TSTP Solution File: NUM424+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM424+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:40:31 EDT 2023
% Result : Theorem 119.85s 32.52s
% Output : Refutation 120.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 35
% Syntax : Number of formulae : 815 ( 332 unt; 13 typ; 0 def)
% Number of atoms : 2010 (1008 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 5592 ( 738 ~; 547 |; 80 &;4178 @)
% ( 2 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 459 ( 0 ^; 448 !; 11 ?; 459 :)
% Comments :
%------------------------------------------------------------------------------
thf(aInteger0_type,type,
aInteger0: $i > $o ).
thf(aDivisorOf0_type,type,
aDivisorOf0: $i > $i > $o ).
thf(sz00_type,type,
sz00: $i ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(xq_type,type,
xq: $i ).
thf(xa_type,type,
xa: $i ).
thf(xb_type,type,
xb: $i ).
thf(sz10_type,type,
sz10: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(20,axiom,
( ( aInteger0 @ xa )
& ( aInteger0 @ xb )
& ( aInteger0 @ xq )
& ( xq != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).
thf(99,plain,
( ( aInteger0 @ xa )
& ( aInteger0 @ xb )
& ( aInteger0 @ xq )
& ( xq != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(101,plain,
aInteger0 @ xq,
inference(cnf,[status(esa)],[99]) ).
thf(1,conjecture,
( ( ? [A: $i] :
( ( aInteger0 @ A )
& ( ( sdtasdt0 @ xq @ A )
= ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
& ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
& ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq ) )
=> ( ? [A: $i] :
( ( aInteger0 @ A )
& ( ( sdtasdt0 @ xq @ A )
= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) )
| ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( sdteqdtlpzmzozddtrp0 @ xb @ xa @ xq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ? [A: $i] :
( ( aInteger0 @ A )
& ( ( sdtasdt0 @ xq @ A )
= ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
& ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
& ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq ) )
=> ( ? [A: $i] :
( ( aInteger0 @ A )
& ( ( sdtasdt0 @ xq @ A )
= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) )
| ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( sdteqdtlpzmzozddtrp0 @ xb @ xa @ xq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(24,plain,
~ ( ( ? [A: $i] :
( ( aInteger0 @ A )
& ( ( sdtasdt0 @ xq @ A )
= ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
& ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
& ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq ) )
=> ( ? [A: $i] :
( ( aInteger0 @ A )
& ( ( sdtasdt0 @ xq @ A )
= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) )
| ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( sdteqdtlpzmzozddtrp0 @ xb @ xa @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
aInteger0 @ sk1,
inference(cnf,[status(esa)],[24]) ).
thf(7,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( aInteger0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
thf(54,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( aInteger0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(55,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( aInteger0 @ ( smndt0 @ A ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(130,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,55]) ).
thf(131,plain,
aInteger0 @ ( smndt0 @ sk1 ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( sk1 ))]]) ).
thf(143,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,55]) ).
thf(144,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
thf(105,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(106,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ A @ sz10 )
= A ) ),
inference(cnf,[status(esa)],[105]) ).
thf(108,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(25915,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,108]) ).
thf(25916,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) @ sz10 )
= ( smndt0 @ ( smndt0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25915:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(14,axiom,
aInteger0 @ sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
thf(79,plain,
aInteger0 @ sz10,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
thf(34,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
& ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(37,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(233,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,37]) ).
thf(234,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ sz10 )
= ( smndt0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[233:[bind(A,$thf( sz10 ))]]) ).
thf(23,axiom,
aInteger0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
thf(113,plain,
aInteger0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(134,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ sz00 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,55]) ).
thf(135,plain,
aInteger0 @ ( smndt0 @ sz00 ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( sz00 ))]]) ).
thf(182,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ sz00 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[135,55]) ).
thf(183,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( smndt0 @ sz00 ))]]) ).
thf(263,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[183,55]) ).
thf(264,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( smndt0 @ ( smndt0 @ sz00 ) ))]]) ).
thf(389,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[264,55]) ).
thf(390,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
thf(89,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(90,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 ) ),
inference(cnf,[status(esa)],[89]) ).
thf(92,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(20204,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ sz00 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,92]) ).
thf(20205,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ sz00 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20204:[bind(A,$thf( sz00 ))]]) ).
thf(13,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
thf(74,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(76,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( A
= ( sdtpldt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(78,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(14749,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ sz00 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[135,78]) ).
thf(14750,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ sz00 ) )
= ( smndt0 @ sz00 ) ),
inference(pattern_uni,[status(thm)],[14749:[bind(A,$thf( smndt0 @ sz00 ))]]) ).
thf(21088,plain,
( ( smndt0 @ sz00 )
= sz00 ),
inference(rewrite,[status(thm)],[20205,14750]) ).
thf(21105,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[390,21088]) ).
thf(31251,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[21105,21088]) ).
thf(19,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
thf(94,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(96,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[94]) ).
thf(98,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(31338,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31251,98]) ).
thf(31339,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[31338:[bind(A,$thf( smndt0 @ ( smndt0 @ sz00 ) ))]]) ).
thf(44422,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ sz00 ) )
= sz00 ),
inference(rewrite,[status(thm)],[31339,21088]) ).
thf(20094,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,92]) ).
thf(20095,plain,
( ( sdtpldt0 @ sk1 @ ( smndt0 @ sk1 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20094:[bind(A,$thf( sk1 ))]]) ).
thf(103,plain,
aInteger0 @ xa,
inference(cnf,[status(esa)],[99]) ).
thf(107,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( A
= ( sdtasdt0 @ sz10 @ A ) ) ),
inference(cnf,[status(esa)],[105]) ).
thf(109,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(27314,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,109]) ).
thf(27315,plain,
( ( sdtasdt0 @ sz10 @ xa )
= xa ),
inference(pattern_uni,[status(thm)],[27314:[bind(A,$thf( xa ))]]) ).
thf(128,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,55]) ).
thf(129,plain,
aInteger0 @ ( smndt0 @ xq ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( xq ))]]) ).
thf(174,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,55]) ).
thf(175,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ),
inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(251,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,55]) ).
thf(252,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> ! [B: $i] :
( ( aDivisorOf0 @ B @ A )
<=> ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
thf(42,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ! [B: $i] :
( ( ( aDivisorOf0 @ B @ A )
=> ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) ) )
& ( ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) )
=> ( aDivisorOf0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,plain,
! [A: $i] :
( ( aInteger0 @ A )
=> ( ! [B: $i] :
( ( aDivisorOf0 @ B @ A )
=> ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) ) )
& ! [B: $i] :
( ( ( aInteger0 @ B )
& ( B != sz00 )
& ? [C: $i] :
( ( aInteger0 @ C )
& ( ( sdtasdt0 @ B @ C )
= A ) ) )
=> ( aDivisorOf0 @ B @ A ) ) ) ),
inference(miniscope,[status(thm)],[42]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ B @ A )
| ( B != sz00 ) ),
inference(cnf,[status(esa)],[43]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B != sz00 )
| ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(53,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ sz00 @ A ) ),
inference(simp,[status(thm)],[52]) ).
thf(4289,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[252,53]) ).
thf(4290,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ),
inference(pattern_uni,[status(thm)],[4289:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ))]]) ).
thf(36,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( smndt0 @ A )
= ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(38,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(332,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,38]) ).
thf(333,plain,
( ( sdtasdt0 @ sk1 @ ( smndt0 @ sz10 ) )
= ( smndt0 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[332:[bind(A,$thf( sk1 ))]]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) )
= ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
thf(86,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) )
= ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C )
| ( ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) )
= ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C ) ) ),
inference(cnf,[status(esa)],[86]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(136,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,55]) ).
thf(137,plain,
aInteger0 @ ( smndt0 @ xa ),
inference(pattern_uni,[status(thm)],[136:[bind(A,$thf( xa ))]]) ).
thf(186,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,55]) ).
thf(187,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(269,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,55]) ).
thf(270,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(397,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[270,55]) ).
thf(398,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ),
inference(pattern_uni,[status(thm)],[397:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ))]]) ).
thf(1548,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[398,55]) ).
thf(1549,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1548:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ))]]) ).
thf(102,plain,
aInteger0 @ xb,
inference(cnf,[status(esa)],[99]) ).
thf(75,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtpldt0 @ A @ sz00 )
= A ) ),
inference(cnf,[status(esa)],[74]) ).
thf(77,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(13908,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,77]) ).
thf(13909,plain,
( ( sdtpldt0 @ xb @ sz00 )
= xb ),
inference(pattern_uni,[status(thm)],[13908:[bind(A,$thf( xb ))]]) ).
thf(140,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,55]) ).
thf(141,plain,
aInteger0 @ ( smndt0 @ sz10 ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( sz10 ))]]) ).
thf(27,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(32,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(202,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ sz10 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[141,32]) ).
thf(203,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( smndt0 @ sz10 ))]]) ).
thf(309,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,38]) ).
thf(310,plain,
( ( sdtasdt0 @ xq @ ( smndt0 @ sz10 ) )
= ( smndt0 @ xq ) ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( xq ))]]) ).
thf(3070,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( smndt0 @ xq ) ),
inference(rewrite,[status(thm)],[203,310]) ).
thf(14330,plain,
( ( ( smndt0 @ xq )
!= xb )
| ( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ xb @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[13909,3070]) ).
thf(14374,plain,
( ( ( smndt0 @ xq )
!= xb )
| ( xb != xb )
| ( ( smndt0 @ xa )
!= sz00 ) ),
inference(simp,[status(thm)],[14330]) ).
thf(14399,plain,
( ( ( smndt0 @ xq )
!= xb )
| ( ( smndt0 @ xa )
!= sz00 ) ),
inference(simp,[status(thm)],[14374]) ).
thf(200,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ sz10 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[141,55]) ).
