%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM512+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:21:13 AM UTC 2025
% Result : Theorem 0.84s 1.05s
% Output : Proof 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 119
% Syntax : Number of formulae : 318 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 3723 (1444 equ)
% Maximal formula atoms : 60 ( 11 avg)
% Number of connectives : 6340 (3075 ~;2585 |; 299 &)
% ( 341 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 140 ( 140 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 745 ( 686 !; 15 ?; 745 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(xr_type,type,
xr: $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(sz10_type,type,
sz10: $i ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(tptp_fun_W1_2_type,type,
tptp_fun_W1_2: $i > $i ).
tff(xk_type,type,
xk: $i ).
tff(xp_type,type,
xp: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(1,plain,
( ( sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) = sdtasdt0(xn,xm) )
<=> ( sdtasdt0(xn,xm) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( aNaturalNumber0(xr)
<=> aNaturalNumber0(xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
tff(4,plain,
( aNaturalNumber0(xr)
& doDivides0(xr,xk) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aNaturalNumber0(xr),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
aNaturalNumber0(xr),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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)],[9]) ).
tff(11,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(12,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
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(transitivity,[status(thm)],[12,10]) ).
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] :
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(17,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)],[16]) ).
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: $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(19,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(20,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)],[19]) ).
tff(21,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(22,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,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)],[22,18]) ).
tff(24,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)],[23]) ).
tff(25,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,15]) ).
tff(27,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)],[26,13]) ).
tff(28,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,8]) ).
tff(29,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(30,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(31,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) )
<=> ( ~ ! [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)],[31,29]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( 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(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)
| ~ ( ~ ( 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)],[33,32]) ).
tff(35,plain,
~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xr),xr)
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ( tptp_fun_W1_2(xr) = sz10 )
| ( tptp_fun_W1_2(xr) = xr ) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ),
inference(unit_resolution,[status(thm)],[34,28,6]) ).
tff(36,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(37,plain,
( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( isPrime0(xr)
<=> isPrime0(xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
isPrime0(xr),
inference(and_elim,[status(thm)],[3]) ).
tff(40,plain,
isPrime0(xr),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,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(42,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)],[41,40]) ).
tff(43,plain,
~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ),
inference(unit_resolution,[status(thm)],[42,37]) ).
tff(44,plain,
( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) )
| ( xr != sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(45,plain,
xr != sz00,
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( doDivides0(xr,xn)
<=> doDivides0(xr,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
tff(48,plain,
doDivides0(xr,xn),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(51,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[50]) ).
tff(52,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[51]) ).
tff(53,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[52,49]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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(57,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
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(transitivity,[status(thm)],[57,55]) ).
tff(59,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(60,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( 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] :
( ! [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(62,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(63,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)],[62]) ).
tff(64,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(65,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,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)],[66]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[68,58]) ).
tff(70,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(71,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(72,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) )
<=> ( ~ ! [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)],[72,70]) ).
tff(74,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( 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(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) ) ) )
| ~ 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)],[74,73]) ).
tff(76,plain,
( ( xr = sz00 )
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ) ),
inference(unit_resolution,[status(thm)],[75,69,53,6,48]) ).
tff(77,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(xn,xr) ) ),
inference(unit_resolution,[status(thm)],[76,45]) ).
tff(78,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(79,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)],[78,77]) ).
tff(80,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(81,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)],[80]) ).
tff(82,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(83,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
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(transitivity,[status(thm)],[83,81]) ).
tff(85,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(86,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)],[85]) ).
tff(87,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(88,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(89,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)],[88]) ).
tff(90,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(91,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,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)],[91,87]) ).
tff(93,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)],[92]) ).
tff(94,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[94,84]) ).
tff(96,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(97,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(98,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) )
| ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) )
| ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) )
<=> ( ~ ! [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)],[98,96]) ).
tff(100,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ 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(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)
| ! [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)],[100,99]) ).
tff(102,plain,
~ ( ~ ( doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ) ),
inference(unit_resolution,[status(thm)],[101,95,53,6]) ).
tff(103,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(104,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)],[103,102]) ).
tff(105,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(106,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)],[105,48]) ).
