%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM473+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:21:05 AM UTC 2025
% Result : Theorem 0.66s 0.83s
% Output : Proof 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 123
% Syntax : Number of formulae : 338 ( 83 unt; 0 typ; 0 def)
% Number of atoms : 3904 (1392 equ)
% Maximal formula atoms : 40 ( 11 avg)
% Number of connectives : 6146 (2835 ~;2371 |; 462 &)
% ( 389 <=>; 89 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 255 ( 255 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 816 ( 741 !; 15 ?; 816 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xl_type,type,
xl: $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xq_type,type,
xq: $i ).
tff(xp_type,type,
xp: $i ).
tff(1,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
tff(3,plain,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( aNaturalNumber0(xl)
<=> aNaturalNumber0(xl) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
aNaturalNumber0(xl),
inference(and_elim,[status(thm)],[3]) ).
tff(8,plain,
aNaturalNumber0(xl),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[12,10]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
<=> ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )),
rewrite(( ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
tff(20,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,13]) ).
tff(25,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[30,25]) ).
tff(32,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ),
inference(unit_resolution,[status(thm)],[33,24,8,5]) ).
tff(35,plain,
( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( doDivides0(xl,xm)
<=> doDivides0(xl,xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
tff(39,plain,
doDivides0(xl,xm),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
doDivides0(xl,xm),
inference(modus_ponens,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(42,plain,
( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ),
inference(unit_resolution,[status(thm)],[42,36]) ).
tff(44,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( xm = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(45,plain,
xm = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) = xm,
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| aNaturalNumber0(tptp_fun_W2_1(xm,xl)) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
aNaturalNumber0(tptp_fun_W2_1(xm,xl)),
inference(unit_resolution,[status(thm)],[47,43]) ).
tff(49,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(57,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[60,50]) ).
tff(62,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl)) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),
inference(unit_resolution,[status(thm)],[67,61,8,48]) ).
tff(69,plain,
sdtasdt0(tptp_fun_W2_1(xm,xl),xl) = xm,
inference(transitivity,[status(thm)],[68,46]) ).
tff(70,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[2]) ).
tff(72,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
^ [W0: $i,W1: $i] :
refl(( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
tff(81,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(unit_resolution,[status(thm)],[91,85,5,72]) ).
tff(93,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[98,93]) ).
tff(100,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ),
inference(unit_resolution,[status(thm)],[101,24,8,92]) ).
tff(103,plain,
( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
<=> doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(and_elim,[status(thm)],[38]) ).
tff(107,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(109,plain,
( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(unit_resolution,[status(thm)],[108,107]) ).
tff(110,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ),
inference(unit_resolution,[status(thm)],[109,104]) ).
tff(111,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtpldt0(xm,xn),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ),
inference(tautology,[status(thm)],[]) ).
tff(115,plain,
aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),
inference(unit_resolution,[status(thm)],[114,110]) ).
tff(116,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ( ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),
inference(unit_resolution,[status(thm)],[121,61,8,115]) ).
tff(123,plain,
sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtpldt0(xm,xn),
inference(transitivity,[status(thm)],[122,113]) ).
tff(124,plain,
( sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl))
<=> sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
inference(monotonicity,[status(thm)],[123,69]) ).
tff(125,plain,
( sdtlseqdt0(sdtpldt0(xm,xn),xm)
<=> sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
<=> ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ( xl != sz00 )
<=> ( xl != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,axiom,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
tff(129,plain,
xl != sz00,
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(133,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(transitivity,[status(thm)],[133,131]) ).
tff(135,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
rewrite(( ( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
rewrite(( ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ~ ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
rewrite(( ~ ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
rewrite(( ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(136,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
tff(141,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[143,136]) ).
tff(145,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[144,134]) ).
tff(146,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
( ( ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ),
inference(transitivity,[status(thm)],[148,146]) ).
tff(150,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(unit_resolution,[status(thm)],[151,145,8,107,129,92]) ).
tff(153,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(tautology,[status(thm)],[]) ).