thf(201,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( smndt0 @ sz10 ))]]) ).
thf(4310,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,53]) ).
thf(4311,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[4310:[bind(A,$thf( smndt0 @ ( smndt0 @ sz10 ) ))]]) ).
thf(227,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,37]) ).
thf(228,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ xa )
= ( smndt0 @ xa ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( xa ))]]) ).
thf(237,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,37]) ).
thf(238,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ sk1 )
= ( smndt0 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( sk1 ))]]) ).
thf(711,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ xa ) )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ sk1 )
!= ( sdtasdt0 @ ( smndt0 @ sz10 ) @ xa ) ) ),
inference(paramod_ordered,[status(thm)],[228,238]) ).
thf(727,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ xa ) )
| ( ( smndt0 @ sz10 )
!= ( smndt0 @ sz10 ) )
| ( sk1 != xa ) ),
inference(simp,[status(thm)],[711]) ).
thf(741,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ xa ) )
| ( sk1 != xa ) ),
inference(simp,[status(thm)],[727]) ).
thf(95,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ A @ sz00 )
= sz00 ) ),
inference(cnf,[status(esa)],[94]) ).
thf(97,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(23581,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,97]) ).
thf(23582,plain,
( ( sdtasdt0 @ sz10 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23581:[bind(A,$thf( sz10 ))]]) ).
thf(26,plain,
aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ),
inference(cnf,[status(esa)],[24]) ).
thf(31,plain,
( ( sdtasdt0 @ xq @ sk1 )
= ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(33,plain,
( ( sdtpldt0 @ xa @ ( smndt0 @ xb ) )
= ( sdtasdt0 @ xq @ sk1 ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(120,plain,
aDivisorOf0 @ xq @ ( sdtasdt0 @ xq @ sk1 ),
inference(rewrite,[status(thm)],[26,33]) ).
thf(214,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( aDivisorOf0 @ xq @ ( smndt0 @ A ) )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
!= ( sdtasdt0 @ xq @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[37,120]) ).
thf(247,plain,
! [A: $i] :
( ( aDivisorOf0 @ xq @ ( smndt0 @ A ) )
| ~ ( aInteger0 @ A )
| ( ( smndt0 @ sz10 )
!= xq )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[214]) ).
thf(250,plain,
( ( aDivisorOf0 @ xq @ ( smndt0 @ sk1 ) )
| ~ ( aInteger0 @ sk1 )
| ( ( smndt0 @ sz10 )
!= xq ) ),
inference(simp,[status(thm)],[247]) ).
thf(58990,plain,
( ( aDivisorOf0 @ xq @ ( smndt0 @ sk1 ) )
| ~ $true
| ( ( smndt0 @ sz10 )
!= xq ) ),
inference(rewrite,[status(thm)],[250,25]) ).
thf(58991,plain,
( ( aDivisorOf0 @ xq @ ( smndt0 @ sk1 ) )
| ( ( smndt0 @ sz10 )
!= xq ) ),
inference(simp,[status(thm)],[58990]) ).
thf(14747,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,78]) ).
thf(14748,plain,
( ( sdtpldt0 @ sz00 @ xa )
= xa ),
inference(pattern_uni,[status(thm)],[14747:[bind(A,$thf( xa ))]]) ).
thf(14019,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[183,77]) ).
thf(14020,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) @ sz00 )
= ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[14019:[bind(A,$thf( smndt0 @ ( smndt0 @ sz00 ) ))]]) ).
thf(58583,plain,
( ( sdtpldt0 @ ( smndt0 @ sz00 ) @ sz00 )
= ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[14020,21088]) ).
thf(91,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( sz00
= ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ),
inference(cnf,[status(esa)],[89]) ).
thf(93,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ~ ( aInteger0 @ A ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(21797,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,93]) ).
thf(21798,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ xq ) ) @ ( smndt0 @ xq ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[21797:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ( aInteger0 @ ( smndt0 @ B ) )
| ( ( aInteger0 @ ( smndt0 @ A ) )
!= ( aInteger0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,55]) ).
thf(139,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( aInteger0 @ ( smndt0 @ ( smndt0 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[138:[bind(A,$thf( C )),bind(B,$thf( smndt0 @ C ))]]) ).
thf(142,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( aInteger0 @ ( smndt0 @ ( smndt0 @ A ) ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(25804,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,108]) ).
thf(25805,plain,
( ( sdtasdt0 @ xq @ sz10 )
= xq ),
inference(pattern_uni,[status(thm)],[25804:[bind(A,$thf( xq ))]]) ).
thf(31304,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31251,109]) ).
thf(31305,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
= ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[31304:[bind(A,$thf( smndt0 @ ( smndt0 @ sz00 ) ))]]) ).
thf(77187,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ sz00 ) )
= ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[31305,21088]) ).
thf(4293,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,53]) ).
thf(4294,plain,
~ ( aDivisorOf0 @ sz00 @ xq ),
inference(pattern_uni,[status(thm)],[4293:[bind(A,$thf( xq ))]]) ).
thf(132,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,55]) ).
thf(133,plain,
aInteger0 @ ( smndt0 @ xb ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( xb ))]]) ).
thf(178,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,55]) ).
thf(179,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(23437,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,97]) ).
thf(23438,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ xb ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23437:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
thf(56,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1521,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[390,55]) ).
thf(1522,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1521:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ))]]) ).
thf(2981,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1522,55]) ).
thf(2982,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2981:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ))]]) ).
thf(21094,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ),
inference(rewrite,[status(thm)],[2982,21088]) ).
thf(46955,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ),
inference(rewrite,[status(thm)],[21094,21088]) ).
thf(46966,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ ( smndt0 @ A ) ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[46955,142]) ).
thf(46967,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[46966:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ))]]) ).
thf(79374,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ),
inference(rewrite,[status(thm)],[46967,21088]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ B )
= ( smndt0 @ B ) )
| ( ( aInteger0 @ ( smndt0 @ A ) )
!= ( aInteger0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,37]) ).
thf(232,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ A ) )
= ( smndt0 @ ( smndt0 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( C )),bind(B,$thf( smndt0 @ C ))]]) ).
thf(248,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ A ) )
= ( smndt0 @ ( smndt0 @ A ) ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(55215,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ A ) )
= ( smndt0 @ ( smndt0 @ A ) ) )
| ( ( aInteger0 @ sz00 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,248]) ).
thf(55216,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ sz00 ) )
= ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[55215:[bind(A,$thf( sz00 ))]]) ).
thf(265,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[183,37]) ).
thf(266,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
= ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( smndt0 @ ( smndt0 @ sz00 ) ))]]) ).
thf(72753,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ sz00 ) )
= ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[266,21088]) ).
thf(80930,plain,
( ( smndt0 @ ( smndt0 @ sz00 ) )
= ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[55216,21088,72753]) ).
thf(80932,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ),
inference(rewrite,[status(thm)],[79374,80930]) ).
thf(82224,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[80932,80930]) ).
thf(82234,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ ( smndt0 @ A ) ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82224,142]) ).
thf(82235,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[82234:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ))]]) ).
thf(83154,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ),
inference(rewrite,[status(thm)],[82235,80930]) ).
thf(83223,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[83154,53]) ).
thf(83224,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[83223:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ))]]) ).
thf(84559,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ),
inference(rewrite,[status(thm)],[83224,80930]) ).
thf(184,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,32]) ).
thf(185,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ xa ) ) ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(13974,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ sz00 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,77]) ).
thf(13975,plain,
( ( sdtpldt0 @ sz00 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[13974:[bind(A,$thf( sz00 ))]]) ).
thf(373,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[252,55]) ).
thf(374,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ),
inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ))]]) ).
thf(4342,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[374,53]) ).
thf(4343,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4342:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ))]]) ).
thf(27243,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,109]) ).
thf(27244,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
= ( smndt0 @ ( smndt0 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[27243:[bind(A,$thf( smndt0 @ ( smndt0 @ sz10 ) ))]]) ).
thf(13969,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,77]) ).
thf(13970,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) @ sz00 )
= ( smndt0 @ ( smndt0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13969:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(287,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,37]) ).
thf(288,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
= ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( smndt0 @ ( smndt0 @ sz10 ) ))]]) ).
thf(13887,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,77]) ).
thf(13888,plain,
( ( sdtpldt0 @ sk1 @ sz00 )
= sk1 ),
inference(pattern_uni,[status(thm)],[13887:[bind(A,$thf( sk1 ))]]) ).
thf(20729,plain,
( ( sk1 = sz00 )
| ( ( sdtpldt0 @ sk1 @ ( smndt0 @ sk1 ) )
!= ( sdtpldt0 @ sk1 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[13888,20095]) ).
thf(20770,plain,
( ( sk1 = sz00 )
| ( sk1 != sk1 )
| ( ( smndt0 @ sk1 )
!= sz00 ) ),
inference(simp,[status(thm)],[20729]) ).
thf(20845,plain,
( ( sk1 = sz00 )
| ( ( smndt0 @ sk1 )
!= sz00 ) ),
inference(simp,[status(thm)],[20770]) ).
thf(257,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,55]) ).
thf(258,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(381,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[258,55]) ).
thf(382,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ))]]) ).
thf(23499,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[382,97]) ).
thf(23500,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23499:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ))]]) ).
thf(23423,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,97]) ).
thf(23424,plain,
( ( sdtasdt0 @ sk1 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23423:[bind(A,$thf( sk1 ))]]) ).
thf(25827,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,108]) ).
thf(25828,plain,
( ( sdtasdt0 @ sk1 @ sz10 )
= sk1 ),
inference(pattern_uni,[status(thm)],[25827:[bind(A,$thf( sk1 ))]]) ).
thf(26682,plain,
( ( sk1 = sz00 )
| ( ( sdtasdt0 @ sk1 @ sz10 )
!= ( sdtasdt0 @ sk1 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[23424,25828]) ).
