%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM529+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:21:17 AM UTC 2025
% Result : Theorem 0.46s 0.66s
% Output : Proof 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 69
% Syntax : Number of formulae : 182 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 2096 ( 766 equ)
% Maximal formula atoms : 36 ( 11 avg)
% Number of connectives : 3288 (1530 ~;1100 |; 370 &)
% ( 236 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 156 ( 156 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 390 ( 340 !; 15 ?; 390 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xn_type,type,
xn: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xq_type,type,
xq: $i ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(1,plain,
( ( sz00 = sdtsldt0(xn,xp) )
<=> ( sdtsldt0(xn,xp) = sz00 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ( sdtsldt0(xn,xp) = sz00 )
<=> ( sz00 = sdtsldt0(xn,xp) ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(3,plain,
( ( sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)) )
<=> ( sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3082) ).
tff(5,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xm,xm),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ( xq = sdtsldt0(xn,xp) )
<=> ( xq = sdtsldt0(xn,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
tff(9,plain,
xq = sdtsldt0(xn,xp),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
sdtsldt0(xn,xp) = xq,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp)) = sdtasdt0(xq,xq),
inference(monotonicity,[status(thm)],[10,10]) ).
tff(12,plain,
sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) = sdtasdt0(xm,xm),
inference(transitivity,[status(thm)],[12,6]) ).
tff(14,plain,
( sdtlseqdt0(xm,xn)
<=> sdtlseqdt0(xm,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
( ( xm != xn )
& sdtlseqdt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3124) ).
tff(16,plain,
sdtlseqdt0(xm,xn),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
sdtlseqdt0(xm,xn),
inference(modus_ponens,[status(thm)],[16,14]) ).
tff(18,plain,
( ( xm != xn )
<=> ( xm != xn ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
xm != xn,
inference(and_elim,[status(thm)],[15]) ).
tff(20,plain,
xm != xn,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
tff(23,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 ) ),
inference(and_elim,[status(thm)],[22]) ).
tff(24,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 ) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[26]) ).
tff(28,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[27,21]) ).
tff(29,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[26]) ).
tff(31,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
<=> ~ ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
<=> ~ ~ ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ~ ~ ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
( ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ( iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
( ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) )
<=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| iLess0(W0,W1) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| iLess0(W0,W1) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| iLess0(W0,W1) ) )
<=> ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) )
<=> ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
tff(40,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[43,33]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( xm = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| iLess0(xm,xn)
| ~ sdtlseqdt0(xm,xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( xm = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| iLess0(xm,xn)
| ~ sdtlseqdt0(xm,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ( xm = xn )
| iLess0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm) )
<=> ( ( xm = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| iLess0(xm,xn)
| ~ sdtlseqdt0(xm,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( xm = xn )
| iLess0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( xm = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| iLess0(xm,xn)
| ~ sdtlseqdt0(xm,xn) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( xm = xn )
| iLess0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( xm = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| iLess0(xm,xn)
| ~ sdtlseqdt0(xm,xn) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( xm = xn )
| iLess0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( xm = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| iLess0(xm,xn)
| ~ sdtlseqdt0(xm,xn) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
iLess0(xm,xn),
inference(unit_resolution,[status(thm)],[50,44,31,28,20,17]) ).
tff(52,plain,
( doDivides0(xp,xn)
<=> doDivides0(xp,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
tff(54,plain,
doDivides0(xp,xn),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
doDivides0(xp,xn),
inference(modus_ponens,[status(thm)],[54,52]) ).
tff(56,plain,
( ( xp != sz00 )
<=> ( xp != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
xp != sz00,
inference(and_elim,[status(thm)],[22]) ).
tff(58,plain,
xp != sz00,
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[25]) ).
tff(61,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,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(63,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)],[62]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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)],[65,63]) ).
tff(67,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(68,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [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)],[67]) ).
tff(69,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [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(70,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(71,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)],[70]) ).
tff(72,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
tff(73,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)],[72,71]) ).
tff(74,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)],[73,69]) ).
tff(75,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)],[74]) ).
tff(76,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[75,68]) ).
tff(77,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[76,66]) ).
tff(78,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) )
<=> ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[83,77,31,61,58,55]) ).
tff(85,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) )
<=> ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) )
<=> ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,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(88,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)],[87]) ).
tff(89,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(90,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)],[89]) ).
tff(91,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)],[90,88]) ).
tff(92,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(93,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [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)],[92]) ).
tff(94,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(95,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(96,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)],[95]) ).
tff(97,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
tff(98,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)],[97,96]) ).
tff(99,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)],[98,94]) ).
tff(100,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)],[99]) ).
