%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM517+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:21:15 AM UTC 2025
% Result : Theorem 0.65s 0.83s
% Output : Proof 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 87
% Syntax : Number of formulae : 219 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 2970 ( 857 equ)
% Maximal formula atoms : 60 ( 13 avg)
% Number of connectives : 4676 (2101 ~;1888 |; 344 &)
% ( 277 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 176 ( 176 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 559 ( 500 !; 15 ?; 559 :)
% Comments :
%------------------------------------------------------------------------------
tff(iLess0_type,type,
iLess0: ( $i * $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(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xr_type,type,
xr: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(sz10_type,type,
sz10: $i ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(tptp_fun_W1_2_type,type,
tptp_fun_W1_2: $i > $i ).
tff(xk_type,type,
xk: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(1,plain,
( aNaturalNumber0(xr)
<=> aNaturalNumber0(xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
tff(3,plain,
( aNaturalNumber0(xr)
& doDivides0(xr,xk) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xr),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aNaturalNumber0(xr),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[11,9]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( isPrime0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( isPrime0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) )
<=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) )
<=> ( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) )),
rewrite(( ( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
tff(21,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( isPrime0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,14]) ).
tff(26,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,12]) ).
tff(27,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,7]) ).
tff(28,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ),
inference(unit_resolution,[status(thm)],[33,27,5]) ).
tff(35,plain,
( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) )
| ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( isPrime0(xr)
<=> isPrime0(xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
isPrime0(xr),
inference(and_elim,[status(thm)],[2]) ).
tff(39,plain,
isPrime0(xr),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) )
| ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
( ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) )
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ),
inference(unit_resolution,[status(thm)],[41,36]) ).
tff(43,plain,
( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) )
| ( xr != sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(44,plain,
xr != sz00,
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( doDivides0(xr,xn)
<=> doDivides0(xr,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
tff(47,plain,
doDivides0(xr,xn),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(50,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[49]) ).
tff(51,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[50]) ).
tff(52,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[51,48]) ).
tff(53,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
rewrite(( ( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
rewrite(( ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
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 != sz00 )
& doDivides0(W0,W1) )
<=> ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ~ ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
rewrite(( ~ ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
rewrite(( ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
tff(64,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[67,57]) ).
tff(69,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( ( xr = sz00 )
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ),
inference(unit_resolution,[status(thm)],[74,68,52,5,47]) ).
tff(76,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ),
inference(unit_resolution,[status(thm)],[75,44]) ).
tff(77,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) )
<=> ( tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) )
<=> ( tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,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(( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
<=> ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )),
rewrite(( ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
tff(90,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[93,83]) ).
tff(95,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) )
| ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) )
| ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) )
| ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) )
| ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
~ ( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ) ),
inference(unit_resolution,[status(thm)],[100,94,52,5]) ).
tff(102,plain,
( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) )
| ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(103,plain,
( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
( ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) )
| ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(105,plain,
( ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ),
inference(unit_resolution,[status(thm)],[104,47]) ).
tff(106,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ),
inference(unit_resolution,[status(thm)],[105,103]) ).
tff(107,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) )
<=> ( tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) )
| ( tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr) ) ),
inference(tautology,[status(thm)],[]) ).
tff(108,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) )
<=> ( tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr) ) )
| ( tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr) ) ),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr),
inference(unit_resolution,[status(thm)],[108,78]) ).
tff(110,plain,
( aNaturalNumber0(tptp_fun_W2_1(xn,xr))
<=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) )
| aNaturalNumber0(tptp_fun_W2_1(xn,xr)) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xr)),
inference(unit_resolution,[status(thm)],[111,106]) ).
tff(113,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(modus_ponens,[status(thm)],[112,110]) ).
tff(114,plain,
( ~ doDivides0(xp,xm)
<=> ~ doDivides0(xp,xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,axiom,
~ ( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(116,plain,
~ doDivides0(xp,xm),
inference(or_elim,[status(thm)],[115]) ).
tff(117,plain,
~ doDivides0(xp,xm),
inference(modus_ponens,[status(thm)],[116,114]) ).