thf(26718,plain,
( ( sk1 = sz00 )
| ( sk1 != sk1 )
| ( sz10 != sz00 ) ),
inference(simp,[status(thm)],[26682]) ).
thf(26794,plain,
( ( sk1 = sz00 )
| ( sz10 != sz00 ) ),
inference(simp,[status(thm)],[26718]) ).
thf(26364,plain,
( ( aDivisorOf0 @ xq @ xq )
| ( ( sdtasdt0 @ xq @ sk1 )
!= ( sdtasdt0 @ xq @ sz10 ) ) ),
inference(paramod_ordered,[status(thm)],[25805,120]) ).
thf(26553,plain,
( ( aDivisorOf0 @ xq @ xq )
| ( xq != xq )
| ( sk1 != sz10 ) ),
inference(simp,[status(thm)],[26364]) ).
thf(26572,plain,
( ( aDivisorOf0 @ xq @ xq )
| ( sk1 != sz10 ) ),
inference(simp,[status(thm)],[26553]) ).
thf(36934,plain,
( ( sz10 != sz00 )
| ( aDivisorOf0 @ xq @ xq )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26794,26572]) ).
thf(36935,plain,
( ( sz10 != sz00 )
| ( aDivisorOf0 @ xq @ xq ) ),
inference(pattern_uni,[status(thm)],[36934:[]]) ).
thf(20208,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,92]) ).
thf(20209,plain,
( ( sdtpldt0 @ xa @ ( smndt0 @ xa ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20208:[bind(A,$thf( xa ))]]) ).
thf(4370,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,53]) ).
thf(4371,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4370:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(21895,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,93]) ).
thf(21896,plain,
( ( sdtpldt0 @ ( smndt0 @ sz10 ) @ sz10 )
= sz00 ),
inference(pattern_uni,[status(thm)],[21895:[bind(A,$thf( sz10 ))]]) ).
thf(21786,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ sz10 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[141,93]) ).
thf(21787,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) @ ( smndt0 @ sz10 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[21786:[bind(A,$thf( smndt0 @ sz10 ))]]) ).
thf(14680,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,78]) ).
thf(14681,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ xa ) )
= ( smndt0 @ xa ) ),
inference(pattern_uni,[status(thm)],[14680:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(17907,plain,
( ( ( smndt0 @ xa )
!= ( smndt0 @ xq ) )
| ( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ sz00 @ ( smndt0 @ xa ) ) ) ),
inference(paramod_ordered,[status(thm)],[14681,3070]) ).
thf(17951,plain,
( ( xa != xq )
| ( xb != sz00 )
| ( ( smndt0 @ xa )
!= ( smndt0 @ xa ) ) ),
inference(simp,[status(thm)],[17907]) ).
thf(18015,plain,
( ( xa != xq )
| ( xb != sz00 ) ),
inference(simp,[status(thm)],[17951]) ).
thf(20077,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,92]) ).
thf(20078,plain,
( ( sdtpldt0 @ xq @ ( smndt0 @ xq ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20077:[bind(A,$thf( xq ))]]) ).
thf(20125,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,92]) ).
thf(20126,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xb ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20125:[bind(A,$thf( xb ))]]) ).
thf(155,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ sz00 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,32]) ).
thf(156,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ sz00 ) ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( sz00 ))]]) ).
thf(23404,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,97]) ).
thf(23405,plain,
( ( sdtasdt0 @ xq @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23404:[bind(A,$thf( xq ))]]) ).
thf(23693,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= sz00 ),
inference(rewrite,[status(thm)],[156,23405]) ).
thf(31499,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xb ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ),
inference(paramod_ordered,[status(thm)],[20126,23693]) ).
thf(31541,plain,
( ( xb != xb )
| ( ( smndt0 @ xb )
!= ( smndt0 @ xa ) ) ),
inference(simp,[status(thm)],[31499]) ).
thf(31560,plain,
( ( smndt0 @ xb )
!= ( smndt0 @ xa ) ),
inference(simp,[status(thm)],[31541]) ).
thf(3045,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1549,55]) ).
thf(3046,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3045:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) ))]]) ).
thf(27223,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,109]) ).
thf(27224,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ ( smndt0 @ xb ) ) )
= ( smndt0 @ ( smndt0 @ xb ) ) ),
inference(pattern_uni,[status(thm)],[27223:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( B != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModRef) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( B != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,plain,
~ ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(123,plain,
( ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
!= ( aDivisorOf0 @ xq @ ( sdtasdt0 @ xq @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[120,28]) ).
thf(124,plain,
( ( xq != xq )
| ( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ sk1 ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ sk1 ) ),
inference(simp,[status(thm)],[124]) ).
thf(24679,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[382,98]) ).
thf(24680,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24679:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ))]]) ).
thf(83217,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[83154,97]) ).
thf(83218,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[83217:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ))]]) ).
thf(86048,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) @ sz00 )
= sz00 ),
inference(rewrite,[status(thm)],[83218,80930]) ).
thf(21714,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,93]) ).
thf(21715,plain,
( ( sdtpldt0 @ ( smndt0 @ xq ) @ xq )
= sz00 ),
inference(pattern_uni,[status(thm)],[21714:[bind(A,$thf( xq ))]]) ).
thf(31634,plain,
( ( sdtpldt0 @ ( smndt0 @ xq ) @ xq )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ),
inference(paramod_ordered,[status(thm)],[21715,23693]) ).
thf(31733,plain,
( ( ( smndt0 @ xq )
!= xb )
| ( ( smndt0 @ xa )
!= xq ) ),
inference(simp,[status(thm)],[31634]) ).
thf(14798,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,78]) ).
thf(14799,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ sk1 ) )
= ( smndt0 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14798:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(20704,plain,
( ( ( smndt0 @ sk1 )
= sz00 )
| ( ( sdtpldt0 @ sk1 @ ( smndt0 @ sk1 ) )
!= ( sdtpldt0 @ sz00 @ ( smndt0 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14799,20095]) ).
thf(20781,plain,
( ( ( smndt0 @ sk1 )
= sz00 )
| ( sk1 != sz00 )
| ( ( smndt0 @ sk1 )
!= ( smndt0 @ sk1 ) ) ),
inference(simp,[status(thm)],[20704]) ).
thf(20847,plain,
( ( ( smndt0 @ sk1 )
= sz00 )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[20781]) ).
thf(27133,plain,
( ( sz10 != sz00 )
| ( ( smndt0 @ sk1 )
= sz00 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26794,20847]) ).
thf(27134,plain,
( ( sz10 != sz00 )
| ( ( smndt0 @ sk1 )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[27133:[]]) ).
thf(4352,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,53]) ).
thf(4353,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[4352:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(14023,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,77]) ).
thf(14024,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= sz10 ),
inference(pattern_uni,[status(thm)],[14023:[bind(A,$thf( sz10 ))]]) ).
thf(21097,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[264,21088]) ).
thf(22055,plain,
aInteger0 @ ( smndt0 @ sz00 ),
inference(rewrite,[status(thm)],[21097,21088]) ).
thf(4316,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ sz10 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[141,53]) ).
thf(4317,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[4316:[bind(A,$thf( smndt0 @ sz10 ))]]) ).
thf(324,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,38]) ).
thf(325,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ sz10 ) )
= ( smndt0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( sz10 ))]]) ).
thf(151,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,32]) ).
thf(152,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ xb ) ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( xb ))]]) ).
thf(13916,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,77]) ).
thf(13917,plain,
( ( sdtpldt0 @ ( smndt0 @ xa ) @ sz00 )
= ( smndt0 @ xa ) ),
inference(pattern_uni,[status(thm)],[13916:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(31445,plain,
( ( ( smndt0 @ xa )
!= sz00 )
| ( ( sdtpldt0 @ ( smndt0 @ xa ) @ sz00 )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) ),
inference(paramod_ordered,[status(thm)],[13917,23693]) ).
thf(31532,plain,
( ( ( smndt0 @ xa )
!= sz00 )
| ( ( smndt0 @ xa )
!= xb )
| ( ( smndt0 @ xa )
!= sz00 ) ),
inference(simp,[status(thm)],[31445]) ).
thf(31556,plain,
( ( ( smndt0 @ xa )
!= sz00 )
| ( ( smndt0 @ xa )
!= xb ) ),
inference(simp,[status(thm)],[31532]) ).
thf(24608,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,98]) ).
thf(24609,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ xb ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24608:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(13894,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,77]) ).
thf(13895,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ xb ) ) @ sz00 )
= ( smndt0 @ ( smndt0 @ xb ) ) ),
inference(pattern_uni,[status(thm)],[13894:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(29,plain,
~ ( sdteqdtlpzmzozddtrp0 @ xb @ xa @ xq ),
inference(cnf,[status(esa)],[24]) ).
thf(215,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,37]) ).
thf(216,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ xb )
= ( smndt0 @ xb ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( xb ))]]) ).
thf(24662,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[398,98]) ).
thf(24663,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24662:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ))]]) ).
thf(25919,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,108]) ).
thf(25920,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ xa ) ) @ sz10 )
= ( smndt0 @ ( smndt0 @ xa ) ) ),
inference(pattern_uni,[status(thm)],[25919:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(145,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,55]) ).
thf(146,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(204,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[146,55]) ).
thf(205,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ))]]) ).
thf(210,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,32]) ).
thf(211,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ))]]) ).
thf(163,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,32]) ).
thf(164,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(25857,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,108]) ).
thf(25858,plain,
( ( sdtasdt0 @ xb @ sz10 )
= xb ),
inference(pattern_uni,[status(thm)],[25857:[bind(A,$thf( xb ))]]) ).
thf(27205,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,109]) ).
thf(27206,plain,
( ( sdtasdt0 @ sz10 @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[27205:[bind(A,$thf( sk1 ))]]) ).