tff(156,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) )
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(unit_resolution,[status(thm)],[155,110]) ).
tff(157,plain,
tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(unit_resolution,[status(thm)],[156,154]) ).
tff(158,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtpldt0(xm,xn),
inference(transitivity,[status(thm)],[159,122,113]) ).
tff(161,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,plain,
( ( ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(transitivity,[status(thm)],[163,161]) ).
tff(165,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ),
inference(unit_resolution,[status(thm)],[166,145,8,5,40,129]) ).
tff(168,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) )
<=> ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) )
<=> ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) ),
inference(unit_resolution,[status(thm)],[168,167]) ).
tff(170,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) )
<=> ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) ),
inference(tautology,[status(thm)],[]) ).
tff(171,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) )
<=> ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) )
| ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) ),
inference(unit_resolution,[status(thm)],[170,43]) ).
tff(172,plain,
tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl),
inference(unit_resolution,[status(thm)],[171,169]) ).
tff(173,plain,
sdtsldt0(xm,xl) = tptp_fun_W2_1(xm,xl),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
sdtasdt0(sdtsldt0(xm,xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
sdtasdt0(sdtsldt0(xm,xl),xl) = xm,
inference(transitivity,[status(thm)],[174,68,46]) ).
tff(176,plain,
( ( sdtasdt0(sdtsldt0(xm,xl),xl) = sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) )
<=> ( xm = sdtpldt0(xm,xn) ) ),
inference(monotonicity,[status(thm)],[175,160]) ).
tff(177,plain,
( ( sdtasdt0(sdtsldt0(xm,xl),xl) != sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) )
<=> ( xm != sdtpldt0(xm,xn) ) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) )
<=> ( sdtasdt0(sdtsldt0(xm,xl),xl) = sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(179,plain,
( ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) != sdtasdt0(sdtsldt0(xm,xl),xl) )
<=> ( sdtasdt0(sdtsldt0(xm,xl),xl) != sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) ) ),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
( aNaturalNumber0(tptp_fun_W2_1(xm,xl))
<=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(181,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(modus_ponens,[status(thm)],[48,180]) ).
tff(182,plain,
( ( xq = sdtsldt0(sdtpldt0(xm,xn),xl) )
<=> ( xq = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,axiom,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
tff(184,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( ( xp = sdtsldt0(xm,xl) )
<=> ( xp = sdtsldt0(xm,xl) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,axiom,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
tff(188,plain,
xp = sdtsldt0(xm,xl),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
sdtsldt0(xm,xl) = xp,
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
<=> sdtlseqdt0(xp,xq) ),
inference(monotonicity,[status(thm)],[189,185]) ).
tff(191,plain,
( sdtlseqdt0(xp,xq)
<=> sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
( ~ sdtlseqdt0(xp,xq)
<=> ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
( ~ sdtlseqdt0(xp,xq)
<=> ~ sdtlseqdt0(xp,xq) ),
inference(rewrite,[status(thm)],[]) ).
tff(194,axiom,
~ sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(195,plain,
~ sdtlseqdt0(xp,xq),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)),
inference(modus_ponens,[status(thm)],[195,192]) ).
tff(197,plain,
( aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
<=> aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(198,plain,
aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)),
inference(modus_ponens,[status(thm)],[115,197]) ).
tff(199,plain,
^ [W0: $i,W1: $i] :
refl(( ( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
<=> ( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(200,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[199]) ).
tff(201,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
<=> ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(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) ) )),
( ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( sdtlseqdt0(W0,W1)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( sdtlseqdt0(W0,W1)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) )),
( ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(202,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(204,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) )
<=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(205,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
tff(207,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[207,203]) ).
tff(209,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[208]) ).
tff(210,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[209,202]) ).
tff(211,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[210,200]) ).
tff(212,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,plain,
( ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) )
<=> ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
( ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) )
<=> ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(215,plain,
( ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) )
<=> ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
( ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) )
<=> ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(transitivity,[status(thm)],[215,213]) ).
tff(217,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(transitivity,[status(thm)],[217,212]) ).
