%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM482+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:21:08 AM UTC 2025
% Result : Theorem 0.14s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 28
% Syntax : Number of formulae : 68 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 1114 ( 507 equ)
% Maximal formula atoms : 52 ( 16 avg)
% Number of connectives : 1645 ( 698 ~; 607 |; 300 &)
% ( 31 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 99 ( 99 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 174 ( 117 !; 48 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sz10_type,type,
sz10: $i ).
tff(xk_type,type,
xk: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(tptp_fun_W1_5_type,type,
tptp_fun_W1_5: $i > $i ).
tff(tptp_fun_W2_6_type,type,
tptp_fun_W2_6: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(1,plain,
( aNaturalNumber0(xk)
<=> aNaturalNumber0(xk) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
tff(3,plain,
aNaturalNumber0(xk),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
tff(12,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ),
inference(unit_resolution,[status(thm)],[19,16,3]) ).
tff(21,plain,
( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) )
| ( sdtasdt0(xk,sz10) = xk ) ),
inference(tautology,[status(thm)],[]) ).
tff(22,plain,
sdtasdt0(xk,sz10) = xk,
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
xk = sdtasdt0(xk,sz10),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( isPrime0(xk)
<=> isPrime0(xk) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ( ( ! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xk) ) )
=> ( ( W0 = sz10 )
| ( W0 = xk ) ) )
& isPrime0(xk) )
=> ? [W0: $i] :
( aNaturalNumber0(W0)
& ( ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xk) )
& ( ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) )
| isPrime0(W0) ) ) )
<=> ~ ( ~ ( ! [W0: $i] :
( ( W0 = sz10 )
| ( W0 = xk )
| ~ ( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) ) ) )
& isPrime0(xk) )
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
& ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
~ ( ( ! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xk) ) )
=> ( ( W0 = sz10 )
| ( W0 = xk ) ) )
& isPrime0(xk) )
=> ? [W0: $i] :
( aNaturalNumber0(W0)
& ( ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xk) )
& ( ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) )
| isPrime0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(27,plain,
~ ( ~ ( ! [W0: $i] :
( ( W0 = sz10 )
| ( W0 = xk )
| ~ ( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) ) ) )
& isPrime0(xk) )
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
& ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ! [W0: $i] :
( ( W0 = sz10 )
| ( W0 = xk )
| ~ ( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) ) ) )
& isPrime0(xk) ),
inference(or_elim,[status(thm)],[27]) ).
tff(29,plain,
isPrime0(xk),
inference(and_elim,[status(thm)],[28]) ).
tff(30,plain,
isPrime0(xk),
inference(modus_ponens,[status(thm)],[29,24]) ).
tff(31,plain,
( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_5(xk),xk)
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ( tptp_fun_W1_5(xk) = xk )
| ( tptp_fun_W1_5(xk) = sz10 ) ) )
| ~ isPrime0(xk) ),
inference(tautology,[status(thm)],[]) ).
tff(32,plain,
( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_5(xk),xk)
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ( tptp_fun_W1_5(xk) = xk )
| ( tptp_fun_W1_5(xk) = sz10 ) ) ) ),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
<=> ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) ) )),
rewrite(( ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) )
<=> ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )),
( ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) )),
( ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
& ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ) )
<=> ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
& ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
& ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ) ),
inference(or_elim,[status(thm)],[27]) ).
tff(44,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
& ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
& ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[44,42]) ).
tff(46,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
& ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[45,42]) ).
tff(47,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aNaturalNumber0(W0),~ aNaturalNumber0(W0))),
nnf_neg(refl($oeq(~ doDivides0(W0,xk),~ doDivides0(W0,xk))),
nnf_neg(proof_bind(^ [W1: $i] :
refl($oeq(~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ),
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) )))),
$oeq(~ ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ),
! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ))),
$oeq(~ ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) ),
( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) ))),
nnf_neg(refl($oeq(~ isPrime0(W0),~ isPrime0(W0))),
nnf_neg(refl($oeq(W0 = sz00,W0 = sz00)),refl($oeq(W0 = sz10,W0 = sz10)),
trans(sk($oeq(~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ),
~ ( ( tptp_fun_W1_5(W0) = W0 )
| ( tptp_fun_W1_5(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_5(W0))
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),W2) ) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ))),
nnf_neg(refl($oeq(tptp_fun_W1_5(W0) != W0,tptp_fun_W1_5(W0) != W0)),refl($oeq(tptp_fun_W1_5(W0) != sz10,tptp_fun_W1_5(W0) != sz10)),
nnf_neg(monotonicity(refl($oeq(aNaturalNumber0(tptp_fun_W1_5(W0)),aNaturalNumber0(tptp_fun_W1_5(W0)))),
sk($oeq(? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),W2) ) ),
( aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) ) ))),
refl($oeq(doDivides0(tptp_fun_W1_5(W0),W0),doDivides0(tptp_fun_W1_5(W0),W0))),
$oeq(( aNaturalNumber0(tptp_fun_W1_5(W0))
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),W2) ) )
& doDivides0(tptp_fun_W1_5(W0),W0) ),
( aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ))),
$oeq(~ ~ ( aNaturalNumber0(tptp_fun_W1_5(W0))
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),W2) ) )
& doDivides0(tptp_fun_W1_5(W0),W0) ),
( aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ))),
$oeq(~ ( ( tptp_fun_W1_5(W0) = W0 )
| ( tptp_fun_W1_5(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_5(W0))
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),W2) ) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ),
( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ))),
$oeq(~ ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ),
( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ))),
$oeq(~ ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ),
( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ))),
$oeq(~ ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ),
( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ))),
$oeq(~ ( aNaturalNumber0(W0)
& ( doDivides0(W0,xk)
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
& ( isPrime0(W0)
| ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1: $i] :
( ( W1 = W0 )
| ( W1 = sz10 )
| ~ ( aNaturalNumber0(W1)
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) ) ) ) ) ),
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(48,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ),
inference(nnf-neg,[status(sab)],[46,47]) ).