thf(28352,plain,
( ( aDivisorOf0 @ xq @ sk1 )
| ( ( sdtasdt0 @ sz10 @ sk1 )
!= ( sdtasdt0 @ xq @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[27206,120]) ).
thf(28549,plain,
( ( aDivisorOf0 @ xq @ sk1 )
| ( sz10 != xq )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[28352]) ).
thf(28599,plain,
( ( aDivisorOf0 @ xq @ sk1 )
| ( sz10 != xq ) ),
inference(simp,[status(thm)],[28549]) ).
thf(4328,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[382,53]) ).
thf(4329,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4328:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ))]]) ).
thf(14696,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ sz10 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[141,78]) ).
thf(14697,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ sz10 ) )
= ( smndt0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[14696:[bind(A,$thf( smndt0 @ sz10 ))]]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 ) )
=> ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
<=> ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
thf(61,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C )
& ( C != sz00 ) )
=> ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
=> ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) )
& ( ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) )
=> ( sdteqdtlpzmzozddtrp0 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24620,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[270,98]) ).
thf(24621,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24620:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ))]]) ).
thf(14653,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,78]) ).
thf(14654,plain,
( ( sdtpldt0 @ sz00 @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[14653:[bind(A,$thf( sk1 ))]]) ).
thf(15138,plain,
( ( sk1 = sz10 )
| ( ( sdtpldt0 @ sz10 @ sz00 )
!= ( sdtpldt0 @ sz00 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[14654,14024]) ).
thf(15211,plain,
( ( sk1 = sz10 )
| ( sz10 != sz00 )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[15138]) ).
thf(58986,plain,
( ( sz10 != sz00 )
| ( sk1 = sz10 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26794,15211]) ).
thf(58987,plain,
( ( sz10 != sz00 )
| ( sk1 = sz10 ) ),
inference(pattern_uni,[status(thm)],[58986:[]]) ).
thf(291,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,55]) ).
thf(292,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( smndt0 @ ( smndt0 @ sz10 ) ))]]) ).
thf(4306,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[292,53]) ).
thf(4307,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ),
inference(pattern_uni,[status(thm)],[4306:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ))]]) ).
thf(30,plain,
sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq,
inference(cnf,[status(esa)],[24]) ).
thf(114,plain,
( ( sdteqdtlpzmzozddtrp0 @ xb @ xa @ xq )
!= ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq ) ),
inference(paramod_ordered,[status(thm)],[30,29]) ).
thf(115,plain,
( ( xb != xa )
| ( xb != xa )
| ( xq != xq ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
xb != xa,
inference(simp,[status(thm)],[115]) ).
thf(23509,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ sz00 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,97]) ).
thf(23510,plain,
( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23509:[bind(A,$thf( sz00 ))]]) ).
thf(23523,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[374,97]) ).
thf(23524,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23523:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ))]]) ).
thf(14660,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,78]) ).
thf(14661,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ ( smndt0 @ xb ) ) )
= ( smndt0 @ ( smndt0 @ xb ) ) ),
inference(pattern_uni,[status(thm)],[14660:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(82328,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82224,98]) ).
thf(82329,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[82328:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ))]]) ).
thf(84030,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
= sz00 ),
inference(rewrite,[status(thm)],[82329,80930]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C )
| ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) )
= ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C ) )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(4322,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[398,53]) ).
thf(4323,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4322:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ))]]) ).
thf(20269,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,92]) ).
thf(20270,plain,
( ( sdtpldt0 @ sz10 @ ( smndt0 @ sz10 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20269:[bind(A,$thf( sz10 ))]]) ).
thf(31476,plain,
( ( sdtpldt0 @ sz10 @ ( smndt0 @ sz10 ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ),
inference(paramod_ordered,[status(thm)],[20270,23693]) ).
thf(31547,plain,
( ( sz10 != xb )
| ( ( smndt0 @ sz10 )
!= ( smndt0 @ xa ) ) ),
inference(simp,[status(thm)],[31476]) ).
thf(83974,plain,
( ( sz10 != xb )
| ( sz10 != xa ) ),
inference(simp,[status(thm)],[31547]) ).
thf(219,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,37]) ).
thf(220,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ xq ) )
= ( smndt0 @ ( smndt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[219:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( ( sdtasdt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ( B = sz00 ) ),
inference(cnf,[status(esa)],[83]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
!= sz00 )
| ( A = sz00 )
| ( B = sz00 )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(21746,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,93]) ).
thf(21747,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ xb ) ) @ ( smndt0 @ xb ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[21746:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(31432,plain,
( ( sdtpldt0 @ sk1 @ ( smndt0 @ sk1 ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ),
inference(paramod_ordered,[status(thm)],[20095,23693]) ).
thf(31529,plain,
( ( sk1 != xb )
| ( ( smndt0 @ sk1 )
!= ( smndt0 @ xa ) ) ),
inference(simp,[status(thm)],[31432]) ).
thf(27247,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,109]) ).
thf(27248,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ xa ) )
= ( smndt0 @ xa ) ),
inference(pattern_uni,[status(thm)],[27247:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(259,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,37]) ).
thf(260,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ xb ) ) )
= ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(21120,plain,
( ( ( smndt0 @ xq )
!= xb )
| ( ( smndt0 @ xa )
!= ( smndt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[21088,14399]) ).
thf(21579,plain,
( ( ( smndt0 @ xq )
!= xb )
| ( xa != sz00 ) ),
inference(simp,[status(thm)],[21120]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B )
& ( aInteger0 @ C ) )
=> ( ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C )
| ( ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(25999,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,108]) ).
thf(26000,plain,
( ( sdtasdt0 @ sz10 @ sz10 )
= sz10 ),
inference(pattern_uni,[status(thm)],[25999:[bind(A,$thf( sz10 ))]]) ).
thf(31300,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31251,97]) ).
thf(31301,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[31300:[bind(A,$thf( smndt0 @ ( smndt0 @ sz00 ) ))]]) ).
thf(43945,plain,
( ( sdtasdt0 @ ( smndt0 @ sz00 ) @ sz00 )
= sz00 ),
inference(rewrite,[status(thm)],[31301,21088]) ).
thf(23513,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,97]) ).
thf(23514,plain,
( ( sdtasdt0 @ xa @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23513:[bind(A,$thf( xa ))]]) ).
thf(24606,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,98]) ).
thf(24607,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ xb ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24606:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C )
| ( C = sz00 )
| ~ ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) )
| ( sdteqdtlpzmzozddtrp0 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[61]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( C = sz00 )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C )
| ~ ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) )
| ( sdteqdtlpzmzozddtrp0 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(24683,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,98]) ).
thf(24684,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24683:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(25843,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,108]) ).
thf(25844,plain,
( ( sdtasdt0 @ ( smndt0 @ xb ) @ sz10 )
= ( smndt0 @ xb ) ),
inference(pattern_uni,[status(thm)],[25843:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(412,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[292,55]) ).
thf(413,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ),
inference(pattern_uni,[status(thm)],[412:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ))]]) ).
thf(4326,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[413,53]) ).
thf(4327,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4326:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ))]]) ).
thf(25887,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,108]) ).
thf(25888,plain,
( ( sdtasdt0 @ ( smndt0 @ xq ) @ sz10 )
= ( smndt0 @ xq ) ),
inference(pattern_uni,[status(thm)],[25887:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(223,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,37]) ).
thf(224,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
= ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(14642,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,78]) ).
thf(14643,plain,
( ( sdtpldt0 @ sz00 @ xq )
= xq ),
inference(pattern_uni,[status(thm)],[14642:[bind(A,$thf( xq ))]]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ( ( smndt0 @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ~ ( aInteger0 @ B )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
!= ( sdtasdt0 @ xq @ B ) ) ),
inference(paramod_ordered,[status(thm)],[37,32]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ( ( smndt0 @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ~ ( aInteger0 @ B )
| ( ( smndt0 @ sz10 )
!= xq )
| ( A != B ) ),
inference(simp,[status(thm)],[243]) ).
thf(249,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( smndt0 @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ~ ( aInteger0 @ A )
| ( ( smndt0 @ sz10 )
!= xq ) ),
inference(simp,[status(thm)],[246]) ).
thf(56839,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( smndt0 @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( smndt0 @ sz10 )
!= xq ) ),
inference(simp,[status(thm)],[249]) ).
thf(82283,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82224,97]) ).
thf(82284,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[82283:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ))]]) ).
thf(83409,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) @ sz00 )
= sz00 ),
inference(rewrite,[status(thm)],[82284,80930]) ).
thf(23479,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,97]) ).
thf(23480,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23479:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ))]]) ).
thf(14674,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,78]) ).
thf(14675,plain,
( ( sdtpldt0 @ sz00 @ xb )
= xb ),
inference(pattern_uni,[status(thm)],[14674:[bind(A,$thf( xb ))]]) ).
thf(31477,plain,
( ( xb != sz00 )
| ( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ sz00 @ xb ) ) ),
inference(paramod_ordered,[status(thm)],[14675,23693]) ).
thf(31533,plain,
( ( xb != sz00 )
| ( xb != sz00 )
| ( ( smndt0 @ xa )
!= xb ) ),
inference(simp,[status(thm)],[31477]) ).
thf(31557,plain,
( ( xb != sz00 )
| ( ( smndt0 @ xa )
!= xb ) ),
inference(simp,[status(thm)],[31533]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ xq @ B )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ A ) )
!= ( aInteger0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,32]) ).
thf(160,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ xq @ ( smndt0 @ A ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( C )),bind(B,$thf( smndt0 @ C ))]]) ).
thf(169,plain,
! [A: $i] :
( ~ ( aInteger0 @ A )
| ( ( sdtasdt0 @ xq @ ( smndt0 @ A ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(23481,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[398,97]) ).
thf(23482,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23481:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ))]]) ).