tff(219,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(220,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ),
inference(unit_resolution,[status(thm)],[220,211]) ).
tff(222,plain,
~ ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ),
inference(unit_resolution,[status(thm)],[221,198,196,181]) ).
tff(223,plain,
( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))
| ( sdtsldt0(sdtpldt0(xm,xn),xl) != sdtsldt0(xm,xl) ) ),
inference(tautology,[status(thm)],[]) ).
tff(224,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) != sdtsldt0(xm,xl),
inference(unit_resolution,[status(thm)],[223,222]) ).
tff(225,plain,
^ [W0: $i] :
refl(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(226,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[225]) ).
tff(227,plain,
^ [W0: $i] :
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(228,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[227]) ).
tff(229,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(transitivity,[status(thm)],[228,226]) ).
tff(230,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
( ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
( ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
rewrite(( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
<=> ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )),
rewrite(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ))),
( ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )),
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(231,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[230]) ).
tff(232,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(233,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )),
( ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )),
rewrite(( ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) )),
( ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) )),
( ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )),
( ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ))),
( ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )),
( ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) )
<=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
rewrite(( ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
( ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) )
<=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) )
<=> ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) ) )),
rewrite(( ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(234,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[233]) ).
tff(235,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
tff(236,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[235,234]) ).
tff(237,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[236,232]) ).
tff(238,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ),
inference(skolemize,[status(sab)],[237]) ).
tff(239,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[238,231]) ).
tff(240,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[239,229]) ).
tff(241,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(242,plain,
( ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(243,plain,
^ [W1: $i,W2: $i] :
rewrite(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) )
| ~ aNaturalNumber0(W1) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(244,plain,
( ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) )
| ~ aNaturalNumber0(W1) )
<=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) ),
inference(quant_intro,[status(thm)],[243]) ).
tff(245,plain,
( ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) ) ),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
( ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) ) ),
inference(transitivity,[status(thm)],[245,242]) ).
tff(247,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) ) ),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) ) ),
inference(transitivity,[status(thm)],[247,241]) ).
tff(249,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) )
| ~ aNaturalNumber0(W1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ) ),
inference(modus_ponens,[status(thm)],[249,248]) ).
tff(251,plain,
! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) ),
inference(unit_resolution,[status(thm)],[250,240,8,129]) ).
tff(252,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(253,plain,
( ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) )
<=> ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(254,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) )
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) ) ),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) )
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) ) ),
inference(transitivity,[status(thm)],[254,252]) ).
tff(256,plain,
( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) )
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(257,plain,
( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xl,W1) = sdtasdt0(xl,W2) )
| ( sdtasdt0(W1,xl) = sdtasdt0(W2,xl) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) ),
inference(modus_ponens,[status(thm)],[256,255]) ).
tff(258,plain,
( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
| ~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ) ),
inference(unit_resolution,[status(thm)],[257,251,181,198]) ).
tff(259,plain,
~ ( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) ) ),
inference(unit_resolution,[status(thm)],[258,224]) ).
tff(260,plain,
( ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(sdtsldt0(xm,xl),xl) )
| ( sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) != sdtasdt0(sdtsldt0(xm,xl),xl) ) ),
inference(tautology,[status(thm)],[]) ).
tff(261,plain,
sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl) != sdtasdt0(sdtsldt0(xm,xl),xl),
inference(unit_resolution,[status(thm)],[260,259]) ).
tff(262,plain,
sdtasdt0(sdtsldt0(xm,xl),xl) != sdtasdt0(sdtsldt0(sdtpldt0(xm,xn),xl),xl),
inference(modus_ponens,[status(thm)],[261,179]) ).
tff(263,plain,
xm != sdtpldt0(xm,xn),
inference(modus_ponens,[status(thm)],[262,177]) ).
tff(264,plain,
( sdtlseqdt0(xm,sdtpldt0(xm,xn))
<=> sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(rewrite,[status(thm)],[]) ).
tff(265,axiom,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1409) ).
