%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM514+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:21:14 AM UTC 2025
% Result : Theorem 7.71s 7.95s
% Output : Proof 7.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 99
% Syntax : Number of formulae : 253 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 3300 (1305 equ)
% Maximal formula atoms : 60 ( 13 avg)
% Number of connectives : 5800 (2857 ~;2373 |; 231 &)
% ( 308 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 104 ( 104 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 624 ( 580 !; 15 ?; 624 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xr_type,type,
xr: $i ).
tff(xk_type,type,
xk: $i ).
tff(xp_type,type,
xp: $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
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(1,plain,
( ( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
<=> ( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2613) ).
tff(3,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( aNaturalNumber0(xr)
<=> aNaturalNumber0(xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
tff(7,plain,
( aNaturalNumber0(xr)
& doDivides0(xr,xk) ),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aNaturalNumber0(xr),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
aNaturalNumber0(xr),
inference(modus_ponens,[status(thm)],[8,5]) ).
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)
| ~ ( ~ ( ( 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(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)
| ~ ( ~ ( ( 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)],[10]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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)],[15,13]) ).
tff(17,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(18,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)],[17]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,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(23,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)],[22]) ).
tff(24,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/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
tff(25,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)],[24,23]) ).
tff(26,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)],[25,21]) ).
tff(27,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)],[26]) ).
tff(28,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)],[27,20]) ).
tff(29,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)],[28,18]) ).
tff(30,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)],[29,16]) ).
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) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[30,11]) ).
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)
| ~ ( ~ ( 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(33,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(34,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)],[33]) ).
tff(35,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)],[34,32]) ).
tff(36,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(37,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)],[36,35]) ).
tff(38,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)],[37,31,9]) ).
tff(39,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(40,plain,
( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( isPrime0(xr)
<=> isPrime0(xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
isPrime0(xr),
inference(and_elim,[status(thm)],[6]) ).
tff(43,plain,
isPrime0(xr),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,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(45,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)],[44,43]) ).
tff(46,plain,
~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ),
inference(unit_resolution,[status(thm)],[45,40]) ).
tff(47,plain,
( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) )
| ( xr != sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
xr != sz00,
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
( doDivides0(xr,xn)
<=> doDivides0(xr,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
tff(51,plain,
doDivides0(xr,xn),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(54,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[54]) ).
tff(56,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[55,52]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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)],[60,58]) ).
tff(62,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(63,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)],[62]) ).
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) ) )
<=> ! [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(65,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(66,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)],[65]) ).
tff(67,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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
tff(68,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)],[67,66]) ).
tff(69,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)],[68,64]) ).
tff(70,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)],[69]) ).
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) ) ) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
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) ) ) ),
inference(modus_ponens,[status(thm)],[71,61]) ).
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) ) ) )
| ~ 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(74,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(75,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)],[74]) ).
tff(76,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)],[75,73]) ).
tff(77,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(78,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)],[77,76]) ).
tff(79,plain,
( ( xr = sz00 )
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ),
inference(unit_resolution,[status(thm)],[78,72,56,9,51]) ).
tff(80,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ),
inference(unit_resolution,[status(thm)],[79,48]) ).
tff(81,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(82,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)],[81,80]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,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)],[85]) ).
tff(87,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)],[86,84]) ).
tff(88,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(89,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)],[88]) ).
tff(90,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(91,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(92,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)],[91]) ).
tff(93,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
tff(94,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)],[93,92]) ).
tff(95,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)],[94,90]) ).
tff(96,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)],[95]) ).
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) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
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) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[97,87]) ).
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)
| ! [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(100,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(101,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)],[100]) ).
tff(102,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)],[101,99]) ).
tff(103,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(104,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)],[103,102]) ).
tff(105,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)],[104,98,56,9]) ).
tff(106,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(107,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)],[106,105]) ).
tff(108,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(109,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)],[108,51]) ).
tff(110,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ),
inference(unit_resolution,[status(thm)],[109,107]) ).
tff(111,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(112,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)],[111,110]) ).
tff(113,plain,
tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr),
inference(unit_resolution,[status(thm)],[112,82]) ).
tff(114,plain,
( aNaturalNumber0(tptp_fun_W2_1(xn,xr))
<=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,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(116,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xr)),
inference(unit_resolution,[status(thm)],[115,110]) ).
