68]) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ( doDivides0 @ A @ D ) ),
inference(pattern_uni,[status(thm)],[314:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ( doDivides0 @ A @ D ) ),
inference(simp,[status(thm)],[315]) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( isPrime0 @ C )
| ~ ( doDivides0 @ C @ ( sdtasdt0 @ A @ B ) )
| ~ ( iLess0 @ ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
| ( doDivides0 @ C @ A )
| ( doDivides0 @ C @ B ) ),
inference(cnf,[status(esa)],[193]) ).
thf(142,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( isPrime0 @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(145,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( isPrime0 @ ( sk3 @ A ) ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(59,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)],[55]) ).
thf(63,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)],[59]) ).
thf(15309,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xp )
| ( ( sdtlseqdt0 @ xp @ sz00 )
!= ( sdtlseqdt0 @ sz00 @ xp ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15192]) ).
thf(15333,plain,
( ~ ( sdtlseqdt0 @ sz00 @ xp )
| ( ( sdtlseqdt0 @ xp @ sz00 )
!= ( sdtlseqdt0 @ sz00 @ xp ) ) ),
inference(simp,[status(thm)],[15309]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( A = B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( iLess0 @ A @ B ) ),
inference(cnf,[status(esa)],[148]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sdtlseqdt0 @ A @ B )
| ( iLess0 @ A @ B ) ),
inference(lifteq,[status(thm)],[149]) ).
thf(32620,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,138]) ).
thf(32621,plain,
( ( sdtpldt0 @ sz00 @ xm )
= xm ),
inference(pattern_uni,[status(thm)],[32620:[bind(A,$thf( xm ))]]) ).
thf(31194,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,137]) ).
thf(31195,plain,
( ( sdtpldt0 @ xn @ sz00 )
= xn ),
inference(pattern_uni,[status(thm)],[31194:[bind(A,$thf( xn ))]]) ).
thf(5466,plain,
( ( xn = sz00 )
| ( aNaturalNumber0 @ ( sk2 @ xn ) )
| ( isPrime0 @ xn )
| ( sdtlseqdt0 @ xr @ sz10 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[1174,180]) ).
thf(5467,plain,
( ( xn = sz00 )
| ( aNaturalNumber0 @ ( sk2 @ xn ) )
| ( isPrime0 @ xn )
| ( sdtlseqdt0 @ xr @ sz10 ) ),
inference(pattern_uni,[status(thm)],[5466:[]]) ).
thf(40975,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ xr @ sz00 )
!= ( sdtmndt0 @ sz00 @ sz00 ) )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,40587]) ).
thf(40976,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtasdt0 @ xr @ sz00 )
!= ( sdtmndt0 @ sz00 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[40975:[]]) ).
thf(28720,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( ( sdtasdt0 @ xn @ xm )
= sz00 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,8031]) ).
thf(28721,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( ( sdtasdt0 @ xn @ xm )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[28720:[]]) ).
thf(14777,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14707,155]) ).
thf(14778,plain,
( ( sdtasdt0 @ sz00 @ ( sk1 @ sz10 @ sz10 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[14777:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(61747,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ xn @ xn ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13456,192]) ).
thf(61748,plain,
( ( sdtasdt0 @ sz10 @ ( sk1 @ xn @ xn ) )
= ( sk1 @ xn @ xn ) ),
inference(pattern_uni,[status(thm)],[61747:[bind(A,$thf( sk1 @ xn @ xn ))]]) ).
thf(5471,plain,
( ( xn = sz00 )
| ( aNaturalNumber0 @ ( sk2 @ xn ) )
| ( isPrime0 @ xn )
| ( sdtlseqdt0 @ xp @ sz10 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[1174,199]) ).
thf(5472,plain,
( ( xn = sz00 )
| ( aNaturalNumber0 @ ( sk2 @ xn ) )
| ( isPrime0 @ xn )
| ( sdtlseqdt0 @ xp @ sz10 ) ),
inference(pattern_uni,[status(thm)],[5471:[]]) ).
thf(32577,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53,138]) ).
thf(32578,plain,
( ( sdtpldt0 @ sz00 @ sz10 )
= sz10 ),
inference(pattern_uni,[status(thm)],[32577:[bind(A,$thf( sz10 ))]]) ).