tff(266,plain,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(268,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) ) ),
inference(quant_intro,[status(thm)],[267]) ).
tff(269,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)
& sdtlseqdt0(W1,W0) )
<=> ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(( ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) ) )),
( ( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(270,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) ) ),
inference(quant_intro,[status(thm)],[269]) ).
tff(271,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(272,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(273,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[272]) ).
tff(274,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
tff(275,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[274,273]) ).
tff(276,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[275,271]) ).
tff(277,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[276]) ).
tff(278,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[277,270]) ).
tff(279,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[278,268]) ).
tff(280,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ( xm = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ( xm = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(281,plain,
( ( ( xm = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ( xm = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(282,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
| ( xm = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ( xm = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) ) ),
inference(monotonicity,[status(thm)],[281]) ).
tff(283,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
| ( xm = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ( xm = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) ) ),
inference(transitivity,[status(thm)],[282,280]) ).
tff(284,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
| ( xm = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(285,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W1,W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ( xm = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
inference(modus_ponens,[status(thm)],[284,283]) ).
tff(286,plain,
( ( xm = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
inference(unit_resolution,[status(thm)],[285,279,5,266,92]) ).
tff(287,plain,
~ sdtlseqdt0(sdtpldt0(xm,xn),xm),
inference(unit_resolution,[status(thm)],[286,263]) ).
tff(288,plain,
~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)),
inference(modus_ponens,[status(thm)],[287,126]) ).
tff(289,plain,
( ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
<=> ( tptp_fun_W2_1(xm,xl) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(290,plain,
( ( tptp_fun_W2_1(xm,xl) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) ) ),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
( ( sdtsldt0(xm,xl) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(292,plain,
( ( tptp_fun_W2_1(xm,xl) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl) )
<=> ( sdtsldt0(xm,xl) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(293,plain,
( ( tptp_fun_W2_1(xm,xl) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) ) ),
inference(transitivity,[status(thm)],[292,291]) ).
tff(294,plain,
( ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
<=> ( tptp_fun_W2_1(xm,xl) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl) ) ),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
<=> ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(296,plain,
( ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
<=> ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) ) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(297,plain,
( ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
<=> ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(transitivity,[status(thm)],[296,295]) ).
tff(298,plain,
( ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) ) ),
inference(symmetry,[status(thm)],[297]) ).
tff(299,plain,
( ( sdtsldt0(sdtpldt0(xm,xn),xl) = sdtsldt0(xm,xl) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) ) ),
inference(transitivity,[status(thm)],[295,298,294,290]) ).
tff(300,plain,
( ( sdtsldt0(sdtpldt0(xm,xn),xl) != sdtsldt0(xm,xl) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) != tptp_fun_W2_1(xm,xl) ) ),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
tptp_fun_W2_1(sdtpldt0(xm,xn),xl) != tptp_fun_W2_1(xm,xl),
inference(modus_ponens,[status(thm)],[224,300]) ).
tff(302,plain,
( sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
<=> sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ),
inference(monotonicity,[status(thm)],[157,172]) ).
tff(303,plain,
( sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))
<=> sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl)) ),
inference(symmetry,[status(thm)],[302]) ).
tff(304,plain,
( ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) )
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(tautology,[status(thm)],[]) ).
tff(305,plain,
( ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) )
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(unit_resolution,[status(thm)],[304,196]) ).
tff(306,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) )
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) )
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(307,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) )
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(308,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) )
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ) ),
inference(modus_ponens,[status(thm)],[307,306]) ).
tff(309,plain,
( sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ( sdtsldt0(xm,xl) = sdtsldt0(sdtpldt0(xm,xn),xl) )
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ) ),
inference(unit_resolution,[status(thm)],[308,211]) ).
tff(310,plain,
sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),
inference(unit_resolution,[status(thm)],[309,181,198,305]) ).
tff(311,plain,
sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl)),
inference(modus_ponens,[status(thm)],[310,303]) ).
tff(312,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
<=> ( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(313,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(quant_intro,[status(thm)],[312]) ).