tff(49,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,xk)
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_5(W0) != W0 )
& ( tptp_fun_W1_5(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_5(W0))
& aNaturalNumber0(tptp_fun_W2_6(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
& doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[49,39]) ).
tff(51,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[50,37]) ).
tff(52,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| doDivides0(xk,xk) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_5(xk),xk)
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ( tptp_fun_W1_5(xk) = xk )
| ( tptp_fun_W1_5(xk) = sz10 ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| doDivides0(xk,xk) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_5(xk),xk)
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ( tptp_fun_W1_5(xk) = xk )
| ( tptp_fun_W1_5(xk) = sz10 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ aNaturalNumber0(xk)
| ~ ( doDivides0(xk,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) ) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ( tptp_fun_W1_5(xk) = sz10 )
| ( tptp_fun_W1_5(xk) = xk )
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ doDivides0(tptp_fun_W1_5(xk),xk) ) ) ) )
<=> ( ~ aNaturalNumber0(xk)
| ~ ( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| doDivides0(xk,xk) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_5(xk),xk)
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ( tptp_fun_W1_5(xk) = xk )
| ( tptp_fun_W1_5(xk) = sz10 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( doDivides0(xk,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) ) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ( tptp_fun_W1_5(xk) = sz10 )
| ( tptp_fun_W1_5(xk) = xk )
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ doDivides0(tptp_fun_W1_5(xk),xk) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| doDivides0(xk,xk) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_5(xk),xk)
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ( tptp_fun_W1_5(xk) = xk )
| ( tptp_fun_W1_5(xk) = sz10 ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( doDivides0(xk,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) ) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ( tptp_fun_W1_5(xk) = sz10 )
| ( tptp_fun_W1_5(xk) = xk )
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ doDivides0(tptp_fun_W1_5(xk),xk) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| doDivides0(xk,xk) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_5(xk),xk)
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ( tptp_fun_W1_5(xk) = xk )
| ( tptp_fun_W1_5(xk) = sz10 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( doDivides0(xk,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) ) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ( tptp_fun_W1_5(xk) = sz10 )
| ( tptp_fun_W1_5(xk) = xk )
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ doDivides0(tptp_fun_W1_5(xk),xk) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,xk)
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_5(W0) = sz10 )
| ( tptp_fun_W1_5(W0) = W0 )
| ~ aNaturalNumber0(tptp_fun_W1_5(W0))
| ~ aNaturalNumber0(tptp_fun_W2_6(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_5(W0),tptp_fun_W2_6(W0)) )
| ~ doDivides0(tptp_fun_W1_5(W0),W0) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| doDivides0(xk,xk) )
| ~ ( isPrime0(xk)
| ~ ( ( xk = sz00 )
| ( xk = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W1_5(xk),xk)
| ( xk != sdtasdt0(tptp_fun_W1_5(xk),tptp_fun_W2_6(xk)) )
| ~ aNaturalNumber0(tptp_fun_W2_6(xk))
| ~ aNaturalNumber0(tptp_fun_W1_5(xk))
| ( tptp_fun_W1_5(xk) = xk )
| ( tptp_fun_W1_5(xk) = sz10 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
~ ( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| doDivides0(xk,xk) ),
inference(unit_resolution,[status(thm)],[57,3,51,32]) ).
tff(59,plain,
( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| doDivides0(xk,xk)
| ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(60,plain,
! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
( aNaturalNumber0(sz10)
<=> aNaturalNumber0(sz10) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
tff(63,plain,
aNaturalNumber0(sz10),
inference(and_elim,[status(thm)],[62]) ).
tff(64,plain,
aNaturalNumber0(sz10),
inference(modus_ponens,[status(thm)],[63,61]) ).
tff(65,plain,
( ( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| ~ aNaturalNumber0(sz10)
| ( xk != sdtasdt0(xk,sz10) ) )
<=> ( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| ~ aNaturalNumber0(sz10)
| ( xk != sdtasdt0(xk,sz10) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| ~ aNaturalNumber0(sz10)
| ( xk != sdtasdt0(xk,sz10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( xk != sdtasdt0(xk,W1) ) )
| ~ aNaturalNumber0(sz10)
| ( xk != sdtasdt0(xk,sz10) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
$false,
inference(unit_resolution,[status(thm)],[67,64,60,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM482+3 : TPTP v9.0.0. Released v4.0.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n001.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:20:04 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start Proof
% See solution above
% 0.23/0.45 % E exiting
%------------------------------------------------------------------------------