thf(140,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( aNaturalNumber0 @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(143,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk3 @ A ) ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(10898,plain,
( ( xn = sz00 )
| ( aNaturalNumber0 @ ( sk2 @ xn ) )
| ( isPrime0 @ xn )
| ( sdtlseqdt0 @ xn @ sz10 )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[1174,10853]) ).
thf(10899,plain,
( ( xn = sz00 )
| ( aNaturalNumber0 @ ( sk2 @ xn ) )
| ( isPrime0 @ xn )
| ( sdtlseqdt0 @ xn @ sz10 ) ),
inference(pattern_uni,[status(thm)],[10898:[]]) ).
thf(18060,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xm @ xm ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17961,154]) ).
thf(18061,plain,
( ( sdtasdt0 @ ( sk1 @ xm @ xm ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[18060:[bind(A,$thf( sk1 @ xm @ xm ))]]) ).
thf(21055,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ xp @ xp ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20948,154]) ).
thf(21056,plain,
( ( sdtasdt0 @ ( sk1 @ xp @ xp ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[21055:[bind(A,$thf( sk1 @ xp @ xp ))]]) ).
thf(31237,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,137]) ).
thf(31238,plain,
( ( sdtpldt0 @ xm @ sz00 )
= xm ),
inference(pattern_uni,[status(thm)],[31237:[bind(A,$thf( xm ))]]) ).
thf(802,plain,
( ( doDivides0 @ xp @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xn @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[196,214]) ).
thf(803,plain,
doDivides0 @ xp @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ),
inference(pattern_uni,[status(thm)],[802:[]]) ).
thf(6774,plain,
( ( doDivides0 @ xp @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ sz00 ) )
| ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ sz00 @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[6143,803]) ).
thf(6792,plain,
( ( doDivides0 @ xp @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ sz00 ) )
| ( xr != sz00 )
| ( xm != xm ) ),
inference(simp,[status(thm)],[6774]) ).
thf(6814,plain,
( ( doDivides0 @ xp @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ sz00 ) )
| ( xr != sz00 ) ),
inference(simp,[status(thm)],[6792]) ).
thf(10998,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ ( sk1 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtlseqdt0 @ sz10 @ sz10 )
!= ( sdtlseqdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10855,75]) ).
thf(10999,plain,
( ( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[10998:[bind(A,$thf( sz10 )),bind(B,$thf( sz10 ))]]) ).
thf(11011,plain,
( ( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 )
| ~ ( aNaturalNumber0 @ sz10 ) ),
inference(simp,[status(thm)],[10999]) ).
thf(23006,plain,
( ( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 )
| ~ $true ),
inference(rewrite,[status(thm)],[11011,53]) ).
thf(23007,plain,
( ( sdtpldt0 @ sz10 @ ( sk1 @ sz10 @ sz10 ) )
= sz10 ),
inference(simp,[status(thm)],[23006]) ).
thf(6757,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ sz00 @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[6143,50]) ).
thf(6779,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( xn != sz00 )
| ( xm != xm ) ),
inference(simp,[status(thm)],[6757]) ).
thf(6846,plain,
( ( ( sdtmndt0 @ sz00 @ ( sdtasdt0 @ xp @ xm ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[6779]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[157]) ).
thf(184,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)],[183]) ).
thf(186,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)],[184]) ).
thf(58910,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14707,191]) ).
thf(58911,plain,
( ( sdtasdt0 @ ( sk1 @ sz10 @ sz10 ) @ sz10 )
= ( sk1 @ sz10 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[58910:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(40780,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xr != sz10 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,3159]) ).
thf(40781,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xr != sz10 ) ),
inference(pattern_uni,[status(thm)],[40780:[]]) ).
thf(28845,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ sz00 @ xn )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,10853]) ).
thf(28846,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( sdtlseqdt0 @ sz00 @ xn ) ),
inference(pattern_uni,[status(thm)],[28845:[]]) ).
thf(28669,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ xn ) )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,13456]) ).
thf(28670,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( aNaturalNumber0 @ ( sk1 @ sz00 @ xn ) ) ),
inference(pattern_uni,[status(thm)],[28669:[]]) ).
thf(48,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(239,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)],[48]) ).
thf(79,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)],[78]) ).
thf(40748,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xr != sz00 )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,3160]) ).
thf(40749,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xr != sz00 ) ),
inference(pattern_uni,[status(thm)],[40748:[]]) ).