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) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[101,91]) ).
tff(103,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ),
inference(unit_resolution,[status(thm)],[108,102,31,61]) ).
tff(110,plain,
( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(111,plain,
( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ),
inference(unit_resolution,[status(thm)],[110,109]) ).
tff(112,plain,
( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(113,plain,
( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ),
inference(unit_resolution,[status(thm)],[112,55]) ).
tff(114,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ),
inference(unit_resolution,[status(thm)],[113,111]) ).
tff(115,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) )
<=> ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) )
| ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(116,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) )
<=> ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) )
| ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp),
inference(unit_resolution,[status(thm)],[116,86]) ).
tff(118,plain,
( aNaturalNumber0(tptp_fun_W2_1(xn,xp))
<=> aNaturalNumber0(sdtsldt0(xn,xp)) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) )
| aNaturalNumber0(tptp_fun_W2_1(xn,xp)) ),
inference(tautology,[status(thm)],[]) ).
tff(120,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xp)),
inference(unit_resolution,[status(thm)],[119,114]) ).
tff(121,plain,
aNaturalNumber0(sdtsldt0(xn,xp)),
inference(modus_ponens,[status(thm)],[120,118]) ).
tff(122,plain,
( isPrime0(xp)
<=> isPrime0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
tff(124,plain,
isPrime0(xp),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
<=> ~ ( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
<=> ~ ~ ( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
<=> ( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) )
<=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) )
<=> ( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 ) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 ) ) )),
rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 ) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 ) ) )),
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 ) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 ) ) )),
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 ) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 ) ) )),
rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 ) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 ) ) )),
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 ) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 ) ) )),
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) )),
rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) )),
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) )),
trans(monotonicity(rewrite(( ( iLess0(W0,xn)
=> ~ isPrime0(W2) )
<=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn) ) )),
( ( ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0) )
=> ( iLess0(W0,xn)
=> ~ isPrime0(W2) ) )
<=> ( ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0) )
=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn) ) ) )),
rewrite(( ( ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0) )
=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn) ) )
<=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) ) ) )),
( ( ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0) )
=> ( iLess0(W0,xn)
=> ~ isPrime0(W2) ) )
<=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
=> ( ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0) )
=> ( iLess0(W0,xn)
=> ~ isPrime0(W2) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) ) ) )
<=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
=> ( ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0) )
=> ( iLess0(W0,xn)
=> ~ isPrime0(W2) ) ) )
<=> ( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
=> ( ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0) )
=> ( iLess0(W0,xn)
=> ~ isPrime0(W2) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
=> ( ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0) )
=> ( iLess0(W0,xn)
=> ~ isPrime0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2963) ).
tff(133,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ isPrime0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) ) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[135,128]) ).
tff(137,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[136,126]) ).
tff(138,plain,
( ( xm != sz00 )
<=> ( xm != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
xm != sz00,
inference(and_elim,[status(thm)],[23]) ).
tff(140,plain,
xm != sz00,
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( xm = sz00 )
| ( xp = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn)
| ( sdtsldt0(xn,xp) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( xm = sz00 )
| ( xp = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn)
| ( sdtsldt0(xn,xp) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ( ( xp = sz00 )
| ( sdtsldt0(xn,xp) = sz00 )
| ( xm = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ iLess0(xm,xn)
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xm) )
<=> ( ( xm = sz00 )
| ( xp = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn)
| ( sdtsldt0(xn,xp) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( xp = sz00 )
| ( sdtsldt0(xn,xp) = sz00 )
| ( xm = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ iLess0(xm,xn)
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( xm = sz00 )
| ( xp = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn)
| ( sdtsldt0(xn,xp) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) ) ) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( xp = sz00 )
| ( sdtsldt0(xn,xp) = sz00 )
| ( xm = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ iLess0(xm,xn)
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( xm = sz00 )
| ( xp = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn)
| ( sdtsldt0(xn,xp) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) ) ) ),
inference(transitivity,[status(thm)],[143,141]) ).