tff(117,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(modus_ponens,[status(thm)],[116,114]) ).
tff(118,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[54]) ).
tff(120,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
^ [W0: $i,W1: $i] :
refl(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,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(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(124,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(129,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[129,125]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[131,124]) ).
tff(133,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[132,122]) ).
tff(134,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) )
<=> ( ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(unit_resolution,[status(thm)],[139,133,120]) ).
tff(141,plain,
aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(unit_resolution,[status(thm)],[140,117]) ).
tff(142,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[53]) ).
tff(144,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,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(xp)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) )
<=> ( ~ ! [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(xp)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
( ( ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
( ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
( ( ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ( ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[148,146]) ).
tff(150,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(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,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(xp)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,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(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,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(xp)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[150,145]) ).
tff(152,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(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,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(xp)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
( ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[153,98,144]) ).
tff(155,plain,
~ ( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) ) ),
inference(unit_resolution,[status(thm)],[154,141]) ).
tff(156,plain,
( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(sdtsldt0(xn,xr),xm),xp)) ) ) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(157,plain,
( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) ),
inference(unit_resolution,[status(thm)],[156,155]) ).
tff(158,plain,
( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
<=> ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,axiom,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(160,plain,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(162,plain,
( ~ ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ) ),
inference(unit_resolution,[status(thm)],[161,160]) ).
tff(163,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) ),
inference(unit_resolution,[status(thm)],[162,157]) ).
tff(164,plain,
( ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
tff(166,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) = sdtsldt0(xk,xr),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
<=> doDivides0(xr,xk) ),
inference(monotonicity,[status(thm)],[167]) ).
tff(170,plain,
( doDivides0(xr,xk)
<=> doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
( doDivides0(xr,xk)
<=> doDivides0(xr,xk) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
doDivides0(xr,xk),
inference(and_elim,[status(thm)],[7]) ).
tff(173,plain,
doDivides0(xr,xk),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp)),
inference(modus_ponens,[status(thm)],[173,170]) ).
tff(175,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(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) )
<=> ( ~ ! [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(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,plain,
( ( ~ aNaturalNumber0(xp)
| ~ ( ~ ( ( xp = sz00 )
| ( xp = sz10 )
| isPrime0(xp)
| ~ ( ( tptp_fun_W1_2(xp) = xp )
| ( tptp_fun_W1_2(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ~ doDivides0(tptp_fun_W1_2(xp),xp) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xp )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xp) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,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(xp)
| ~ ( ~ ( ( xp = sz00 )
| ( xp = sz10 )
| isPrime0(xp)
| ~ ( ( tptp_fun_W1_2(xp) = xp )
| ( tptp_fun_W1_2(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ~ doDivides0(tptp_fun_W1_2(xp),xp) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xp )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xp) ) ) ) ) )
<=> ( ~ ! [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(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,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(xp)
| ~ ( ~ ( ( xp = sz00 )
| ( xp = sz10 )
| isPrime0(xp)
| ~ ( ( tptp_fun_W1_2(xp) = xp )
| ( tptp_fun_W1_2(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ~ doDivides0(tptp_fun_W1_2(xp),xp) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xp )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xp) ) ) ) ) )
<=> ( ~ ! [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(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[177,175]) ).
tff(179,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(xp)
| ~ ( ~ ( ( xp = sz00 )
| ( xp = sz10 )
| isPrime0(xp)
| ~ ( ( tptp_fun_W1_2(xp) = xp )
| ( tptp_fun_W1_2(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ~ doDivides0(tptp_fun_W1_2(xp),xp) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xp )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xp) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,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(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ),
inference(unit_resolution,[status(thm)],[180,31,144]) ).
tff(182,plain,
( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) )
| ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(183,plain,
( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ),
inference(unit_resolution,[status(thm)],[182,181]) ).
tff(184,plain,
( isPrime0(xp)
<=> isPrime0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
tff(186,plain,
isPrime0(xp),
inference(and_elim,[status(thm)],[185]) ).
tff(187,plain,
isPrime0(xp),
inference(modus_ponens,[status(thm)],[186,184]) ).
tff(188,plain,
( ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) )
| ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(189,plain,
( ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) )
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ),
inference(unit_resolution,[status(thm)],[188,187]) ).
tff(190,plain,
~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ),
inference(unit_resolution,[status(thm)],[189,183]) ).
