TSTP Solution File: NUM508+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM508+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 : Sun Sep 18 13:10:09 EDT 2022
% Result : Theorem 0.16s 0.40s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 72
% Syntax : Number of formulae : 157 ( 37 unt; 18 typ; 0 def)
% Number of atoms : 2943 ( 956 equ)
% Maximal formula atoms : 88 ( 21 avg)
% Number of connectives : 4599 (1946 ~;1805 |; 670 &)
% ( 131 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 151 ( 151 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 11 >; 7 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-6 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 464 ( 308 !; 125 ?; 464 :)
% Comments :
%------------------------------------------------------------------------------
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(xr_type,type,
xr: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xk_type,type,
xk: $i ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(sz10_type,type,
sz10: $i ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(tptp_fun_W3_5_type,type,
tptp_fun_W3_5: ( $i * $i ) > $i ).
tff(tptp_fun_W3_6_type,type,
tptp_fun_W3_6: $i > $i ).
tff(tptp_fun_W4_7_type,type,
tptp_fun_W4_7: $i > $i ).
tff(tptp_fun_W3_4_type,type,
tptp_fun_W3_4: ( $i * $i ) > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(1,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(3,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[3]) ).
tff(8,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(17,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[20,10]) ).
tff(22,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(unit_resolution,[status(thm)],[24,21,8,5]) ).
tff(26,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[2]) ).
tff(28,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[34,21,28,25]) ).
tff(36,plain,
( aNaturalNumber0(xr)
<=> aNaturalNumber0(xr) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
( aNaturalNumber0(xr)
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xk = sdtasdt0(xr,W0) ) )
& doDivides0(xr,xk)
& ( xr != sz00 )
& ( xr != sz10 )
& ! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xr = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xr) ) )
=> ( ( W0 = sz10 )
| ( W0 = xr ) ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
tff(38,plain,
( aNaturalNumber0(xr)
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xk = sdtasdt0(xr,W0) ) )
& doDivides0(xr,xk)
& ( xr != sz00 )
& ( xr != sz10 )
& ! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xr = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xr) ) )
=> ( ( W0 = sz10 )
| ( W0 = xr ) ) ) ),
inference(and_elim,[status(thm)],[37]) ).
tff(39,plain,
( aNaturalNumber0(xr)
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xk = sdtasdt0(xr,W0) ) )
& doDivides0(xr,xk)
& ( xr != sz00 )
& ( xr != sz10 ) ),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
( aNaturalNumber0(xr)
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xk = sdtasdt0(xr,W0) ) )
& doDivides0(xr,xk)
& ( xr != sz00 ) ),
inference(and_elim,[status(thm)],[39]) ).
tff(41,plain,
( aNaturalNumber0(xr)
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xk = sdtasdt0(xr,W0) ) )
& doDivides0(xr,xk) ),
inference(and_elim,[status(thm)],[40]) ).
tff(42,plain,
( aNaturalNumber0(xr)
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xk = sdtasdt0(xr,W0) ) ) ),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
aNaturalNumber0(xr),
inference(and_elim,[status(thm)],[42]) ).
tff(44,plain,
aNaturalNumber0(xr),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) )
<=> ( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)),
inference(unit_resolution,[status(thm)],[50,21,44,25]) ).
tff(52,plain,
( ~ doDivides0(xr,xn)
<=> ~ doDivides0(xr,xn) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xr,W0) ) )
| doDivides0(xr,xn)
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xr,W0) ) )
| doDivides0(xr,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(54,plain,
~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xr,W0) ) )
| doDivides0(xr,xn)
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xr,W0) ) ) ),
inference(or_elim,[status(thm)],[53]) ).
tff(55,plain,
~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xr,W0) ) )
| doDivides0(xr,xn) ),
inference(or_elim,[status(thm)],[54]) ).
tff(56,plain,
~ doDivides0(xr,xn),
inference(or_elim,[status(thm)],[55]) ).
tff(57,plain,
~ doDivides0(xr,xn),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) )
| doDivides0(xr,xn) ),
inference(tautology,[status(thm)],]) ).
tff(59,plain,
( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) ),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
<=> doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xr,W0) = xk ) )
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xm) = sdtasdt0(xr,W0) ) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
tff(62,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(and_elim,[status(thm)],[61]) ).
tff(63,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(modus_ponens,[status(thm)],[62,60]) ).
tff(64,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) )
| ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(tautology,[status(thm)],]) ).
tff(65,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) ),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( isPrime0(xr)
<=> isPrime0(xr) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
isPrime0(xr),
inference(and_elim,[status(thm)],[37]) ).
tff(68,plain,
isPrime0(xr),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) )
| ~ isPrime0(xr) ),
inference(tautology,[status(thm)],]) ).
tff(70,plain,
( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
( ~ doDivides0(xr,xm)
<=> ~ doDivides0(xr,xm) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
~ doDivides0(xr,xm),
inference(or_elim,[status(thm)],[53]) ).
tff(73,plain,
~ doDivides0(xr,xm),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) )
| doDivides0(xr,xm) ),
inference(tautology,[status(thm)],]) ).
