%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM496+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:10 AM UTC 2025
% Result : Theorem 0.18s 0.48s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 83
% Syntax : Number of formulae : 219 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 3069 (1120 equ)
% Maximal formula atoms : 60 ( 14 avg)
% Number of connectives : 4987 (2277 ~;2066 |; 344 &)
% ( 255 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 140 ( 140 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 515 ( 449 !; 30 ?; 515 :)
% Comments :
%------------------------------------------------------------------------------
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_0_type,type,
tptp_fun_W2_0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xn_type,type,
xn: $i ).
tff(xr_type,type,
xr: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xm_type,type,
xm: $i ).
tff(tptp_fun_W1_3_type,type,
tptp_fun_W1_3: $i > $i ).
tff(sz10_type,type,
sz10: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(tptp_fun_W1_2_type,type,
tptp_fun_W1_2: $i > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(1,plain,
( ( xr = sdtmndt0(xn,xp) )
<=> ( xr = sdtmndt0(xn,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
tff(3,plain,
xr = sdtmndt0(xn,xp),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sdtmndt0(xn,xp) = xr,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( sdtlseqdt0(xp,xn)
<=> sdtlseqdt0(xp,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
tff(7,plain,
sdtlseqdt0(xp,xn),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(10,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[9]) ).
tff(14,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[14,12]) ).
tff(16,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
rewrite(( ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
rewrite(( ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[37,31,15,11,7]) ).
tff(39,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) )
<=> ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) )
<=> ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,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(( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) ) )),
rewrite(( ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
( ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
rewrite(( ( ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
tff(52,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[55,45]) ).
tff(57,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ) ) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ ( ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ) ),
inference(unit_resolution,[status(thm)],[62,56,15,11]) ).
tff(64,plain,
( ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(65,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(67,plain,
( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(unit_resolution,[status(thm)],[66,7]) ).
tff(68,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ),
inference(unit_resolution,[status(thm)],[67,65]) ).
tff(69,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) )
<=> ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn )
| ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(70,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) )
<=> ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) ) )
| ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp),
inference(unit_resolution,[status(thm)],[70,40]) ).
tff(72,plain,
tptp_fun_W2_0(xn,xp) = xr,
inference(transitivity,[status(thm)],[71,4]) ).
tff(73,plain,
( doDivides0(xp,tptp_fun_W2_0(xn,xp))
<=> doDivides0(xp,xr) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( doDivides0(xp,xr)
<=> doDivides0(xp,tptp_fun_W2_0(xn,xp)) ),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ doDivides0(xp,xm)
<=> ~ doDivides0(xp,xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,axiom,
~ ( doDivides0(xp,xn)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(77,plain,
~ doDivides0(xp,xm),
inference(or_elim,[status(thm)],[76]) ).
tff(78,plain,
~ doDivides0(xp,xm),
inference(modus_ponens,[status(thm)],[77,75]) ).
tff(79,plain,
( ( doDivides0(xp,xr)
| doDivides0(xp,xm) )
<=> ( doDivides0(xp,xr)
| doDivides0(xp,xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,axiom,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2027) ).
tff(81,plain,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(modus_ponens,[status(thm)],[81,79]) ).
tff(83,plain,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(modus_ponens,[status(thm)],[82,79]) ).
tff(84,plain,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(modus_ponens,[status(thm)],[84,79]) ).
tff(86,plain,
doDivides0(xp,xr),
inference(unit_resolution,[status(thm)],[85,78]) ).
tff(87,plain,
doDivides0(xp,tptp_fun_W2_0(xn,xp)),
inference(modus_ponens,[status(thm)],[86,74]) ).
tff(88,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn )
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) = xn ) ),
inference(tautology,[status(thm)],[]) ).
tff(89,plain,
sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) = xn,
inference(unit_resolution,[status(thm)],[88,68]) ).
tff(90,plain,
( doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
<=> doDivides0(xp,xn) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( doDivides0(xp,xn)
<=> doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp))) ),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ doDivides0(xp,xn)
<=> ~ doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp))) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ~ doDivides0(xp,xn)
<=> ~ doDivides0(xp,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
~ doDivides0(xp,xn),
inference(or_elim,[status(thm)],[76]) ).
tff(95,plain,
~ doDivides0(xp,xn),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
~ doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp))),
inference(modus_ponens,[status(thm)],[95,92]) ).
tff(97,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(98,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)],[97]) ).
tff(99,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(100,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)],[99]) ).
tff(101,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(102,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)],[101]) ).
tff(103,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)],[102,100]) ).
tff(104,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(105,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)],[104]) ).
tff(106,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(107,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)],[106]) ).
tff(108,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(109,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(110,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)],[109]) ).
tff(111,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
tff(112,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)],[111,110]) ).
tff(113,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)],[112,108]) ).
tff(114,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)],[113]) ).
tff(115,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)],[114,107]) ).
tff(116,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)],[115,105]) ).
tff(117,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)],[116,103]) ).