tff(118,plain,
( ~ doDivides0(xp,sdtsldt0(xn,xr))
<=> ~ doDivides0(xp,sdtsldt0(xn,xr)) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(or_elim,[status(thm)],[115]) ).
tff(120,plain,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
<=> doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,axiom,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2529) ).
tff(123,plain,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
( isPrime0(xp)
<=> isPrime0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(126,plain,
isPrime0(xp),
inference(and_elim,[status(thm)],[125]) ).
tff(127,plain,
isPrime0(xp),
inference(modus_ponens,[status(thm)],[126,124]) ).
tff(128,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,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(rewrite(( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ~ ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
( ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ~ ~ ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
rewrite(( ~ ~ ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
( ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
( ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
rewrite(( ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
( ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
trans(monotonicity(trans(monotonicity(rewrite(( ( doDivides0(W2,W0)
| doDivides0(W2,W1) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) )),
( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) )
<=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) ) )),
rewrite(( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) )
<=> ( doDivides0(W2,W1)
| 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))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )),
( ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) )
<=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ) )),
rewrite(( ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )),
( ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(134,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
tff(136,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(skolemize,[status(sab)],[137]) ).
tff(139,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ),
inference(modus_ponens,[status(thm)],[138,131]) ).
tff(140,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ),
inference(modus_ponens,[status(thm)],[139,129]) ).
tff(141,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[49]) ).
tff(143,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[50]) ).
tff(146,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
( ( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) )
<=> ( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(transitivity,[status(thm)],[149,147]) ).
tff(151,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(unit_resolution,[status(thm)],[152,146,143,140,127,123,120,117]) ).
tff(154,plain,
~ iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[153,113]) ).
tff(155,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(156,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)],[155]) ).
tff(157,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(158,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)],[157]) ).
tff(159,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(160,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(161,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)],[160]) ).
tff(162,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(163,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[163,159]) ).
tff(165,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[164]) ).
tff(166,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[165,158]) ).
tff(167,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[166,156]) ).
tff(168,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ( aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ) ),
inference(transitivity,[status(thm)],[170,168]) ).
tff(172,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(unit_resolution,[status(thm)],[173,167,146]) ).
tff(175,plain,
aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)),
inference(unit_resolution,[status(thm)],[174,113]) ).
tff(176,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
( ( aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ) ),
inference(transitivity,[status(thm)],[178,176]) ).
tff(180,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(unit_resolution,[status(thm)],[181,167,143]) ).
tff(183,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)),
inference(unit_resolution,[status(thm)],[182,175]) ).
tff(184,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(185,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(186,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)],[185,184]) ).
tff(187,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(unit_resolution,[status(thm)],[186,167,52,146]) ).
tff(188,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(189,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(190,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)],[189]) ).
tff(191,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)],[190,188]) ).
tff(192,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(193,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)],[192,191]) ).
tff(194,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[193,167,143,187]) ).
tff(195,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,axiom,
( ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) )
& sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2686) ).
tff(197,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(and_elim,[status(thm)],[196]) ).
tff(198,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(modus_ponens,[status(thm)],[197,195]) ).
tff(199,plain,
( ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) )
<=> ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(200,plain,
sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(and_elim,[status(thm)],[196]) ).
tff(201,plain,
sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,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(203,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)],[202]) ).
tff(204,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(205,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)],[204]) ).
tff(206,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(207,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(208,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)],[207]) ).
tff(209,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(210,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[210,206]) ).
tff(212,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(skolemize,[status(sab)],[211]) ).
tff(213,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[212,205]) ).
tff(214,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[213,203]) ).
tff(215,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(216,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
( iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(unit_resolution,[status(thm)],[217,214,201,198,194]) ).
tff(219,plain,
$false,
inference(unit_resolution,[status(thm)],[218,183,154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM517+1 : TPTP v9.0.0. Released v4.0.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:23:01 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.65/0.83 % SZS status Theorem
% 0.65/0.83 % SZS output start Proof
% See solution above
% 0.65/0.87 % E exiting
%------------------------------------------------------------------------------