thf(23702,plain,
( ( aDivisorOf0 @ xq @ sz00 )
| ( ( sdtasdt0 @ xq @ sk1 )
!= ( sdtasdt0 @ xq @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[23405,120]) ).
thf(23823,plain,
( ( aDivisorOf0 @ xq @ sz00 )
| ( xq != xq )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[23702]) ).
thf(23850,plain,
( ( aDivisorOf0 @ xq @ sz00 )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[23823]) ).
thf(35442,plain,
( ( sz10 != sz00 )
| ( aDivisorOf0 @ xq @ sz00 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26794,23850]) ).
thf(35443,plain,
( ( sz10 != sz00 )
| ( aDivisorOf0 @ xq @ sz00 ) ),
inference(pattern_uni,[status(thm)],[35442:[]]) ).
thf(22109,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ sz00 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22055,32]) ).
thf(22110,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[22109:[bind(A,$thf( smndt0 @ sz00 ))]]) ).
thf(64547,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ sz00 ) ),
inference(rewrite,[status(thm)],[22110,21088]) ).
thf(4300,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,53]) ).
thf(4301,plain,
~ ( aDivisorOf0 @ sz00 @ sk1 ),
inference(pattern_uni,[status(thm)],[4300:[bind(A,$thf( sk1 ))]]) ).
thf(338,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,38]) ).
thf(339,plain,
( ( sdtasdt0 @ ( smndt0 @ xb ) @ ( smndt0 @ sz10 ) )
= ( smndt0 @ ( smndt0 @ xb ) ) ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(4314,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,53]) ).
thf(4315,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ xa ) ),
inference(pattern_uni,[status(thm)],[4314:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(24577,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,98]) ).
thf(24578,plain,
( ( sdtasdt0 @ sz00 @ xq )
= sz00 ),
inference(pattern_uni,[status(thm)],[24577:[bind(A,$thf( xq ))]]) ).
thf(1583,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[413,55]) ).
thf(1584,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1583:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ))]]) ).
thf(255,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,32]) ).
thf(256,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ ( smndt0 @ xq ) ) ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(4332,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,53]) ).
thf(4333,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ xa ) ) ),
inference(pattern_uni,[status(thm)],[4332:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(24693,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,98]) ).
thf(24694,plain,
( ( sdtasdt0 @ sz00 @ xa )
= sz00 ),
inference(pattern_uni,[status(thm)],[24693:[bind(A,$thf( xa ))]]) ).
thf(27239,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,109]) ).
thf(27240,plain,
( ( sdtasdt0 @ sz10 @ xb )
= xb ),
inference(pattern_uni,[status(thm)],[27239:[bind(A,$thf( xb ))]]) ).
thf(23475,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,97]) ).
thf(23476,plain,
( ( sdtasdt0 @ ( smndt0 @ xq ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23475:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(172,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,32]) ).
thf(173,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(23573,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[146,97]) ).
thf(23574,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23573:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( aInteger0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntegers) ).
thf(41,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24592,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,98]) ).
thf(24593,plain,
( ( sdtasdt0 @ sz00 @ sk1 )
= sz00 ),
inference(pattern_uni,[status(thm)],[24592:[bind(A,$thf( sk1 ))]]) ).
thf(13931,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ sz10 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[141,77]) ).
thf(13932,plain,
( ( sdtpldt0 @ ( smndt0 @ sz10 ) @ sz00 )
= ( smndt0 @ sz10 ) ),
inference(pattern_uni,[status(thm)],[13931:[bind(A,$thf( smndt0 @ sz10 ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(342,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,38]) ).
thf(343,plain,
( ( sdtasdt0 @ xb @ ( smndt0 @ sz10 ) )
= ( smndt0 @ xb ) ),
inference(pattern_uni,[status(thm)],[342:[bind(A,$thf( xb ))]]) ).
thf(31789,plain,
( ( sk1 != xa )
| ( ( smndt0 @ sk1 )
!= ( smndt0 @ xb ) ) ),
inference(paramod_ordered,[status(thm)],[741,31560]) ).
thf(31814,plain,
( ( sk1 != xa )
| ( sk1 != xb ) ),
inference(simp,[status(thm)],[31789]) ).
thf(23507,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,97]) ).
thf(23508,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ xa ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23507:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(31437,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ xq @ ( smndt0 @ xq ) ) ),
inference(paramod_ordered,[status(thm)],[20078,23693]) ).
thf(31528,plain,
( ( xb != xq )
| ( ( smndt0 @ xa )
!= ( smndt0 @ xq ) ) ),
inference(simp,[status(thm)],[31437]) ).
thf(1494,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[382,55]) ).
thf(1495,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1494:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ))]]) ).
thf(2914,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1495,55]) ).
thf(2915,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2914:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) ))]]) ).
thf(25963,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,108]) ).
thf(25964,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ xq ) ) @ sz10 )
= ( smndt0 @ ( smndt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[25963:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(82463,plain,
( ( xb != xq )
| ( xa != xq ) ),
inference(simp,[status(thm)],[31528]) ).
thf(13880,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,77]) ).
thf(13881,plain,
( ( sdtpldt0 @ xq @ sz00 )
= xq ),
inference(pattern_uni,[status(thm)],[13880:[bind(A,$thf( xq ))]]) ).
thf(161,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,32]) ).
thf(162,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ sz10 ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( sz10 ))]]) ).
thf(26355,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= xq ),
inference(rewrite,[status(thm)],[162,25805]) ).
thf(32617,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ xq @ sz00 ) ),
inference(paramod_ordered,[status(thm)],[13881,26355]) ).
thf(32649,plain,
( ( xb != xq )
| ( ( smndt0 @ xa )
!= sz00 ) ),
inference(simp,[status(thm)],[32617]) ).
thf(42287,plain,
( ( xb != xq )
| ( ( smndt0 @ xa )
!= ( smndt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[21088,32649]) ).
thf(42289,plain,
( ( xb != xq )
| ( xa != sz00 ) ),
inference(simp,[status(thm)],[42287]) ).
thf(21766,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,93]) ).
thf(21767,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ xa ) ) @ ( smndt0 @ xa ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[21766:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(47704,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ xa ) ) @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) ),
inference(paramod_ordered,[status(thm)],[21767,23693]) ).
thf(47845,plain,
( ( ( smndt0 @ ( smndt0 @ xa ) )
!= xb )
| ( ( smndt0 @ xa )
!= ( smndt0 @ xa ) ) ),
inference(simp,[status(thm)],[47704]) ).
thf(47931,plain,
( ( smndt0 @ ( smndt0 @ xa ) )
!= xb ),
inference(simp,[status(thm)],[47845]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ B @ A )
| ( aInteger0 @ B ) ),
inference(cnf,[status(esa)],[43]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C )
| ( C = sz00 )
| ~ ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
| ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( C = sz00 )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C )
| ~ ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
| ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(31435,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ sz00 @ sz00 ) ),
inference(paramod_ordered,[status(thm)],[13975,23693]) ).
thf(31515,plain,
( ( xb != sz00 )
| ( ( smndt0 @ xa )
!= sz00 ) ),
inference(simp,[status(thm)],[31435]) ).
thf(35054,plain,
( ( xb != sz00 )
| ( ( smndt0 @ xa )
!= ( smndt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[21088,31515]) ).
thf(35058,plain,
( ( xb != sz00 )
| ( xa != sz00 ) ),
inference(simp,[status(thm)],[35054]) ).
thf(27184,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,109]) ).
thf(27185,plain,
( ( sdtasdt0 @ sz10 @ xq )
= xq ),
inference(pattern_uni,[status(thm)],[27184:[bind(A,$thf( xq ))]]) ).
thf(14775,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,78]) ).
thf(14776,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ ( smndt0 @ xq ) ) )
= ( smndt0 @ ( smndt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[14775:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(85188,plain,
( ( ( smndt0 @ xa )
!= xb )
| ( ( smndt0 @ xa )
!= ( smndt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[21088,31556]) ).
thf(85194,plain,
( ( ( smndt0 @ xa )
!= xb )
| ( xa != sz00 ) ),
inference(simp,[status(thm)],[85188]) ).
thf(13906,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,77]) ).
thf(13907,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) @ sz00 )
= ( smndt0 @ ( smndt0 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[13906:[bind(A,$thf( smndt0 @ ( smndt0 @ sz10 ) ))]]) ).
thf(147,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,32]) ).
thf(148,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ xq ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( xq ))]]) ).
thf(27398,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,109]) ).
thf(27399,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ sk1 ) )
= ( smndt0 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[27398:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(24687,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,98]) ).
thf(24688,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ xa ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24687:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(20277,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,92]) ).
thf(20278,plain,
( ( sdtpldt0 @ ( smndt0 @ sk1 ) @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20277:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(23497,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[413,97]) ).
thf(23498,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23497:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ))]]) ).
thf(23503,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,97]) ).
thf(23504,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23503:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C )
| ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) )
= ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(13972,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,77]) ).
thf(13973,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ xa ) ) @ sz00 )
= ( smndt0 @ ( smndt0 @ xa ) ) ),
inference(pattern_uni,[status(thm)],[13972:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(1466,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[374,55]) ).
thf(1467,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1466:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ))]]) ).
thf(4340,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1467,53]) ).
thf(4341,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4340:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) ))]]) ).
thf(14294,plain,
( ~ ( aDivisorOf0 @ xq @ xb )
| ( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ xb @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[13909,28]) ).
thf(14366,plain,
( ~ ( aDivisorOf0 @ xq @ xb )
| ( xb != xb )
| ( ( smndt0 @ xa )
!= sz00 ) ),
inference(simp,[status(thm)],[14294]) ).
thf(14393,plain,
( ~ ( aDivisorOf0 @ xq @ xb )
| ( ( smndt0 @ xa )
!= sz00 ) ),
inference(simp,[status(thm)],[14366]) ).