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) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[117,98]) ).
tff(119,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ( ~ aNaturalNumber0(xp)
| ~ ( ~ ( ( xp = sz00 )
| ( xp = sz10 )
| isPrime0(xp)
| ~ ( ( tptp_fun_W1_2(xp) = xp )
| ( tptp_fun_W1_2(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ~ doDivides0(tptp_fun_W1_2(xp),xp) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xp )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xp) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ( xp = sz00 )
| ( xp = sz10 )
| isPrime0(xp)
| ~ ( ( tptp_fun_W1_2(xp) = xp )
| ( tptp_fun_W1_2(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ~ doDivides0(tptp_fun_W1_2(xp),xp) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xp )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xp) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ( xp = sz00 )
| ( xp = sz10 )
| isPrime0(xp)
| ~ ( ( tptp_fun_W1_2(xp) = xp )
| ( tptp_fun_W1_2(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ~ doDivides0(tptp_fun_W1_2(xp),xp) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = xp )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,xp) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[121,119]) ).
tff(123,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(124,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| isPrime0(W0)
| ~ ( ( tptp_fun_W1_2(W0) = W0 )
| ( tptp_fun_W1_2(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(W0))
| ~ doDivides0(tptp_fun_W1_2(W0),W0) ) )
| ~ ( ~ isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
~ ( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ) ),
inference(unit_resolution,[status(thm)],[124,118,11]) ).
tff(126,plain,
( ~ ( isPrime0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(xp),xp)
| ~ aNaturalNumber0(tptp_fun_W1_2(xp))
| ( tptp_fun_W1_2(xp) = sz10 )
| ( tptp_fun_W1_2(xp) = xp ) ) )
| ~ ( ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) )
| ~ isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(127,plain,
( ~ isPrime0(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,
( isPrime0(xp)
<=> isPrime0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
tff(130,plain,
isPrime0(xp),
inference(and_elim,[status(thm)],[129]) ).
tff(131,plain,
isPrime0(xp),
inference(modus_ponens,[status(thm)],[130,128]) ).
tff(132,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(133,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)],[132,131]) ).
tff(134,plain,
~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ),
inference(unit_resolution,[status(thm)],[133,127]) ).
tff(135,plain,
( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ( xp != sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(136,plain,
xp != sz00,
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ( xp != sz10 ) ),
inference(tautology,[status(thm)],[]) ).
tff(138,plain,
xp != sz10,
inference(unit_resolution,[status(thm)],[137,134]) ).
tff(139,plain,
^ [W0: $i] :
refl(( ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
<=> ~ ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
<=> ~ ~ ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )),
rewrite(( ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )),
( ( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
<=> ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) ) )),
quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) )
<=> ( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ))),
( ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) )
<=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )),
( ( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,axiom,
! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
tff(147,plain,
! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) ) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ),
inference(modus_ponens,[status(thm)],[150,140]) ).
tff(152,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ~ aNaturalNumber0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ~ aNaturalNumber0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,plain,
( ( ( xp = sz00 )
| ( xp = sz10 )
| ~ aNaturalNumber0(xp)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) )
<=> ( ~ aNaturalNumber0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,plain,
( ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ( ( xp = sz00 )
| ( xp = sz10 )
| ~ aNaturalNumber0(xp)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) )
<=> ( ( xp = sz00 )
| ( xp = sz10 )
| ~ aNaturalNumber0(xp)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ) ),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
( ( ( xp = sz00 )
| ( xp = sz10 )
| ~ aNaturalNumber0(xp)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) )
<=> ( ~ aNaturalNumber0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ) ),
inference(transitivity,[status(thm)],[155,153]) ).
tff(157,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ( xp = sz00 )
| ( xp = sz10 )
| ~ aNaturalNumber0(xp)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ~ aNaturalNumber0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ) ),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ( xp = sz00 )
| ( xp = sz10 )
| ~ aNaturalNumber0(xp)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ~ aNaturalNumber0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ) ),
inference(transitivity,[status(thm)],[157,152]) ).
tff(159,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ( xp = sz00 )
| ( xp = sz10 )
| ~ aNaturalNumber0(xp)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ~ aNaturalNumber0(xp)
| ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ) ),
inference(unit_resolution,[status(thm)],[160,151,11]) ).
