TSTP Solution File: NUM513+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM513+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sun Sep 18 13:10:11 EDT 2022
% Result : Theorem 87.61s 55.21s
% Output : Proof 87.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 117
% Syntax : Number of formulae : 281 ( 67 unt; 14 typ; 0 def)
% Number of atoms : 3313 (1341 equ)
% Maximal formula atoms : 60 ( 12 avg)
% Number of connectives : 5334 (2437 ~;2242 |; 290 &)
% ( 309 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 149 ( 149 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 2 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 702 ( 641 !; 15 ?; 702 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xr_type,type,
xr: $i ).
tff(xn_type,type,
xn: $i ).
tff(xp_type,type,
xp: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
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(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(1,plain,
( aNaturalNumber0(xr)
<=> aNaturalNumber0(xr) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
tff(3,plain,
( aNaturalNumber0(xr)
& doDivides0(xr,xk) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xr),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aNaturalNumber0(xr),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [W0: $i] :
rewrite(
( ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
refl(
( ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(
( ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[11,9]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(
( ( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [W0: $i] :
rewrite(
( ( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( isPrime0(W0)
| ~ ( ( W0 != sz00 ) )
| ~ ( ( W0 != sz10 ) )
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( isPrime0(W0)
| ~ ( ( W0 != sz00 ) )
| ~ ( ( W0 != sz10 ) )
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) )
<=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) )
<=> ( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) )),
rewrite(
( ( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
tff(21,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( isPrime0(W0)
| ~ ( ( W0 != sz00 ) )
| ~ ( ( W0 != sz10 ) )
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& doDivides0(W1,W0) ) ) ) )
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_2(W0))
& doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,14]) ).
tff(26,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) )
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,12]) ).
tff(27,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,7]) ).
tff(28,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( 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 = 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 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( ( xr = sz00 )
| ( xr = sz10 )
| isPrime0(xr)
| ~ ( ( tptp_fun_W1_2(xr) = xr )
| ( tptp_fun_W1_2(xr) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xr))
| ~ doDivides0(tptp_fun_W1_2(xr),xr) ) )
| ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xr )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xr) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xr)
| ~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ ( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ) ),
inference(unit_resolution,[status(thm)],[33,27,5]) ).
tff(35,plain,
( ~ ( isPrime0(xr)
| ( xr = sz00 )
| ( xr = sz10 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) )
| ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(36,plain,
( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( isPrime0(xr)
<=> isPrime0(xr) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
isPrime0(xr),
inference(and_elim,[status(thm)],[2]) ).
tff(39,plain,
isPrime0(xr),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) )
| ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(41,plain,
( ~ ( ~ isPrime0(xr)
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) )
| ~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ) ),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
~ ( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) ) ),
inference(unit_resolution,[status(thm)],[41,36]) ).
tff(43,plain,
( ( xr = sz00 )
| ( xr = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xr )
| ~ doDivides0(W1,xr) )
| ( xr != sz00 ) ),
inference(tautology,[status(thm)],]) ).
tff(44,plain,
xr != sz00,
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( doDivides0(xr,xn)
<=> doDivides0(xr,xn) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
tff(47,plain,
doDivides0(xr,xn),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(50,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[49]) ).
tff(51,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[50]) ).
tff(52,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[51,48]) ).
tff(53,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(
monotonicity(
rewrite(
( ( ( W0 != 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) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
rewrite(
( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i] :
rewrite(
( ( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
<=> ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ))),
( ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
<=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )),
( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
rewrite(
( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
tff(66,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[69,59]) ).
tff(71,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
inference(modus_ponens,[status(thm)],[70,54]) ).
tff(72,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ( xr = sz00 )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ) ),
inference(unit_resolution,[status(thm)],[77,71,52,5,47]) ).
tff(79,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) ),
inference(unit_resolution,[status(thm)],[78,44]) ).
tff(80,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[50]) ).
tff(82,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) )
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xm,xn),xr) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) )
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xm,xn),xr) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) )
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xm,xn),xr) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(W2,xn),xr) ) )
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xm,xn),xr) ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xm,xn),xr),
inference(unit_resolution,[status(thm)],[85,82,79]) ).
tff(87,plain,
sdtsldt0(sdtasdt0(xm,xn),xr) = sdtasdt0(xm,sdtsldt0(xn,xr)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,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(89,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)],[88]) ).
tff(90,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(91,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)],[90]) ).
tff(92,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(93,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(94,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)],[93]) ).
tff(95,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(96,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[99,89]) ).