tff(107,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ),
inference(unit_resolution,[status(thm)],[106,104]) ).
tff(108,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) )
<=> ( tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr) ) )
| ~ 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(109,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)],[108,107]) ).
tff(110,plain,
tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr),
inference(unit_resolution,[status(thm)],[109,79]) ).
tff(111,plain,
( aNaturalNumber0(tptp_fun_W2_1(xn,xr))
<=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,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(113,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xr)),
inference(unit_resolution,[status(thm)],[112,107]) ).
tff(114,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(modus_ponens,[status(thm)],[113,111]) ).
tff(115,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[51]) ).
tff(117,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,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(119,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)],[118]) ).
tff(120,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(121,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)],[120]) ).
tff(122,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(123,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(124,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)],[123]) ).
tff(125,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(126,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[127]) ).
tff(129,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[128,121]) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[129,119]) ).
tff(131,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
( ( aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,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(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,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(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(transitivity,[status(thm)],[133,131]) ).
tff(135,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(136,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(unit_resolution,[status(thm)],[136,130,117,114]) ).
tff(138,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,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(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(141,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(144,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(146,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[146,142]) ).
tff(148,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[148,141]) ).
tff(150,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[149,139]) ).
tff(151,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ) ),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ) ),
inference(transitivity,[status(thm)],[153,151]) ).
tff(155,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
( ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(unit_resolution,[status(thm)],[156,150,6]) ).
tff(158,plain,
sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(unit_resolution,[status(thm)],[157,137]) ).
tff(159,plain,
( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
<=> ( sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) = sdtasdt0(xn,xm) ) ),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
<=> ( sdtasdt0(xn,xm) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(transitivity,[status(thm)],[159,1]) ).
tff(161,plain,
( ( sdtasdt0(xn,xm) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) )
<=> ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) ) ),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
sdtasdt0(tptp_fun_W2_1(xn,xr),xm) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(monotonicity,[status(thm)],[110]) ).
tff(163,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(tptp_fun_W2_1(xn,xr),xm),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(167,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(169,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(172,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) ),
inference(quant_intro,[status(thm)],[171]) ).
tff(173,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
tff(174,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
inference(skolemize,[status(sab)],[175]) ).
tff(177,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[176,169]) ).
tff(178,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[177,167]) ).
tff(179,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,plain,
( ( ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ~ aNaturalNumber0(xr) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ~ aNaturalNumber0(xr) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) ) ) ),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ~ aNaturalNumber0(xr) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) ) ) ),
inference(transitivity,[status(thm)],[181,179]) ).
tff(183,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ~ aNaturalNumber0(xr) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)) ) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xr,sdtasdt0(tptp_fun_W2_1(xn,xr),xm)),
inference(unit_resolution,[status(thm)],[184,178,117,6,113]) ).
tff(186,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) )
| ( xn = sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(187,plain,
xn = sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),
inference(unit_resolution,[status(thm)],[186,107]) ).
tff(188,plain,
sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) = xn,
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm) = sdtasdt0(xn,xm),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
sdtasdt0(xn,xm) = sdtasdt0(sdtasdt0(xr,tptp_fun_W2_1(xn,xr)),xm),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(transitivity,[status(thm)],[190,185,165]) ).
tff(192,plain,
sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm),
inference(modus_ponens,[status(thm)],[191,161]) ).
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)],[195,130,53,117]) ).
tff(197,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
<=> doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,axiom,
( sdtlseqdt0(xr,xk)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
tff(199,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(and_elim,[status(thm)],[198]) ).
tff(200,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(modus_ponens,[status(thm)],[199,197]) ).
tff(201,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(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),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(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(202,plain,
( ( ( xr = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),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(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) ) ) ),
inference(monotonicity,[status(thm)],[202]) ).
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) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),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(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) ) ) ),
inference(transitivity,[status(thm)],[203,201]) ).