tff(191,plain,
( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ( xp != sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(192,plain,
xp != sz00,
inference(unit_resolution,[status(thm)],[191,190]) ).
tff(193,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(194,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(unit_resolution,[status(thm)],[195,133,56,120]) ).
tff(197,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(and_elim,[status(thm)],[185]) ).
tff(199,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,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(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) )
<=> ( ~ ! [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(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
( ( ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(202,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) )
<=> ( ~ ! [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(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ) ),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) )
<=> ( ~ ! [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(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ) ),
inference(transitivity,[status(thm)],[202,200]) ).
tff(204,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,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(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
( ( xp = sz00 )
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ),
inference(unit_resolution,[status(thm)],[205,72,144,199,196]) ).
tff(207,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
inference(unit_resolution,[status(thm)],[206,192]) ).
tff(208,plain,
( ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,plain,
( ~ ( ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) )
<=> ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,plain,
( ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ ( ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) )
<=> ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) ),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
( ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ ( ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) )
<=> ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) ),
inference(transitivity,[status(thm)],[210,208]) ).
tff(212,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ ( ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) )
<=> ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ),
inference(unit_resolution,[status(thm)],[213,207]) ).
tff(215,plain,
( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) )
| aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(tautology,[status(thm)],[]) ).
tff(216,plain,
aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[215,214]) ).
tff(217,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(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),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(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(218,plain,
( ( ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,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(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),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(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ) ) ),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,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(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),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(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ) ) ),
inference(transitivity,[status(thm)],[219,217]) ).
tff(221,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(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,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(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
( ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ) ),
inference(unit_resolution,[status(thm)],[222,72,9]) ).
tff(224,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ),
inference(unit_resolution,[status(thm)],[223,216,48,174]) ).
tff(225,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) )
<=> ( tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr) = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) )
<=> ( tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr) = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ),
inference(unit_resolution,[status(thm)],[225,224]) ).
tff(227,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(xr)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),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(xr)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,plain,
( ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(229,plain,
( ~ ( ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) )
| ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(230,plain,
( ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) )
| ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
( ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) )
| ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[230,228]) ).
tff(232,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(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) )
| ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != 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(xr)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,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(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) )
| ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != 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(xr)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[232,227]) ).
tff(234,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(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) )
| ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,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(xr)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[234,233]) ).
tff(236,plain,
( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[235,98,9]) ).
tff(237,plain,
~ ( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ) ),
inference(unit_resolution,[status(thm)],[236,216]) ).
tff(238,plain,
( ~ ( doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) )
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(239,plain,
( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ),
inference(unit_resolution,[status(thm)],[238,237]) ).
tff(240,plain,
( ~ ( ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) )
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(241,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) ),
inference(unit_resolution,[status(thm)],[240,239,174]) ).
tff(242,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) )
<=> ( tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr) = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) )
| ( tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr) = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ),
inference(tautology,[status(thm)],[]) ).
tff(243,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ) )
<=> ( tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr) = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) )
| ( tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr) = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr) ) ),
inference(unit_resolution,[status(thm)],[242,241]) ).
tff(244,plain,
tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr) = sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr),
inference(unit_resolution,[status(thm)],[243,226]) ).
tff(245,plain,
tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr) = sdtsldt0(xk,xr),
inference(transitivity,[status(thm)],[244,168]) ).
tff(246,plain,
( aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
<=> aNaturalNumber0(sdtsldt0(xk,xr)) ),
inference(monotonicity,[status(thm)],[245]) ).
tff(247,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(xr,tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) )
| aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) ),
inference(tautology,[status(thm)],[]) ).
tff(248,plain,
aNaturalNumber0(tptp_fun_W2_1(sdtsldt0(sdtasdt0(xn,xm),xp),xr)),
inference(unit_resolution,[status(thm)],[247,241]) ).
tff(249,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(modus_ponens,[status(thm)],[248,246]) ).
tff(250,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(251,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(252,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)) ) ),
inference(modus_ponens,[status(thm)],[251,250]) ).
tff(253,plain,
$false,
inference(unit_resolution,[status(thm)],[252,249,163,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM514+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:21:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 7.71/7.95 % SZS status Theorem
% 7.71/7.95 % SZS output start Proof
% See solution above
% 7.83/8.04 % E exiting
%------------------------------------------------------------------------------