thf(21335,plain,
( ~ ( aDivisorOf0 @ xq @ xb )
| ( ( smndt0 @ xa )
!= ( smndt0 @ sz00 ) ) ),
inference(paramod_ordered,[status(thm)],[21088,14393]) ).
thf(21428,plain,
( ~ ( aDivisorOf0 @ xq @ xb )
| ( xa != sz00 ) ),
inference(simp,[status(thm)],[21335]) ).
thf(27352,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,109]) ).
thf(27353,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ ( smndt0 @ xq ) ) )
= ( smndt0 @ ( smndt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[27352:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(31340,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31251,108]) ).
thf(31341,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) @ sz10 )
= ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[31340:[bind(A,$thf( smndt0 @ ( smndt0 @ sz00 ) ))]]) ).
thf(78459,plain,
( ( sdtasdt0 @ ( smndt0 @ sz00 ) @ sz10 )
= ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[31341,21088]) ).
thf(4308,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[270,53]) ).
thf(4309,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ),
inference(pattern_uni,[status(thm)],[4308:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ))]]) ).
thf(312,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,38]) ).
thf(313,plain,
( ( sdtasdt0 @ ( smndt0 @ xq ) @ ( smndt0 @ sz10 ) )
= ( smndt0 @ ( smndt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(235,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,37]) ).
thf(236,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ sk1 ) )
= ( smndt0 @ ( smndt0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[235:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(23457,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,97]) ).
thf(23458,plain,
( ( sdtasdt0 @ ( smndt0 @ xa ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23457:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(4336,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,53]) ).
thf(4337,plain,
~ ( aDivisorOf0 @ sz00 @ xa ),
inference(pattern_uni,[status(thm)],[4336:[bind(A,$thf( xa ))]]) ).
thf(273,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,32]) ).
thf(274,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ ( smndt0 @ xa ) ) ) ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(4304,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,53]) ).
thf(4305,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ xb ) ),
inference(pattern_uni,[status(thm)],[4304:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(25865,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,108]) ).
thf(25866,plain,
( ( sdtasdt0 @ ( smndt0 @ xa ) @ sz10 )
= ( smndt0 @ xa ) ),
inference(pattern_uni,[status(thm)],[25865:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27302,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,109]) ).
thf(27303,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
= ( smndt0 @ ( smndt0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[27302:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(4368,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,53]) ).
thf(4369,plain,
~ ( aDivisorOf0 @ sz00 @ sz10 ),
inference(pattern_uni,[status(thm)],[4368:[bind(A,$thf( sz10 ))]]) ).
thf(244,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[146,37]) ).
thf(245,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) )
= ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[244:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ))]]) ).
thf(32565,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ sz00 @ xq ) ),
inference(paramod_ordered,[status(thm)],[14643,26355]) ).
thf(32629,plain,
( ( xb != sz00 )
| ( ( smndt0 @ xa )
!= xq ) ),
inference(simp,[status(thm)],[32565]) ).
thf(24741,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[258,98]) ).
thf(24742,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24741:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ))]]) ).
thf(15207,plain,
( ( sk1 = xb )
| ( ( sdtpldt0 @ xb @ sz00 )
!= ( sdtpldt0 @ sz00 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[14654,13909]) ).
thf(15212,plain,
( ( sk1 = xb )
| ( xb != sz00 )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[15207]) ).
thf(23583,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,97]) ).
thf(23584,plain,
( ( sdtasdt0 @ ( smndt0 @ sk1 ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23583:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(14705,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,78]) ).
thf(14706,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ xq ) )
= ( smndt0 @ xq ) ),
inference(pattern_uni,[status(thm)],[14705:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(212,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ xq )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,37]) ).
thf(213,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ xq )
= ( smndt0 @ xq ) ),
inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( xq ))]]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(239,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,37]) ).
thf(240,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ xb ) )
= ( smndt0 @ ( smndt0 @ xb ) ) ),
inference(pattern_uni,[status(thm)],[239:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(4295,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1549,53]) ).
thf(4296,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4295:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ) ))]]) ).
thf(23447,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[270,97]) ).
thf(23448,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23447:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ))]]) ).
thf(21836,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,93]) ).
thf(21837,plain,
( ( sdtpldt0 @ ( smndt0 @ xa ) @ xa )
= sz00 ),
inference(pattern_uni,[status(thm)],[21836:[bind(A,$thf( xa ))]]) ).
thf(344,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,38]) ).
thf(345,plain,
( ( sdtasdt0 @ ( smndt0 @ xa ) @ ( smndt0 @ sz10 ) )
= ( smndt0 @ ( smndt0 @ xa ) ) ),
inference(pattern_uni,[status(thm)],[344:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(24638,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[252,98]) ).
thf(24639,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24638:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ))]]) ).
thf(22085,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ sz00 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22055,38]) ).
thf(22086,plain,
( ( sdtasdt0 @ ( smndt0 @ sz00 ) @ ( smndt0 @ sz10 ) )
= ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[22085:[bind(A,$thf( smndt0 @ sz00 ))]]) ).
thf(62861,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ sz10 ) )
= ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[22086,21088]) ).
thf(80935,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[46955,80930]) ).
thf(82021,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[80935,80930]) ).
thf(24624,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,98]) ).
thf(24625,plain,
( ( sdtasdt0 @ sz00 @ xb )
= sz00 ),
inference(pattern_uni,[status(thm)],[24624:[bind(A,$thf( xb ))]]) ).
thf(13976,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,77]) ).
thf(13977,plain,
( ( sdtpldt0 @ xa @ sz00 )
= xa ),
inference(pattern_uni,[status(thm)],[13976:[bind(A,$thf( xa ))]]) ).
thf(15205,plain,
( ( sk1 = xa )
| ( ( sdtpldt0 @ xa @ sz00 )
!= ( sdtpldt0 @ sz00 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[14654,13977]) ).
thf(15216,plain,
( ( sk1 = xa )
| ( xa != sz00 )
| ( sk1 != sz00 ) ),
inference(simp,[status(thm)],[15205]) ).
thf(25841,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,108]) ).
thf(25842,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ xb ) ) @ sz10 )
= ( smndt0 @ ( smndt0 @ xb ) ) ),
inference(pattern_uni,[status(thm)],[25841:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(208,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,55]) ).
thf(209,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ))]]) ).
thf(437,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,55]) ).
thf(438,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[437:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ))]]) ).
thf(14738,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,78]) ).
thf(14739,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
= ( smndt0 @ ( smndt0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14738:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( ( aInteger0 @ A )
& ( aInteger0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4330,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,53]) ).
thf(4331,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[4330:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(60799,plain,
( ( sz10 != sz00 )
| ( ( smndt0 @ sz10 )
= sz00 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[58987,27134]) ).
thf(60800,plain,
( ( sz10 != sz00 )
| ( ( smndt0 @ sz10 )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[60799:[]]) ).
thf(4318,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,53]) ).
thf(4319,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ xq ) ),
inference(pattern_uni,[status(thm)],[4318:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(21727,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ sk1 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,93]) ).
thf(21728,plain,
( ( sdtpldt0 @ ( smndt0 @ sk1 ) @ sk1 )
= sz00 ),
inference(pattern_uni,[status(thm)],[21727:[bind(A,$thf( sk1 ))]]) ).
thf(24773,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,98]) ).
thf(24774,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ sk1 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24773:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(24656,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,98]) ).
thf(24657,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ xq ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24656:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(4324,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[264,53]) ).
thf(4325,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[4324:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ))]]) ).
thf(21104,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[4325,21088]) ).
thf(21639,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[21104,21088]) ).
thf(4291,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1584,53]) ).
thf(4292,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4291:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) ))]]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( B = sz00 )
| ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
inference(cnf,[status(esa)],[110]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( B = sz00 )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
inference(lifteq,[status(thm)],[111]) ).
thf(24628,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,98]) ).
thf(24629,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24628:[bind(A,$thf( smndt0 @ ( smndt0 @ sz10 ) ))]]) ).
thf(610,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ xq ) )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ sk1 )
!= ( sdtasdt0 @ ( smndt0 @ sz10 ) @ xq ) ) ),
inference(paramod_ordered,[status(thm)],[213,238]) ).
thf(618,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ xq ) )
| ( ( smndt0 @ sz10 )
!= ( smndt0 @ sz10 ) )
| ( sk1 != xq ) ),
inference(simp,[status(thm)],[610]) ).
thf(627,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ xq ) )
| ( sk1 != xq ) ),
inference(simp,[status(thm)],[618]) ).
thf(31808,plain,
( ( sk1 != xq )
| ( ( smndt0 @ xa )
!= ( smndt0 @ xq ) )
| ( ( smndt0 @ sk1 )
!= ( smndt0 @ xb ) ) ),
inference(paramod_ordered,[status(thm)],[627,31560]) ).
thf(31813,plain,
( ( sk1 != xq )
| ( xa != xq )
| ( sk1 != xb ) ),
inference(simp,[status(thm)],[31808]) ).
thf(326,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,38]) ).
thf(327,plain,
( ( sdtasdt0 @ ( smndt0 @ sk1 ) @ ( smndt0 @ sz10 ) )
= ( smndt0 @ ( smndt0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(3128,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1584,55]) ).
thf(3129,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3128:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) ))]]) ).
thf(267,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[183,32]) ).
thf(268,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[267:[bind(A,$thf( smndt0 @ ( smndt0 @ sz00 ) ))]]) ).
thf(75762,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[268,21088]) ).
thf(2849,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1467,55]) ).
thf(2850,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2849:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) ))]]) ).
thf(176,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,32]) ).
thf(177,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ xb ) ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(24660,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,98]) ).
thf(24661,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24660:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ))]]) ).
thf(26005,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,108]) ).