tff(162,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp)) ),
inference(unit_resolution,[status(thm)],[161,138,136]) ).
tff(163,plain,
( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp))
| aNaturalNumber0(tptp_fun_W1_3(xp)) ),
inference(tautology,[status(thm)],[]) ).
tff(164,plain,
aNaturalNumber0(tptp_fun_W1_3(xp)),
inference(unit_resolution,[status(thm)],[163,162]) ).
tff(165,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(tptp_fun_W1_3(xp))
| ~ ( ~ ( isPrime0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp))
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) ) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(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(tptp_fun_W1_3(xp))
| ~ ( ~ ( isPrime0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp))
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) ) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
( ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ ( ~ ( ( tptp_fun_W1_3(xp) = sz00 )
| ( tptp_fun_W1_3(xp) = sz10 )
| isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp)) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz00 )
| ( tptp_fun_W1_3(xp) = sz10 )
| ~ ! [W1: $i] :
( ( W1 = tptp_fun_W1_3(xp) )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ ( ~ ( isPrime0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp))
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) ) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,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(tptp_fun_W1_3(xp))
| ~ ( ~ ( ( tptp_fun_W1_3(xp) = sz00 )
| ( tptp_fun_W1_3(xp) = sz10 )
| isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp)) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz00 )
| ( tptp_fun_W1_3(xp) = sz10 )
| ~ ! [W1: $i] :
( ( W1 = tptp_fun_W1_3(xp) )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,tptp_fun_W1_3(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(tptp_fun_W1_3(xp))
| ~ ( ~ ( isPrime0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp))
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) ) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,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(tptp_fun_W1_3(xp))
| ~ ( ~ ( ( tptp_fun_W1_3(xp) = sz00 )
| ( tptp_fun_W1_3(xp) = sz10 )
| isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp)) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz00 )
| ( tptp_fun_W1_3(xp) = sz10 )
| ~ ! [W1: $i] :
( ( W1 = tptp_fun_W1_3(xp) )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,tptp_fun_W1_3(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(tptp_fun_W1_3(xp))
| ~ ( ~ ( isPrime0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp))
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) ) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[167,165]) ).
tff(169,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(tptp_fun_W1_3(xp))
| ~ ( ~ ( ( tptp_fun_W1_3(xp) = sz00 )
| ( tptp_fun_W1_3(xp) = sz10 )
| isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp)) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz00 )
| ( tptp_fun_W1_3(xp) = sz10 )
| ~ ! [W1: $i] :
( ( W1 = tptp_fun_W1_3(xp) )
| ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,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(tptp_fun_W1_3(xp))
| ~ ( ~ ( isPrime0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp))
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) ) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
~ ( ~ ( isPrime0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp))
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) ) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ) ),
inference(unit_resolution,[status(thm)],[170,118,164]) ).
tff(172,plain,
( ~ ( isPrime0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ( ~ doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)),tptp_fun_W1_3(xp))
| ~ aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10 )
| ( tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp) ) ) )
| ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) )
| ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(173,plain,
( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ),
inference(unit_resolution,[status(thm)],[172,171]) ).
tff(174,plain,
( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp))
| isPrime0(tptp_fun_W1_3(xp)) ),
inference(tautology,[status(thm)],[]) ).
tff(175,plain,
isPrime0(tptp_fun_W1_3(xp)),
inference(unit_resolution,[status(thm)],[174,162]) ).
tff(176,plain,
( ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) )
| ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(177,plain,
( ~ ( ~ isPrime0(tptp_fun_W1_3(xp))
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) )
| ~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ) ),
inference(unit_resolution,[status(thm)],[176,175]) ).
tff(178,plain,
~ ( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) ) ),
inference(unit_resolution,[status(thm)],[177,173]) ).
tff(179,plain,
( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = sz00 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = tptp_fun_W1_3(xp) )
| ~ doDivides0(W1,tptp_fun_W1_3(xp)) )
| ( tptp_fun_W1_3(xp) != sz10 ) ),
inference(tautology,[status(thm)],[]) ).
tff(180,plain,
tptp_fun_W1_3(xp) != sz10,
inference(unit_resolution,[status(thm)],[179,178]) ).
tff(181,plain,
( ( xp = sz00 )
| ( xp = sz10 )
| ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(182,plain,
! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) ),
inference(unit_resolution,[status(thm)],[181,134]) ).
tff(183,plain,
( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ~ isPrime0(tptp_fun_W1_3(xp))
| doDivides0(tptp_fun_W1_3(xp),xp) ),
inference(tautology,[status(thm)],[]) ).