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) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(206,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(sdtasdt0(xn,xm))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) ) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
( ( xr = sz00 )
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) ) ),
inference(unit_resolution,[status(thm)],[206,69,6,200,196]) ).
tff(208,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) ),
inference(unit_resolution,[status(thm)],[207,45]) ).
tff(209,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xr) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xm),xr) = sdtsldt0(sdtasdt0(xn,xm),xr) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xm),xr) = sdtsldt0(sdtasdt0(xn,xm),xr) ) ),
inference(unit_resolution,[status(thm)],[209,208]) ).
tff(211,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(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),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(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(212,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,plain,
( ~ ( ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[214,212]) ).
tff(216,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(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != 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(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,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(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != 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(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[216,211]) ).
tff(218,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(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) )
| ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(219,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(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
~ ( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ) ),
inference(unit_resolution,[status(thm)],[219,95,6,196]) ).
tff(221,plain,
( ~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,W2) ) ) )
| ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) )
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(222,plain,
( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ),
inference(unit_resolution,[status(thm)],[221,220]) ).
tff(223,plain,
( ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) )
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(224,plain,
( ~ ( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ),
inference(unit_resolution,[status(thm)],[223,200]) ).
tff(225,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ),
inference(unit_resolution,[status(thm)],[224,222]) ).
tff(226,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xm),xr) = sdtsldt0(sdtasdt0(xn,xm),xr) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
| ( tptp_fun_W2_1(sdtasdt0(xn,xm),xr) = sdtsldt0(sdtasdt0(xn,xm),xr) ) ),
inference(tautology,[status(thm)],[]) ).
tff(227,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xm),xr) = sdtsldt0(sdtasdt0(xn,xm),xr) ) )
| ( tptp_fun_W2_1(sdtasdt0(xn,xm),xr) = sdtsldt0(sdtasdt0(xn,xm),xr) ) ),
inference(unit_resolution,[status(thm)],[226,225]) ).
tff(228,plain,
tptp_fun_W2_1(sdtasdt0(xn,xm),xr) = sdtsldt0(sdtasdt0(xn,xm),xr),
inference(unit_resolution,[status(thm)],[227,210]) ).
tff(229,plain,
sdtsldt0(sdtasdt0(xn,xm),xr) = tptp_fun_W2_1(sdtasdt0(xn,xm),xr),
inference(symmetry,[status(thm)],[228]) ).
tff(230,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[50]) ).
tff(232,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[231,230]) ).
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(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,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(xn,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(234,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(235,plain,
( ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(236,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[236,234]) ).
tff(238,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(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,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(xn,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,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(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,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(xn,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[238,233]) ).
tff(240,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(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,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(xn,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ) ),
inference(unit_resolution,[status(thm)],[241,95,232,196]) ).
tff(243,plain,
( ~ ( doDivides0(xp,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) )
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(244,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ),
inference(unit_resolution,[status(thm)],[243,242]) ).
tff(245,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(246,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
tff(247,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(and_elim,[status(thm)],[246]) ).
tff(248,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(modus_ponens,[status(thm)],[247,245]) ).
tff(249,plain,
( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) )
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(250,plain,
( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ) ),
inference(unit_resolution,[status(thm)],[249,248]) ).
tff(251,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ),
inference(unit_resolution,[status(thm)],[250,244]) ).
tff(252,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(253,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[252,251]) ).
tff(254,plain,
sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm),
inference(symmetry,[status(thm)],[253]) ).
tff(255,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(256,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(257,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)],[256]) ).
tff(258,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)],[257,255]) ).
tff(259,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(260,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)],[259,258]) ).
tff(261,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)],[260,28,232]) ).
tff(262,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(263,plain,
( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ),
inference(unit_resolution,[status(thm)],[262,261]) ).
tff(264,plain,
( isPrime0(xp)
<=> isPrime0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(265,plain,
isPrime0(xp),
inference(and_elim,[status(thm)],[246]) ).
tff(266,plain,
isPrime0(xp),
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,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(268,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)],[267,266]) ).
tff(269,plain,
~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ),
inference(unit_resolution,[status(thm)],[268,263]) ).
tff(270,plain,
( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ( xp != sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(271,plain,
xp != sz00,
inference(unit_resolution,[status(thm)],[270,269]) ).
tff(272,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)
| ( xp = sz00 )
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ 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)
| ( xp = sz00 )
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ 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(273,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)
| ( xp = sz00 )
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ 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(274,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)
| ( xp = sz00 )
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ) ),
inference(monotonicity,[status(thm)],[273]) ).