thf(26006,plain,
( ( sdtasdt0 @ ( smndt0 @ sk1 ) @ sz10 )
= ( smndt0 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26005:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(24677,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[413,98]) ).
thf(24678,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24677:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ))]]) ).
thf(14004,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,77]) ).
thf(14005,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ xq ) ) @ sz00 )
= ( smndt0 @ ( smndt0 @ xq ) ) ),
inference(pattern_uni,[status(thm)],[14004:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( B = sz00 )
| ~ ( aInteger0 @ C )
| ( ( sdtasdt0 @ B @ C )
!= A )
| ( aDivisorOf0 @ B @ A ) ),
inference(cnf,[status(esa)],[43]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( B = sz00 )
| ( ( sdtasdt0 @ B @ C )
!= A )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ~ ( aInteger0 @ C )
| ( aDivisorOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( A = sz00 )
| ~ ( aInteger0 @ ( sdtasdt0 @ A @ B ) )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( aDivisorOf0 @ A @ ( sdtasdt0 @ A @ B ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(23461,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[252,97]) ).
thf(23462,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23461:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ))]]) ).
thf(20168,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,92]) ).
thf(20169,plain,
( ( sdtpldt0 @ ( smndt0 @ xq ) @ ( smndt0 @ ( smndt0 @ xq ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20168:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(14794,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,78]) ).
thf(14795,plain,
( ( sdtpldt0 @ sz00 @ sz10 )
= sz10 ),
inference(pattern_uni,[status(thm)],[14794:[bind(A,$thf( sz10 ))]]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(23439,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,97]) ).
thf(23440,plain,
( ( sdtasdt0 @ ( smndt0 @ xb ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23439:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(27273,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,109]) ).
thf(27274,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ xq ) )
= ( smndt0 @ xq ) ),
inference(pattern_uni,[status(thm)],[27273:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(24632,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,98]) ).
thf(24633,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ xa ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24632:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(638,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ xb ) )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ sk1 )
!= ( sdtasdt0 @ ( smndt0 @ sz10 ) @ xb ) ) ),
inference(paramod_ordered,[status(thm)],[238,216]) ).
thf(646,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ xb ) )
| ( ( smndt0 @ sz10 )
!= ( smndt0 @ sz10 ) )
| ( sk1 != xb ) ),
inference(simp,[status(thm)],[638]) ).
thf(656,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ xb ) )
| ( sk1 != xb ) ),
inference(simp,[status(thm)],[646]) ).
thf(153,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,32]) ).
thf(154,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( smndt0 @ ( smndt0 @ sk1 ) ))]]) ).
thf(24759,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[146,98]) ).
thf(24760,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24759:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ))]]) ).
thf(13896,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,77]) ).
thf(13897,plain,
( ( sdtpldt0 @ ( smndt0 @ xb ) @ sz00 )
= ( smndt0 @ xb ) ),
inference(pattern_uni,[status(thm)],[13896:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(79447,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79374,53]) ).
thf(79448,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[79447:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ))]]) ).
thf(84695,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ),
inference(rewrite,[status(thm)],[79448,80930]) ).
thf(23441,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[292,97]) ).
thf(23442,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23441:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ))]]) ).
thf(23547,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,97]) ).
thf(23548,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ xq ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23547:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(27225,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,109]) ).
thf(27226,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ xb ) )
= ( smndt0 @ xb ) ),
inference(pattern_uni,[status(thm)],[27225:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(14672,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,78]) ).
thf(14673,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
= ( smndt0 @ ( smndt0 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[14672:[bind(A,$thf( smndt0 @ ( smndt0 @ sz10 ) ))]]) ).
thf(217,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ sz10 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[141,37]) ).
thf(218,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ sz10 ) )
= ( smndt0 @ ( smndt0 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( smndt0 @ sz10 ))]]) ).
thf(100,plain,
xq != sz00,
inference(cnf,[status(esa)],[99]) ).
thf(104,plain,
xq != sz00,
inference(lifteq,[status(thm)],[100]) ).
thf(318,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,38]) ).
thf(319,plain,
( ( sdtasdt0 @ xa @ ( smndt0 @ sz10 ) )
= ( smndt0 @ xa ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( xa ))]]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(14025,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,77]) ).
thf(14026,plain,
( ( sdtpldt0 @ ( smndt0 @ sk1 ) @ sz00 )
= ( smndt0 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14025:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(157,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,32]) ).
thf(158,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ xa ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( xa ))]]) ).
thf(14741,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,78]) ).
thf(14742,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ ( smndt0 @ xa ) ) )
= ( smndt0 @ ( smndt0 @ xa ) ) ),
inference(pattern_uni,[status(thm)],[14741:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(14662,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,78]) ).
thf(14663,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ xb ) )
= ( smndt0 @ xb ) ),
inference(pattern_uni,[status(thm)],[14662:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(4320,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,53]) ).
thf(4321,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4320:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ))]]) ).
thf(24703,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[374,98]) ).
thf(24704,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24703:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ))]]) ).
thf(206,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[146,32]) ).
thf(207,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ))]]) ).
thf(17863,plain,
( ~ ( aDivisorOf0 @ xq @ ( smndt0 @ xa ) )
| ( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtpldt0 @ sz00 @ ( smndt0 @ xa ) ) ) ),
inference(paramod_ordered,[status(thm)],[14681,28]) ).
thf(17975,plain,
( ~ ( aDivisorOf0 @ xq @ ( smndt0 @ xa ) )
| ( xb != sz00 )
| ( ( smndt0 @ xa )
!= ( smndt0 @ xa ) ) ),
inference(simp,[status(thm)],[17863]) ).
thf(18029,plain,
( ~ ( aDivisorOf0 @ xq @ ( smndt0 @ xa ) )
| ( xb != sz00 ) ),
inference(simp,[status(thm)],[17975]) ).
thf(11453,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[438,55]) ).
thf(11454,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[11453:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ) ))]]) ).
thf(271,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,37]) ).
thf(272,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ xa ) ) )
= ( smndt0 @ ( smndt0 @ ( smndt0 @ xa ) ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(23557,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[258,97]) ).
thf(23558,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23557:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ))]]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B )
| ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) )
| ~ ( aInteger0 @ A )
| ~ ( aInteger0 @ B ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(22631,plain,
( ( xa != sz00 )
| ( ( aDivisorOf0 @ xq @ ( sdtasdt0 @ xq @ sk1 ) )
!= ( aDivisorOf0 @ xq @ xb ) ) ),
inference(paramod_ordered,[status(thm)],[120,21428]) ).
thf(22651,plain,
( ( xa != sz00 )
| ( xq != xq )
| ( ( sdtasdt0 @ xq @ sk1 )
!= xb ) ),
inference(simp,[status(thm)],[22631]) ).
thf(22656,plain,
( ( xa != sz00 )
| ( ( sdtasdt0 @ xq @ sk1 )
!= xb ) ),
inference(simp,[status(thm)],[22651]) ).
thf(20137,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,92]) ).
thf(20138,plain,
( ( sdtpldt0 @ ( smndt0 @ xa ) @ ( smndt0 @ ( smndt0 @ xa ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20137:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ B @ A )
| ( ( sdtasdt0 @ B @ ( sk2 @ B @ A ) )
= A ) ),
inference(cnf,[status(esa)],[43]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ B @ ( sk2 @ B @ A ) )
= A )
| ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(25861,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,108]) ).
thf(25862,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) @ sz10 )
= ( smndt0 @ ( smndt0 @ sz10 ) ) ),
inference(pattern_uni,[status(thm)],[25861:[bind(A,$thf( smndt0 @ ( smndt0 @ sz10 ) ))]]) ).
thf(4366,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1495,53]) ).
thf(4367,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4366:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ) ))]]) ).
thf(27306,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz10 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xa ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[187,109]) ).
thf(27307,plain,
( ( sdtasdt0 @ sz10 @ ( smndt0 @ ( smndt0 @ xa ) ) )
= ( smndt0 @ ( smndt0 @ xa ) ) ),
inference(pattern_uni,[status(thm)],[27306:[bind(A,$thf( smndt0 @ ( smndt0 @ xa ) ))]]) ).
thf(261,plain,
! [A: $i] :
( ( ( sdtasdt0 @ xq @ A )
!= ( sdtpldt0 @ xb @ ( smndt0 @ xa ) ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,32]) ).
thf(262,plain,
( ( sdtpldt0 @ xb @ ( smndt0 @ xa ) )
!= ( sdtasdt0 @ xq @ ( smndt0 @ ( smndt0 @ xb ) ) ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(14790,plain,
! [A: $i] :
( ( ( sdtpldt0 @ sz00 @ A )
= A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[183,78]) ).
thf(14791,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz00 ) ) )
= ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(pattern_uni,[status(thm)],[14790:[bind(A,$thf( smndt0 @ ( smndt0 @ sz00 ) ))]]) ).
thf(61898,plain,
( ( sdtpldt0 @ sz00 @ ( smndt0 @ sz00 ) )
= ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[14791,21088]) ).
thf(24767,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ sz10 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,98]) ).
thf(24768,plain,
( ( sdtasdt0 @ sz00 @ sz10 )
= sz00 ),
inference(pattern_uni,[status(thm)],[24767:[bind(A,$thf( sz10 ))]]) ).
thf(82289,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82224,53]) ).
thf(82290,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ),
inference(pattern_uni,[status(thm)],[82289:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ))]]) ).
thf(82540,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ),
inference(rewrite,[status(thm)],[82290,80930]) ).
thf(4356,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[258,53]) ).
thf(4357,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ) ),
inference(pattern_uni,[status(thm)],[4356:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ xb ) ) ))]]) ).
thf(21756,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,93]) ).
thf(21757,plain,
( ( sdtpldt0 @ ( smndt0 @ xb ) @ xb )
= sz00 ),
inference(pattern_uni,[status(thm)],[21756:[bind(A,$thf( xb ))]]) ).