thf(14716,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ ( sk1 @ sz10 @ sz10 ) )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14707,154]) ).
thf(14717,plain,
( ( sdtasdt0 @ ( sk1 @ sz10 @ sz10 ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[14716:[bind(A,$thf( sk1 @ sz10 @ sz10 ))]]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ B @ A )
| ( B = sz10 )
| ( B = A ) ),
inference(cnf,[status(esa)],[86]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B = sz10 )
| ( B = A )
| ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ B @ A ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( B = sz00 ) ),
inference(cnf,[status(esa)],[104]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
!= sz00 )
| ( B = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(800,plain,
( ( ( sdtmndt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) @ ( sdtasdt0 @ xp @ xm ) )
!= ( sdtasdt0 @ xr @ xm ) )
| ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xn @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[196,50]) ).
thf(801,plain,
( ( sdtmndt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) @ ( sdtasdt0 @ xp @ xm ) )
!= ( sdtasdt0 @ xr @ xm ) ),
inference(pattern_uni,[status(thm)],[800:[]]) ).
thf(2999,plain,
( ( doDivides0 @ xp @ ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ xr @ xm ) ) )
| ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[1523,803]) ).
thf(3016,plain,
( ( doDivides0 @ xp @ ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ xr @ xm ) ) )
| ( xp != xp )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[2999]) ).
thf(3030,plain,
( ( doDivides0 @ xp @ ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ xr @ xm ) ) )
| ( xm != sz00 ) ),
inference(simp,[status(thm)],[3016]) ).
thf(31272,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[119,137]) ).
thf(31273,plain,
( ( sdtpldt0 @ sz00 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[31272:[bind(A,$thf( sz00 ))]]) ).
thf(43411,plain,
( ( xr != sz00 )
| ( xn != sz00 )
| ( xp != xp ) ),
inference(paramod_ordered,[status(thm)],[32497,252]) ).
thf(43412,plain,
( ( xr != sz00 )
| ( xn != sz00 ) ),
inference(pattern_uni,[status(thm)],[43411:[]]) ).
thf(28728,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( xp != xn )
| ( xn != xn ) ),
inference(paramod_ordered,[status(thm)],[27776,16818]) ).
thf(28729,plain,
( ( sdtlseqdt0 @ sz10 @ xn )
| ( xp != xn ) ),
inference(pattern_uni,[status(thm)],[28728:[]]) ).
thf(40633,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xp != xr )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,3157]) ).
thf(40634,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( ( sdtmndt0 @ sz00 @ sz00 )
!= sz00 )
| ( xp != xr ) ),
inference(pattern_uni,[status(thm)],[40633:[]]) ).
thf(172,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)],[169]) ).
thf(177,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)],[172]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ( ( sdtasdt0 @ A @ ( sdtsldt0 @ B @ A ) )
= B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B ) ),
inference(simp,[status(thm)],[177]) ).
thf(43387,plain,
( ( xr != sz00 )
| ( xn != sz10 )
| ( xp != xp ) ),
inference(paramod_ordered,[status(thm)],[32497,253]) ).
thf(43388,plain,
( ( xr != sz00 )
| ( xn != sz10 ) ),
inference(pattern_uni,[status(thm)],[43387:[]]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( B = sz00 )
| ( sdtlseqdt0 @ A @ B ) ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( doDivides0 @ A @ B )
| ( sdtlseqdt0 @ A @ B ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(40588,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ xm )
| ( xm != xm ) ),
inference(paramod_ordered,[status(thm)],[36787,10865]) ).
thf(40589,plain,
( ( sdtlseqdt0 @ sz10 @ xm )
| ( sdtlseqdt0 @ sz00 @ xm ) ),
inference(pattern_uni,[status(thm)],[40588:[]]) ).
thf(58804,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53,191]) ).
thf(58805,plain,
( ( sdtasdt0 @ sz10 @ sz10 )
= sz10 ),
inference(pattern_uni,[status(thm)],[58804:[bind(A,$thf( sz10 ))]]) ).
thf(91,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A = sz10 )
| ( ( sk2 @ A )
!= A )
| ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[86]) ).