tff(184,plain,
doDivides0(tptp_fun_W1_3(xp),xp),
inference(unit_resolution,[status(thm)],[183,162]) ).
tff(185,plain,
( ( ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = xp ) )
<=> ( ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = xp ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
( ( ( tptp_fun_W1_3(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = xp )
| ~ doDivides0(tptp_fun_W1_3(xp),xp) )
<=> ( ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = xp ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
( ( ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ( tptp_fun_W1_3(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = xp )
| ~ doDivides0(tptp_fun_W1_3(xp),xp) )
<=> ( ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = xp ) ) ),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ( ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ( tptp_fun_W1_3(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = xp )
| ~ doDivides0(tptp_fun_W1_3(xp),xp) )
<=> ( ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = xp ) ) ),
inference(transitivity,[status(thm)],[187,185]) ).
tff(189,plain,
( ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ( tptp_fun_W1_3(xp) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ( tptp_fun_W1_3(xp) = xp )
| ~ doDivides0(tptp_fun_W1_3(xp),xp) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
( ~ ! [W1: $i] :
( ( W1 = sz10 )
| ~ aNaturalNumber0(W1)
| ( W1 = xp )
| ~ doDivides0(W1,xp) )
| ~ aNaturalNumber0(tptp_fun_W1_3(xp))
| ~ doDivides0(tptp_fun_W1_3(xp),xp)
| ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = xp ) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
( ( tptp_fun_W1_3(xp) = sz10 )
| ( tptp_fun_W1_3(xp) = xp ) ),
inference(unit_resolution,[status(thm)],[190,164,184,182]) ).
tff(192,plain,
tptp_fun_W1_3(xp) = xp,
inference(unit_resolution,[status(thm)],[191,180]) ).
tff(193,plain,
xp = tptp_fun_W1_3(xp),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
( doDivides0(xp,xp)
<=> doDivides0(tptp_fun_W1_3(xp),xp) ),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
( doDivides0(tptp_fun_W1_3(xp),xp)
<=> doDivides0(xp,xp) ),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
doDivides0(xp,xp),
inference(modus_ponens,[status(thm)],[184,195]) ).
tff(197,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn )
| aNaturalNumber0(tptp_fun_W2_0(xn,xp)) ),
inference(tautology,[status(thm)],[]) ).
tff(198,plain,
aNaturalNumber0(tptp_fun_W2_0(xn,xp)),
inference(unit_resolution,[status(thm)],[197,68]) ).
tff(199,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
<=> ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) )),
inference(bind,[status(th)],[]) ).
tff(200,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) ),
inference(quant_intro,[status(thm)],[199]) ).
tff(201,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
<=> ~ ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) )),
( ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
<=> ~ ~ ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) )),
rewrite(( ~ ~ ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
<=> ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) )),
( ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
<=> ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) )),
( ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) )
<=> ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) )),
rewrite(( ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
<=> ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) )),
( ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) )
<=> ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) )),
inference(bind,[status(th)],[]) ).
tff(202,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(204,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
rewrite(( ( ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
=> doDivides0(W0,sdtpldt0(W1,W2)) )
<=> ( ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
| doDivides0(W0,sdtpldt0(W1,W2)) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
| doDivides0(W0,sdtpldt0(W1,W2)) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
| doDivides0(W0,sdtpldt0(W1,W2)) ) )
<=> ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) )
<=> ( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) ) )),
inference(bind,[status(th)],[]) ).
tff(205,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivSum) ).
tff(207,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) ),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) ),
inference(modus_ponens,[status(thm)],[207,203]) ).
tff(209,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,W2) ) ),
inference(skolemize,[status(sab)],[208]) ).
tff(210,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ),
inference(modus_ponens,[status(thm)],[209,202]) ).
tff(211,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) ),
inference(modus_ponens,[status(thm)],[210,200]) ).
tff(212,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,plain,
( ( doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
| doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) ) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
| doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) ) ),
inference(transitivity,[status(thm)],[214,212]) ).
tff(216,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
| doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,W2) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
( doDivides0(xp,sdtpldt0(xp,tptp_fun_W2_0(xn,xp)))
| ~ doDivides0(xp,xp)
| ~ doDivides0(xp,tptp_fun_W2_0(xn,xp)) ),
inference(unit_resolution,[status(thm)],[217,211,11,198]) ).
tff(219,plain,
$false,
inference(unit_resolution,[status(thm)],[218,196,96,87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM496+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n008.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 01:17:48 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 % SZS output start Proof
% See solution above
% 0.18/0.52 % E exiting
%------------------------------------------------------------------------------