thf(23451,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,97]) ).
thf(23452,plain,
( ( sdtasdt0 @ xb @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23451:[bind(A,$thf( xb ))]]) ).
thf(241,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ xa ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,37]) ).
thf(242,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ xa ) )
= ( smndt0 @ ( smndt0 @ xa ) ) ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( smndt0 @ xa ))]]) ).
thf(4302,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xb ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,53]) ).
thf(4303,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ xb ) ) ),
inference(pattern_uni,[status(thm)],[4302:[bind(A,$thf( smndt0 @ ( smndt0 @ xb ) ))]]) ).
thf(767,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ sz10 ) )
| ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ sk1 )
!= ( sdtasdt0 @ ( smndt0 @ sz10 ) @ sz10 ) ) ),
inference(paramod_ordered,[status(thm)],[238,234]) ).
thf(787,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ sz10 ) )
| ( ( smndt0 @ sz10 )
!= ( smndt0 @ sz10 ) )
| ( sk1 != sz10 ) ),
inference(simp,[status(thm)],[767]) ).
thf(801,plain,
( ( ( smndt0 @ sk1 )
= ( smndt0 @ sz10 ) )
| ( sk1 != sz10 ) ),
inference(simp,[status(thm)],[787]) ).
thf(13936,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ sz00 )
= A )
| ( ( aInteger0 @ ( smndt0 @ xq ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[129,77]) ).
thf(13937,plain,
( ( sdtpldt0 @ ( smndt0 @ xq ) @ sz00 )
= ( smndt0 @ xq ) ),
inference(pattern_uni,[status(thm)],[13936:[bind(A,$thf( smndt0 @ xq ))]]) ).
thf(24614,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[292,98]) ).
thf(24615,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24614:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) ))]]) ).
thf(4344,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[209,53]) ).
thf(4345,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4344:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ))]]) ).
thf(20157,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ sz10 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[141,92]) ).
thf(20158,plain,
( ( sdtpldt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20157:[bind(A,$thf( smndt0 @ sz10 ))]]) ).
thf(4362,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[146,53]) ).
thf(4363,plain,
~ ( aDivisorOf0 @ sz00 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[4362:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ))]]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( aInteger0 @ A )
| ~ ( aDivisorOf0 @ B @ A )
| ( aInteger0 @ ( sk2 @ B @ A ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(21903,plain,
! [A: $i] :
( ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ sk1 ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[131,93]) ).
thf(21904,plain,
( ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) @ ( smndt0 @ sk1 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[21903:[bind(A,$thf( smndt0 @ sk1 ))]]) ).
thf(4334,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ sz00 )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,53]) ).
thf(4335,plain,
~ ( aDivisorOf0 @ sz00 @ sz00 ),
inference(pattern_uni,[status(thm)],[4334:[bind(A,$thf( sz00 ))]]) ).
thf(79562,plain,
! [A: $i] :
( ( aInteger0 @ ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79374,55]) ).
thf(79563,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[79562:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ))]]) ).
thf(84857,plain,
aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sz00 ) ) ) ) ),
inference(rewrite,[status(thm)],[79563,80930]) ).
thf(4312,plain,
! [A: $i] :
( ~ ( aDivisorOf0 @ sz00 @ A )
| ( ( aInteger0 @ xb )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,53]) ).
thf(4313,plain,
~ ( aDivisorOf0 @ sz00 @ xb ),
inference(pattern_uni,[status(thm)],[4312:[bind(A,$thf( xb ))]]) ).
thf(221,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,37]) ).
thf(222,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) )
= ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( smndt0 @ ( smndt0 @ ( smndt0 @ ( smndt0 @ sk1 ) ) ) ))]]) ).
thf(20113,plain,
! [A: $i] :
( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ xb ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[133,92]) ).
thf(20114,plain,
( ( sdtpldt0 @ ( smndt0 @ xb ) @ ( smndt0 @ ( smndt0 @ xb ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[20113:[bind(A,$thf( smndt0 @ xb ))]]) ).
thf(23455,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,97]) ).
thf(23456,plain,
( ( sdtasdt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[23455:[bind(A,$thf( smndt0 @ ( smndt0 @ sz10 ) ))]]) ).
thf(253,plain,
! [A: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
= ( smndt0 @ A ) )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,37]) ).
thf(254,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ xq ) ) )
= ( smndt0 @ ( smndt0 @ ( smndt0 @ xq ) ) ) ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(25929,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aInteger0 @ xa )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,108]) ).
thf(25930,plain,
( ( sdtasdt0 @ xa @ sz10 )
= xa ),
inference(pattern_uni,[status(thm)],[25929:[bind(A,$thf( xa ))]]) ).
thf(17950,plain,
( ( ( smndt0 @ xa )
!= ( smndt0 @ xq ) )
| ( xb != sz00 )
| ( ( smndt0 @ xa )
!= ( smndt0 @ xa ) ) ),
inference(simp,[status(thm)],[17907]) ).
thf(18014,plain,
( ( ( smndt0 @ xa )
!= ( smndt0 @ xq ) )
| ( xb != sz00 ) ),
inference(simp,[status(thm)],[17950]) ).
thf(24727,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aInteger0 @ ( smndt0 @ ( smndt0 @ xq ) ) )
!= ( aInteger0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[175,98]) ).
thf(24728,plain,
( ( sdtasdt0 @ sz00 @ ( smndt0 @ ( smndt0 @ xq ) ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[24727:[bind(A,$thf( smndt0 @ ( smndt0 @ xq ) ))]]) ).
thf(80937,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ sz00 ) )
= ( smndt0 @ sz00 ) ),
inference(rewrite,[status(thm)],[72753,80930]) ).
thf(82648,plain,
( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ sz00 )
= sz00 ),
inference(rewrite,[status(thm)],[80937,21088]) ).
thf(156575,plain,
$false,
inference(cvc4,[status(thm)],[101,25916,234,44422,20095,27315,4290,333,88,1549,14399,4311,741,23582,58991,14748,120,58583,21798,142,25805,77187,4294,23438,56,84559,185,13975,4343,27244,42,13970,24,288,20845,23500,36935,37,20209,4371,21896,21787,18015,25,20078,31560,3046,27224,110,125,24680,86048,31733,27134,4353,14024,22055,4317,325,152,228,78,31556,93,24609,13895,29,216,24663,25920,211,238,164,25858,28599,4329,14697,179,61,24621,58987,4307,116,14654,74,89,133,23510,23524,14661,84030,292,248,60,4323,270,83974,220,102,85,201,21747,31529,13917,27248,260,21579,137,33,28,38,70,26000,43945,23514,92,252,24607,65,24684,25844,14681,4327,25888,224,97,14643,56839,83409,23480,31557,169,23482,141,35443,64547,21715,53,4301,339,77,82224,23850,4315,24578,1584,109,256,4333,24694,14799,27240,23476,173,129,23574,41,24593,13932,73,343,105,31814,205,23508,31528,398,2915,25964,82463,42289,47931,45,64,35058,27185,14776,85194,23693,32,34,13907,148,27399,24688,20278,31515,23498,23504,59,413,13973,31547,4341,3070,21428,27353,78459,4309,20847,26572,71,313,25828,144,236,86,23458,382,54,187,4337,113,274,4305,13888,25866,39,27303,4369,245,32629,24742,15212,98,23584,14706,213,66,240,4296,23448,21837,345,24639,103,108,62861,82021,24625,15216,25842,20270,14675,438,14739,80,4331,1467,60800,374,4319,209,21728,24774,24657,21639,4292,112,24629,31813,327,3129,310,75762,83154,2850,177,24661,26006,26355,24678,14005,21767,50,23462,20169,14795,67,23440,27274,32649,24633,656,154,175,24760,23424,13897,84695,23442,627,80930,23548,99,27226,21088,14673,218,104,14393,20126,23405,319,40,14026,258,158,14742,55,14663,4321,24704,207,18029,11454,272,23558,82,22656,20138,146,30,51,25862,4367,27307,262,61898,24768,82540,4357,1495,79,21757,94,23452,242,4303,801,13977,13937,24615,68,27206,4345,20158,4363,131,13909,47,21904,4335,84857,13881,83,4313,222,20114,26794,23456,254,25930,18014,24728,82648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM424+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n017.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 16:12:46 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.92/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (127ms).
% 1.36/0.98 % [INFO] Running in sequential loop mode.
% 1.71/1.18 % [INFO] eprover registered as external prover.
% 1.71/1.18 % [INFO] cvc4 registered as external prover.
% 1.71/1.18 % [INFO] Scanning for conjecture ...
% 1.71/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.88/1.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.88/1.26 % [INFO] Found a conjecture and 21 axioms. Running axiom selection ...
% 1.99/1.30 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 1.99/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.99/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.22/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 2.22/1.33 % [INFO] Type checking passed.
% 2.22/1.34 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 119.85/32.51 % External prover 'cvc4' found a proof!
% 119.85/32.51 % [INFO] Killing All external provers ...
% 119.85/32.51 % Time passed: 31995ms (effective reasoning time: 31531ms)
% 119.85/32.51 % 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)>
% 119.85/32.52 % Axioms used in derivation (21): mAddComm, mAddNeg, mMulOne, mAddZero, mAddAsso, mIntMult, mDivisor, mIntNeg, mMulMinOne, mMulComm, mMulZero, mEquMod, mZeroDiv, mDistrib, mMulAsso, mIntPlus, mEquModRef, mIntegers, m__704, mIntOne, mIntZero
% 119.85/32.52 % No. of inferences in proof: 802
% 119.85/32.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 31995 ms resp. 31531 ms w/o parsing
% 120.04/32.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 120.04/32.63 % [INFO] Killing All external provers ...
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