tff(145,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( xp = sz00 )
| ( sdtsldt0(xn,xp) = sz00 )
| ( xm = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ iLess0(xm,xn)
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ iLess0(W0,xn)
| ( sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( xm = sz00 )
| ( xp = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn)
| ( sdtsldt0(xn,xp) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) ) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ~ iLess0(xm,xn)
| ( sdtsldt0(xn,xp) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm) ) ),
inference(unit_resolution,[status(thm)],[146,28,61,140,58,137,124]) ).
tff(148,plain,
sdtsldt0(xn,xp) = sz00,
inference(unit_resolution,[status(thm)],[147,121,51,13]) ).
tff(149,plain,
sz00 = sdtsldt0(xn,xp),
inference(modus_ponens,[status(thm)],[148,2]) ).
tff(150,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) )
| ~ ( ( ~ aNaturalNumber0(sz00)
| ( xn != sdtasdt0(xp,sz00) ) )
<=> ( sz00 = sdtsldt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
~ ( ( ~ aNaturalNumber0(sz00)
| ( xn != sdtasdt0(xp,sz00) ) )
<=> ( sz00 = sdtsldt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[150,84]) ).
tff(152,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(153,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(155,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
tff(160,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[162,155]) ).
tff(164,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[163,153]) ).
tff(165,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ( sdtasdt0(xp,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xp) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ( sdtasdt0(xp,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ( sdtasdt0(xp,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xp)
| ~ ( ( sdtasdt0(xp,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xp) ) ) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
~ ( ( sdtasdt0(xp,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xp) ) ),
inference(unit_resolution,[status(thm)],[167,164,61]) ).
tff(169,plain,
( ( sdtasdt0(xp,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xp) )
| ( sdtasdt0(xp,sz00) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(170,plain,
sdtasdt0(xp,sz00) = sz00,
inference(unit_resolution,[status(thm)],[169,168]) ).
tff(171,plain,
( ( xn = sdtasdt0(xp,sz00) )
<=> ( xn = sz00 ) ),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
( ( xn = sz00 )
<=> ( xn = sdtasdt0(xp,sz00) ) ),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ( xn != sz00 )
<=> ( xn != sdtasdt0(xp,sz00) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ( xn != sz00 )
<=> ( xn != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
xn != sz00,
inference(and_elim,[status(thm)],[24]) ).
tff(176,plain,
xn != sz00,
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
xn != sdtasdt0(xp,sz00),
inference(modus_ponens,[status(thm)],[176,173]) ).
tff(178,plain,
( ~ aNaturalNumber0(sz00)
| ( xn != sdtasdt0(xp,sz00) )
| ( xn = sdtasdt0(xp,sz00) ) ),
inference(tautology,[status(thm)],[]) ).
tff(179,plain,
( ~ aNaturalNumber0(sz00)
| ( xn != sdtasdt0(xp,sz00) ) ),
inference(unit_resolution,[status(thm)],[178,177]) ).
tff(180,plain,
( ( ( ~ aNaturalNumber0(sz00)
| ( xn != sdtasdt0(xp,sz00) ) )
<=> ( sz00 = sdtsldt0(xn,xp) ) )
| ~ ( ~ aNaturalNumber0(sz00)
| ( xn != sdtasdt0(xp,sz00) ) )
| ( sz00 != sdtsldt0(xn,xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(181,plain,
sz00 != sdtsldt0(xn,xp),
inference(unit_resolution,[status(thm)],[180,179,151]) ).
tff(182,plain,
$false,
inference(unit_resolution,[status(thm)],[181,149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM529+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:23:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.46/0.66 % SZS status Theorem
% 0.46/0.66 % SZS output start Proof
% See solution above
% 0.52/0.69 % E exiting
%------------------------------------------------------------------------------