TSTP Solution File: NUM500+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sun Sep 18 13:10:06 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 47
% Syntax : Number of formulae : 93 ( 21 unt; 14 typ; 0 def)
% Number of atoms : 1369 ( 571 equ)
% Maximal formula atoms : 52 ( 17 avg)
% Number of connectives : 2018 ( 852 ~; 692 |; 419 &)
% ( 47 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 124 ( 124 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 8 >; 3 *; 0 +; 0 <<)
% Number of predicates : 18 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 202 ( 113 !; 79 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(tptp_fun_W1_3_type,type,
tptp_fun_W1_3: $i > $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(tptp_fun_W1_11_type,type,
tptp_fun_W1_11: $i > $i ).
tff(tptp_fun_W2_12_type,type,
tptp_fun_W2_12: $i > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sz10_type,type,
sz10: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(xk_type,type,
xk: $i ).
tff(1,plain,
( ( xk != sz10 )
<=> ( sdtsldt0(sdtasdt0(xn,xm),xp) != sz10 ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( xk != sz10 )
<=> ( xk != sz10 ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( ( xk = sz00 )
| ( xk = sz10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
tff(4,plain,
xk != sz10,
inference(or_elim,[status(thm)],[3]) ).
tff(5,plain,
xk != sz10,
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) != sz10,
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ( xk != sz00 )
<=> ( sdtsldt0(sdtasdt0(xn,xm),xp) != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( ( xk != sz00 )
<=> ( xk != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
xk != sz00,
inference(or_elim,[status(thm)],[3]) ).
tff(10,plain,
xk != sz00,
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) != sz00,
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( aNaturalNumber0(xk)
<=> aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( aNaturalNumber0(xk)
<=> aNaturalNumber0(xk) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
( aNaturalNumber0(xk)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
& ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
tff(15,plain,
( aNaturalNumber0(xk)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ) ),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
aNaturalNumber0(xk),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
aNaturalNumber0(xk),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)),
inference(modus_ponens,[status(thm)],[17,12]) ).
tff(19,plain,
^ [W0: $i] :
refl(
( ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
<=> ~ ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
<=> ~ ~ ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )),
rewrite(
( ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )),
( ( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) )),
rewrite(
( ( ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
<=> ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) ) )),
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) )
<=> ( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ))),
( ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) )
<=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )),
( ( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) )
<=> ! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
tff(27,plain,
! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ? [W1: $i] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [W0: $i] :
( ~ ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
| ( aNaturalNumber0(tptp_fun_W1_3(W0))
& doDivides0(tptp_fun_W1_3(W0),W0)
& isPrime0(tptp_fun_W1_3(W0)) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ( sdtsldt0(sdtasdt0(xn,xm),xp) = sz00 )
| ( sdtsldt0(sdtasdt0(xn,xm),xp) = sz10 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ( sdtsldt0(sdtasdt0(xn,xm),xp) = sz00 )
| ( sdtsldt0(sdtasdt0(xn,xm),xp) = sz10 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ( sdtsldt0(sdtasdt0(xn,xm),xp) = sz00 )
| ( sdtsldt0(sdtasdt0(xn,xm),xp) = sz10 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(W0))
| ~ doDivides0(tptp_fun_W1_3(W0),W0)
| ~ isPrime0(tptp_fun_W1_3(W0)) ) )
| ( sdtsldt0(sdtasdt0(xn,xm),xp) = sz00 )
| ( sdtsldt0(sdtasdt0(xn,xm),xp) = sz10 )
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ),
inference(unit_resolution,[status(thm)],[34,31,18,11,6]) ).
tff(36,plain,
( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ),
inference(tautology,[status(thm)],]) ).
tff(37,plain,
isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) )
| ~ isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ),
inference(tautology,[status(thm)],]) ).
tff(39,plain,
( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(tautology,[status(thm)],]) ).
tff(41,plain,
doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[40,35]) ).
tff(42,plain,
( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) )
| ~ doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) ),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ),
inference(tautology,[status(thm)],]) ).
tff(45,plain,
aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),
inference(unit_resolution,[status(thm)],[44,35]) ).
tff(46,plain,
^ [W0: $i] :
refl(
( ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
^ [W0: $i] :
rewrite(
( ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[49,47]) ).