tff(101,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ) ),
inference(transitivity,[status(thm)],[103,101]) ).
tff(105,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(unit_resolution,[status(thm)],[106,100,52,82]) ).
tff(108,plain,
sdtsldt0(sdtasdt0(xm,xn),xr) = sdtsldt0(sdtasdt0(xn,xm),xr),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
sdtsldt0(sdtasdt0(xn,xm),xr) = sdtsldt0(sdtasdt0(xm,xn),xr),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[49]) ).
tff(112,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,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 )
| ~ ( ( 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 = 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 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,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 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,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 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,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 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[115,113]) ).
tff(117,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(118,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 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ( 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 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ),
inference(unit_resolution,[status(thm)],[118,27,112]) ).
tff(120,plain,
( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ( 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 = 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(121,plain,
( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ),
inference(unit_resolution,[status(thm)],[120,119]) ).
tff(122,plain,
( isPrime0(xp)
<=> isPrime0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(123,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(124,plain,
isPrime0(xp),
inference(and_elim,[status(thm)],[123]) ).
tff(125,plain,
isPrime0(xp),
inference(modus_ponens,[status(thm)],[124,122]) ).
tff(126,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(127,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)],[126,125]) ).
tff(128,plain,
~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ),
inference(unit_resolution,[status(thm)],[127,121]) ).
tff(129,plain,
( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ( xp != sz00 ) ),
inference(tautology,[status(thm)],]) ).
tff(130,plain,
xp != sz00,
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,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(132,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)],[131]) ).
tff(133,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(134,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)],[133]) ).
tff(135,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(136,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(137,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)],[136]) ).
tff(138,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(139,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[139,135]) ).
tff(141,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[140]) ).
tff(142,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[141,134]) ).
tff(143,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[142,132]) ).
tff(144,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(145,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(146,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)],[145,144]) ).
tff(147,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(unit_resolution,[status(thm)],[146,143,52,82]) ).
tff(148,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(and_elim,[status(thm)],[123]) ).
tff(150,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(152,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[151]) ).
tff(153,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(154,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[153]) ).
tff(155,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[154,152]) ).
tff(156,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i] :
rewrite(
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
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] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
rewrite(
( ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [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) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(157,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] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,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(159,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(160,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)],[159]) ).
tff(161,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
tff(162,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)],[161,160]) ).
tff(163,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)],[162,158]) ).
tff(164,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)],[163]) ).
tff(165,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[164,157]) ).
tff(166,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[165,155]) ).
tff(167,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(168,plain,
( ( ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ) ),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[169,167]) ).
tff(171,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
( ( xp = sz00 )
| ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[172,166,112,150,147]) ).
tff(174,plain,
! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) ),
inference(unit_resolution,[status(thm)],[173,130]) ).
tff(175,plain,
( ( ~ ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) )
<=> ( ~ ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,plain,
( ( $true
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) )
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,plain,
( ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) )
<=> ( $true
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ( ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) )
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ),
inference(transitivity,[status(thm)],[178,176]) ).
tff(180,plain,
( ( ~ ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ( ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) )
<=> ( ~ ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ( ~ ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ( ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) )
<=> ( ~ ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) ),
inference(transitivity,[status(thm)],[180,175]) ).
tff(182,plain,
( ~ ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ( ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( ~ ! [W2: $i] :
( ( W2 = sdtsldt0(sdtasdt0(xn,xm),xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
~ ( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ),
inference(unit_resolution,[status(thm)],[183,174]) ).
tff(185,plain,
( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ) ),
inference(tautology,[status(thm)],]) ).
tff(186,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[185,184]) ).
tff(187,plain,
sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) = sdtsldt0(sdtasdt0(xn,xm),xr),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ( sdtasdt0(xn,xm) != sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) )
| aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(tautology,[status(thm)],]) ).
tff(190,plain,
aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[189,184]) ).
tff(191,plain,
( doDivides0(xr,xk)
<=> doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(rewrite,[status(thm)],]) ).
tff(192,plain,
( doDivides0(xr,xk)
<=> doDivides0(xr,xk) ),
inference(rewrite,[status(thm)],]) ).
tff(193,plain,
doDivides0(xr,xk),
inference(and_elim,[status(thm)],[3]) ).
tff(194,plain,
doDivides0(xr,xk),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp)),
inference(modus_ponens,[status(thm)],[194,191]) ).
tff(196,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(197,plain,
( ( ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) )
<=> ( ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(198,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) ) ),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) ) ),
inference(transitivity,[status(thm)],[198,196]) ).