tff(314,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) ) )),
rewrite(( ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
<=> ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )),
trans(monotonicity(rewrite(( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
<=> ~ ( ( W1 = W2 )
| ( W0 = sz00 )
| ~ sdtlseqdt0(W1,W2) ) )),
( ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
<=> ~ ~ ( ( W1 = W2 )
| ( W0 = sz00 )
| ~ sdtlseqdt0(W1,W2) ) )),
rewrite(( ~ ~ ( ( W1 = W2 )
| ( W0 = sz00 )
| ~ sdtlseqdt0(W1,W2) )
<=> ( ( W1 = W2 )
| ( W0 = sz00 )
| ~ sdtlseqdt0(W1,W2) ) )),
( ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
<=> ( ( W1 = W2 )
| ( W0 = sz00 )
| ~ sdtlseqdt0(W1,W2) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ( W1 = W2 )
| ( W0 = sz00 )
| ~ sdtlseqdt0(W1,W2) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ( W1 = W2 )
| ( W0 = sz00 )
| ~ sdtlseqdt0(W1,W2) )
<=> ( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) )
<=> ( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(315,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(quant_intro,[status(thm)],[314]) ).
tff(316,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(317,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
trans(monotonicity(rewrite(( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
<=> ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) )),
trans(monotonicity(rewrite(( ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) ) )
<=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) ) ) )),
( ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
<=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )),
rewrite(( ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
<=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )),
( ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
<=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )),
( ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
<=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
rewrite(( ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
<=> ( ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
( ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
<=> ( ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) ) )),
inference(bind,[status(th)],[]) ).
tff(318,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) ) ),
inference(quant_intro,[status(thm)],[317]) ).
tff(319,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
tff(320,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) ),
inference(modus_ponens,[status(thm)],[319,318]) ).
tff(321,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) ),
inference(modus_ponens,[status(thm)],[320,316]) ).
tff(322,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) )
| ~ ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) ) ),
inference(skolemize,[status(sab)],[321]) ).
tff(323,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ),
inference(modus_ponens,[status(thm)],[322,315]) ).
tff(324,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ),
inference(modus_ponens,[status(thm)],[323,313]) ).
tff(325,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(326,plain,
( ( ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ( xl = sz00 )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(327,plain,
( ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) )
<=> ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(328,plain,
( ( ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ( xl = sz00 )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) )
<=> ( ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ( xl = sz00 )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ) ),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
( ( ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ( xl = sz00 )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ) ),
inference(transitivity,[status(thm)],[328,326]) ).
tff(330,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ( xl = sz00 )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ) ),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ( xl = sz00 )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ) ),
inference(transitivity,[status(thm)],[330,325]) ).
tff(332,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ( xl = sz00 )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ sdtlseqdt0(W1,W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
| ~ sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
| ~ sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ),
inference(modus_ponens,[status(thm)],[332,331]) ).
tff(334,plain,
( ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(xm,xl) )
| ~ sdtlseqdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),tptp_fun_W2_1(xm,xl))
| ~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ) ),
inference(unit_resolution,[status(thm)],[333,324,8,129,48,115]) ).
tff(335,plain,
~ ( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ),
inference(unit_resolution,[status(thm)],[334,311,301]) ).
tff(336,plain,
( ( sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl) = sdtasdt0(tptp_fun_W2_1(xm,xl),xl) )
| ~ sdtlseqdt0(sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),sdtasdt0(xl,tptp_fun_W2_1(xm,xl)))
| ~ sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl))
| sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)) ),
inference(tautology,[status(thm)],[]) ).
tff(337,plain,
sdtlseqdt0(sdtasdt0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl),xl),sdtasdt0(tptp_fun_W2_1(xm,xl),xl)),
inference(unit_resolution,[status(thm)],[336,335]) ).
tff(338,plain,
$false,
inference(unit_resolution,[status(thm)],[337,288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM473+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:13:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.66/0.83 % SZS status Theorem
% 0.66/0.83 % SZS output start Proof
% See solution above
% 0.70/0.88 % E exiting
%------------------------------------------------------------------------------