tff(51,plain,
^ [W0: $i] :
rewrite(
( ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
<=> ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) ) )),
rewrite(
( ( ~ isPrime0(W0)
& ( ~ ( ( W0 != sz00 ) )
| ~ ( ( W0 != sz10 ) )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) )
<=> ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )),
( ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ~ ( ( W0 != sz00 ) )
| ~ ( ( W0 != sz10 ) )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) )),
rewrite(
( ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) )),
( ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ~ ( ( W0 != sz00 ) )
| ~ ( ( W0 != sz10 ) )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ~ ( ( W0 != sz00 ) )
| ~ ( ( W0 != sz10 ) )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = 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,sdtsldt0(sdtasdt0(xn,xm),xp))
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = 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(56,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,sdtsldt0(sdtasdt0(xn,xm),xp))
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = 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(57,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(58,plain,
( ~ ? [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] :
( 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(59,axiom,
~ ? [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/sandbox/benchmark/theBenchmark.p',m__) ).
tff(60,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)],[59,58]) ).
tff(61,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)],[60,57]) ).
tff(62,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)],[61,57]) ).
tff(63,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)],[62,57]) ).
tff(64,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = 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)],[63,56]) ).
tff(65,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = 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)],[64,55]) ).
tff(66,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = 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)],[65,55]) ).
tff(67,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = 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)],[66,55]) ).
tff(68,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aNaturalNumber0(W0),~ aNaturalNumber0(W0))),
nnf_neg(refl($oeq(~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp)),~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp)))),
nnf_neg(
proof_bind(
^ [W1: $i] :
refl(
$oeq(
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ),
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) )))),
$oeq(
~ ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ),
! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ))),
$oeq(
~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) ),
( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) ))),
nnf_neg(refl($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_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_11(W0))
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),W2) ) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ))),
nnf_neg(refl($oeq(tptp_fun_W1_11(W0) != W0,tptp_fun_W1_11(W0) != W0)),refl($oeq(tptp_fun_W1_11(W0) != sz10,tptp_fun_W1_11(W0) != sz10)),
nnf_neg(
monotonicity(refl($oeq(aNaturalNumber0(tptp_fun_W1_11(W0)),aNaturalNumber0(tptp_fun_W1_11(W0)))),
sk(
$oeq(
? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),W2) ) ),
( aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) ) ))),
refl($oeq(doDivides0(tptp_fun_W1_11(W0),W0),doDivides0(tptp_fun_W1_11(W0),W0))),
$oeq(
( aNaturalNumber0(tptp_fun_W1_11(W0))
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),W2) ) )
& doDivides0(tptp_fun_W1_11(W0),W0) ),
( aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ))),
$oeq(
~ ~ ( aNaturalNumber0(tptp_fun_W1_11(W0))
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),W2) ) )
& doDivides0(tptp_fun_W1_11(W0),W0) ),
( aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ))),
$oeq(
~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ ( aNaturalNumber0(tptp_fun_W1_11(W0))
& ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),W2) ) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ),
( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(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_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(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_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(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_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ))),
$oeq(
~ ( aNaturalNumber0(W0)
& ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ? [W1: $i] :
( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = 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,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ~ ( ( W0 != sz00 ) )
| ~ ( ( W0 != sz10 ) )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ))),
inference(bind,[status(th)],]) ).
tff(69,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ~ ( ( W0 != sz00 ) )
| ~ ( ( W0 != sz10 ) )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ),
inference(nnf-neg,[status(sab)],[67,68]) ).
tff(70,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ~ doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
& ! [W1: $i] :
~ ( aNaturalNumber0(W1)
& ( sdtsldt0(sdtasdt0(xn,xm),xp) = sdtasdt0(W0,W1) ) ) )
| ( ~ isPrime0(W0)
& ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( tptp_fun_W1_11(W0) != W0 )
& ( tptp_fun_W1_11(W0) != sz10 )
& aNaturalNumber0(tptp_fun_W1_11(W0))
& aNaturalNumber0(tptp_fun_W2_12(W0))
& ( W0 = sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
& doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[69,54]) ).
tff(71,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[70,52]) ).
tff(72,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[71,50]) ).
tff(73,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
| ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
| ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) )
<=> ( ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
| ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
| ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
| ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
| ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
| ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W0,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(W0,W1) ) ) )
| ~ ( isPrime0(W0)
| ~ ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( tptp_fun_W1_11(W0) = W0 )
| ( tptp_fun_W1_11(W0) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(W0))
| ~ aNaturalNumber0(tptp_fun_W2_12(W0))
| ( W0 != sdtasdt0(tptp_fun_W1_11(W0),tptp_fun_W2_12(W0)) )
| ~ doDivides0(tptp_fun_W1_11(W0),W0) ) ) ) )
| ~ aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtsldt0(sdtasdt0(xn,xm),xp) != sdtasdt0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)),W1) ) ) )
| ~ ( isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))
| ~ ( ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz10 )
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) = sz00 )
| ~ ( ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) )
| ( tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) = sz10 )
| ~ aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ~ aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))))
| ( tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W2_12(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp)))) )
| ~ doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))),tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn,xm),xp))) ) ) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,72,45,43,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 11:32:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------