tff(75,plain,
( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
<=> ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )),
rewrite(
( ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) ) )),
monotonicity(
monotonicity(
rewrite(
( ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) )
<=> ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )),
( ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
( ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
rewrite(
( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) ) )),
( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
^ [W0: $i,W1: $i,W2: $i] :
rewrite(
( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W3: $i] :
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
<=> ~ ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )),
( ~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
<=> ~ ~ ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) )
<=> ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )),
( ~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
<=> ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ))),
( ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
<=> ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )),
( ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
<=> ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )),
rewrite(
( ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
<=> ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )),
( ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
<=> ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )),
rewrite(
( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
<=> ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) ) )),
rewrite(
( ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) ) )),
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) )
<=> ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) )),
( ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) )
<=> ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )),
rewrite(
( ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) )
<=> ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )),
( ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) )
<=> ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )),
( ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
rewrite(
( ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
( ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
rewrite(
( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
<=> ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) ) )),
rewrite(
( ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
<=> ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) ) )),
rewrite(
( ( ( ~ isPrime0(W2)
& ( ~ ( ( W2 != sz00 ) )
| ~ ( ( W2 != sz10 ) )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ( ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) )),
( ( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ~ ( ( W2 != sz00 ) )
| ~ ( ( W2 != sz10 ) )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) )),
rewrite(
( ( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
( ( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ~ ( ( W2 != sz00 ) )
| ~ ( ( W2 != sz10 ) )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ~ ( ( W2 != sz00 ) )
| ~ ( ( W2 != sz10 ) )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
trans(
monotonicity(
rewrite(
( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) )),
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
<=> ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) )),
rewrite(
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
<=> ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) )),
( ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) )),
rewrite(
( ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) ) )),
( ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) ) )),
( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) )
<=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) ) ) )),
rewrite(
( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )),
( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )),
( ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) )
<=> ( ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ) )),
rewrite(
( ( ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )),
( ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
tff(91,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ~ ( ( W2 != sz00 ) )
| ~ ( ( W2 != sz10 ) )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[94,84]) ).
tff(96,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[95,82]) ).
tff(97,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) ),
inference(modus_ponens,[status(thm)],[96,77]) ).
tff(98,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ( ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) )
<=> ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) )
<=> ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
<=> ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
<=> ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) ) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) )
| ~ doDivides0(xr,xn) )
<=> ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) )
| ~ doDivides0(xr,xn) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) ) ) ),
inference(monotonicity,[status(thm)],[104,103,100]) ).
tff(106,plain,
( ( ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) )
| ~ doDivides0(xr,xn) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) ) ) ),
inference(transitivity,[status(thm)],[105,99]) ).
tff(107,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) )
| ~ doDivides0(xr,xn) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) ) ) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) )
| ~ doDivides0(xr,xn) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) ) ) ),
inference(transitivity,[status(thm)],[107,98]) ).
tff(109,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) )
| ~ doDivides0(xr,xn) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = W2 )
| ( tptp_fun_W3_6(W2) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xr,xm))
| ( xm != sdtasdt0(xr,tptp_fun_W3_4(xr,xm)) ) )
| ~ ( isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( tptp_fun_W3_6(xr) = xr )
| ( tptp_fun_W3_6(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W3_6(xr))
| ~ aNaturalNumber0(tptp_fun_W4_7(xr))
| ( xr != sdtasdt0(tptp_fun_W3_6(xr),tptp_fun_W4_7(xr)) )
| ~ doDivides0(tptp_fun_W3_6(xr),xr) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W3) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(tptp_fun_W3_5(xr,xn))
| ( xn != sdtasdt0(xr,tptp_fun_W3_5(xr,xn)) ) ) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[110,8,5,97,44,75,70,65,59]) ).
tff(112,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(rewrite,[status(thm)],]) ).
tff(113,axiom,
( ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) )
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),W0) = sdtpldt0(sdtpldt0(xn,xm),xp) ) )
& sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2478) ).
tff(114,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(and_elim,[status(thm)],[113]) ).
tff(115,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(modus_ponens,[status(thm)],[114,112]) ).
tff(116,plain,
( ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) )
<=> ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) )
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),W0) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ) ),
inference(and_elim,[status(thm)],[113]) ).
tff(118,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(and_elim,[status(thm)],[117]) ).
tff(119,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(modus_ponens,[status(thm)],[118,116]) ).
tff(120,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(
monotonicity(
rewrite(
( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
<=> ~ ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
<=> ~ ~ ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(
( ~ ~ ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
( ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ( iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(
( ( iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
( ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) )
<=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| iLess0(W0,W1) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| iLess0(W0,W1) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| iLess0(W0,W1) ) )
<=> ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) )
<=> ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
tff(128,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[131,121]) ).
tff(133,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) )
<=> ( ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
$false,
inference(unit_resolution,[status(thm)],[138,132,119,115,111,51,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : NUM508+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Sep 2 11:16:18 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.16/0.40 % SZS status Theorem
% 0.16/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------