thf(100,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( ( sk2 @ A )
!= A )
| ~ ( aNaturalNumber0 @ A )
| ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(34260,plain,
! [A: $i] :
( ( A = sz00 )
| ( A = sz10 )
| ( aNaturalNumber0 @ ( sk3 @ A ) )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[224,143]) ).
thf(34261,plain,
( ( xn = sz00 )
| ( xn = sz10 )
| ( aNaturalNumber0 @ ( sk3 @ xn ) ) ),
inference(pattern_uni,[status(thm)],[34260:[bind(A,$thf( xn ))]]) ).
thf(112693,plain,
$false,
inference(cvc4,[status(thm)],[69,138,101,1767,30927,32643,6808,32695,58978,31256,249,22759,58991,68045,440,5842,44299,120,247,3044,23251,20986,61779,4762,58901,174,61856,43566,32678,3046,10865,110,125,196,28815,27776,61560,13456,31289,78,1875,15878,164,179,32497,21024,84,5834,6081,216,211,39753,253,147,61,221,132,133,28747,116,24881,15360,3157,13286,117,10875,85,28700,42740,28807,102,1768,10855,1174,58798,70,192,61884,137,165,32540,5843,252,197,6143,8031,43422,224,6168,3028,16818,1953,156,16144,53,188,36787,109,28672,40902,51415,225,77,40591,193,40743,3032,212,28848,60977,6129,129,10879,61986,1874,4902,134,73,128,40711,205,5833,6812,61894,1515,28803,31197,40587,1510,148,13466,64,180,3158,40555,43358,161,28852,61967,176,191,5831,826,118,13492,31163,71,14743,54,144,49,236,31300,58765,13531,18003,31254,86,159,24671,187,68036,15192,3155,3160,6815,81,1877,103,213,66,6817,155,108,198,32641,58873,6811,3159,223,80,167,18041,162,32576,209,342,194,145,63,15333,150,32621,6826,31195,20948,50,199,5467,40976,182,28721,14707,67,14778,61748,154,5472,32578,143,10899,99,18061,21056,1126,104,31238,6814,23007,6846,158,186,139,1523,55,114,75,119,58911,10853,214,151,168,146,51,40781,183,28846,28670,210,239,1495,79,195,40749,14717,94,17961,107,126,801,3030,31273,43412,43528,28729,1500,40634,200,68,178,43388,803,83,40589,1769,58805,222,100,34261,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM490+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 17:14:05 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.90/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/0.99 % [INFO] Parsing done (154ms).
% 1.38/1.00 % [INFO] Running in sequential loop mode.
% 1.77/1.21 % [INFO] eprover registered as external prover.
% 1.77/1.21 % [INFO] cvc4 registered as external prover.
% 1.77/1.22 % [INFO] Scanning for conjecture ...
% 1.95/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.30 % [INFO] Found a conjecture and 46 axioms. Running axiom selection ...
% 2.27/1.36 % [INFO] Axiom selection finished. Selected 46 axioms (removed 0 axioms).
% 2.35/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.42 % [INFO] Problem is first-order (TPTP FOF).
% 2.59/1.43 % [INFO] Type checking passed.
% 2.59/1.43 % [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 ...
% 89.25/23.80 % External prover 'cvc4' found a proof!
% 89.25/23.80 % [INFO] Killing All external provers ...
% 89.25/23.80 % Time passed: 23282ms (effective reasoning time: 22795ms)
% 89.25/23.80 % 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)>
% 89.25/23.80 % Axioms used in derivation (46): mSortsC, mAddComm, mPrimDiv, m_MulZero, mZeroMul, mZeroAdd, mLENTr, mMonMul, mIH_03, mDivMin, mAMDistr, mLETotal, mMonAdd, mLEAsym, mAddCanc, mDivSum, mDivTrans, m_MulUnit, mDefPrime, m__1894, mSortsC_01, m__1860, m__1870, m__1951, mMulCanc, mLETran, m__1799, mDefDiff, mDivAsso, m__1837, mMonMul2, mAddAsso, mIH, mMulAsso, mDefDiv, mDefLE, mDefQuot, m__1883, mSortsB_02, m_AddZero, mSortsB, mNatSort, mMulComm, m__1924, mDivLE, mLERefl
% 89.25/23.80 % No. of inferences in proof: 627
% 89.25/23.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23282 ms resp. 22795 ms w/o parsing
% 89.44/23.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 89.44/23.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------