tff(275,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)
| ( xp = sz00 )
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ) ),
inference(transitivity,[status(thm)],[274,272]) ).
tff(276,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(277,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)
| ( xp = sz00 )
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ 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)],[276,275]) ).
tff(278,plain,
( ( xp = sz00 )
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ),
inference(unit_resolution,[status(thm)],[277,69,232,248,196]) ).
tff(279,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
inference(unit_resolution,[status(thm)],[278,271]) ).
tff(280,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(281,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
inference(unit_resolution,[status(thm)],[280,279]) ).
tff(282,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W2_1(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(283,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) )
| ( tptp_fun_W2_1(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
inference(unit_resolution,[status(thm)],[282,251]) ).
tff(284,plain,
tptp_fun_W2_1(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(unit_resolution,[status(thm)],[283,281]) ).
tff(285,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = tptp_fun_W2_1(sdtasdt0(xn,xm),xp),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
( ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(287,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
tff(288,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(modus_ponens,[status(thm)],[287,286]) ).
tff(289,plain,
xk = tptp_fun_W2_1(sdtasdt0(xn,xm),xp),
inference(transitivity,[status(thm)],[288,285]) ).
tff(290,plain,
sdtasdt0(xp,xk) = sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xm),xp)),
inference(monotonicity,[status(thm)],[289]) ).
tff(291,plain,
sdtasdt0(xp,xk) = sdtasdt0(xn,xm),
inference(transitivity,[status(thm)],[290,254]) ).
tff(292,plain,
sdtsldt0(sdtasdt0(xp,xk),xr) = sdtsldt0(sdtasdt0(xn,xm),xr),
inference(monotonicity,[status(thm)],[291]) ).
tff(293,plain,
sdtsldt0(sdtasdt0(xp,xk),xr) = tptp_fun_W2_1(sdtasdt0(xn,xm),xr),
inference(transitivity,[status(thm)],[292,229]) ).
tff(294,plain,
sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) = sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr),
inference(monotonicity,[status(thm)],[293]) ).
tff(295,plain,
sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
| aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ),
inference(tautology,[status(thm)],[]) ).
tff(297,plain,
aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr)),
inference(unit_resolution,[status(thm)],[296,225]) ).
tff(298,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(299,plain,
( ( ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
<=> ( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(300,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ) ),
inference(transitivity,[status(thm)],[300,298]) ).
tff(302,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(303,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ),
inference(modus_ponens,[status(thm)],[302,301]) ).
tff(304,plain,
sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)),
inference(unit_resolution,[status(thm)],[303,150,6,297]) ).
tff(305,plain,
sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) = sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr),xr),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xm),xr))
| ( sdtasdt0(xn,xm) != sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(307,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,tptp_fun_W2_1(sdtasdt0(xn,xm),xr)),
inference(unit_resolution,[status(thm)],[306,225]) ).
tff(308,plain,
sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr),
inference(transitivity,[status(thm)],[307,305,295]) ).
tff(309,plain,
( ~ ~ ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
| ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) )
<=> ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
| ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(310,plain,
( ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
& ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) )
<=> ~ ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
| ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(311,plain,
( ~ ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
& ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) )
<=> ~ ~ ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
| ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ) ),
inference(monotonicity,[status(thm)],[310]) ).
tff(312,plain,
( ~ ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
& ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) )
<=> ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
| ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ) ),
inference(transitivity,[status(thm)],[311,309]) ).
tff(313,plain,
( ~ ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
& ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) )
<=> ~ ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
& ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(314,axiom,
~ ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
& ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(315,plain,
~ ( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
& ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ),
inference(modus_ponens,[status(thm)],[314,313]) ).
tff(316,plain,
( ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
| ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ),
inference(modus_ponens,[status(thm)],[315,312]) ).
tff(317,plain,
sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm),
inference(unit_resolution,[status(thm)],[316,308]) ).
tff(318,plain,
$false,
inference(unit_resolution,[status(thm)],[317,192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM512+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 01:19:50 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.84/1.05 % SZS status Theorem
% 0.84/1.05 % SZS output start Proof
% See solution above
% 0.92/1.11 % E exiting
%------------------------------------------------------------------------------