tff(200,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(201,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) ),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,plain,
( ( xr = sz00 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) ),
inference(unit_resolution,[status(thm)],[201,71,5,195]) ).
tff(203,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ),
inference(unit_resolution,[status(thm)],[202,190,44]) ).
tff(204,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) )
| ~ aNaturalNumber0(xp)
| ( sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) )
| ~ aNaturalNumber0(xp)
| ( sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(205,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) )
| ~ aNaturalNumber0(xp)
| ( sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(206,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(W2,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) )
| ~ aNaturalNumber0(xp)
| ( sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr) ) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr),
inference(unit_resolution,[status(thm)],[206,112,203]) ).
tff(208,plain,
sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtasdt0(xm,sdtsldt0(xn,xr)),
inference(transitivity,[status(thm)],[207,188,109,87]) ).
tff(209,plain,
( ( sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
<=> ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
( ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
<=> ( sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(212,plain,
( ( ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) ),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[213,211]) ).
tff(215,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(216,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ( xr = sz00 )
| ~ doDivides0(xr,xn)
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
( ( xr = sz00 )
| ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[216,166,52,5,47]) ).
tff(218,plain,
! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) ),
inference(unit_resolution,[status(thm)],[217,44]) ).
tff(219,plain,
( ~ ! [W2: $i] :
( ( W2 = sdtsldt0(xn,xr) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xr,W2) ) ) )
| ( ( 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)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
( ( 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)) ) ) ),
inference(unit_resolution,[status(thm)],[219,218]) ).
tff(221,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(222,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)],[221]) ).
tff(223,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(224,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)],[223]) ).
tff(225,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)],[224,222]) ).
tff(226,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(227,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)],[226]) ).
tff(228,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(229,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(230,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)],[229]) ).
tff(231,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
tff(232,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)],[231,230]) ).
tff(233,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)],[232,228]) ).
tff(234,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)],[233]) ).
tff(235,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[234,227]) ).
tff(236,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)],[235,225]) ).
tff(237,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)
| ~ ( ~ 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(rewrite,[status(thm)],]) ).
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(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(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(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(modus_ponens,[status(thm)],[238,237]) ).
tff(240,plain,
~ ( ~ ( ~ 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(unit_resolution,[status(thm)],[239,236,52,5]) ).
tff(241,plain,
( ~ ( ~ 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) ) ) )
| ~ doDivides0(xr,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(242,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)],[241,240]) ).
tff(243,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(244,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)],[243,47]) ).
tff(245,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ),
inference(unit_resolution,[status(thm)],[244,242]) ).
tff(246,plain,
( ~ ( ( 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) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xr))
| ( xn != sdtasdt0(xr,tptp_fun_W2_1(xn,xr)) ) ),
inference(tautology,[status(thm)],]) ).
tff(247,plain,
( ~ ( ( 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(unit_resolution,[status(thm)],[246,245]) ).
tff(248,plain,
tptp_fun_W2_1(xn,xr) = sdtsldt0(xn,xr),
inference(unit_resolution,[status(thm)],[247,220]) ).
tff(249,plain,
( aNaturalNumber0(tptp_fun_W2_1(xn,xr))
<=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,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(251,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xr)),
inference(unit_resolution,[status(thm)],[250,245]) ).
tff(252,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(modus_ponens,[status(thm)],[251,249]) ).
tff(253,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(254,plain,
( ( ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(255,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ) ),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ) ),
inference(transitivity,[status(thm)],[255,253]) ).
tff(257,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) )
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],]) ).
tff(258,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(modus_ponens,[status(thm)],[257,256]) ).
tff(259,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(unit_resolution,[status(thm)],[258,100,82]) ).
tff(260,plain,
sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(unit_resolution,[status(thm)],[259,252]) ).
tff(261,plain,
sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(modus_ponens,[status(thm)],[260,210]) ).
tff(262,plain,
( ( sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm) )
<=> ( sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) != sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(263,plain,
( ( sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm) )
<=> ( sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(264,axiom,
sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(265,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm),
inference(modus_ponens,[status(thm)],[264,263]) ).
tff(266,plain,
sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) != sdtasdt0(sdtsldt0(xn,xr),xm),
inference(modus_ponens,[status(thm)],[265,262]) ).
tff(267,plain,
$false,
inference(unit_resolution,[status(thm)],[266,261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM513+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 11:18:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 87.61/55.21 % SZS status Theorem
% 87.61/55.21 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------