%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM491+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:21:09 AM UTC 2025
% Result : Theorem 0.12s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of formulae : 72 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 725 ( 148 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 1292 ( 686 ~; 448 |; 76 &)
% ( 73 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 187 ( 158 !; 15 ?; 187 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xm_type,type,
xm: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(1,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(3,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[2]) ).
tff(7,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
^ [W0: $i,W1: $i] :
refl(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(17,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[20,10]) ).
tff(22,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(unit_resolution,[status(thm)],[24,21,8,4]) ).
tff(26,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
<=> ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )),
rewrite(( ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
tff(37,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,30]) ).
tff(42,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[47,42]) ).
tff(49,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
~ ( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) ) ),
inference(unit_resolution,[status(thm)],[50,41,4,25]) ).
tff(52,plain,
( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp,xm),xp))
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xp,xm),xp)) ) ) )
| doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( ~ doDivides0(xp,sdtasdt0(xp,xm))
<=> ~ doDivides0(xp,sdtasdt0(xp,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
~ doDivides0(xp,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(56,plain,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(58,plain,
( ~ ( doDivides0(xp,sdtasdt0(xp,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) ),
inference(unit_resolution,[status(thm)],[58,53]) ).
tff(60,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ( ~ aNaturalNumber0(xm)
| $false )
<=> ~ aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( sdtasdt0(xp,xm) = sdtasdt0(xp,xm) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( sdtasdt0(xp,xm) != sdtasdt0(xp,xm) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( sdtasdt0(xp,xm) != sdtasdt0(xp,xm) )
<=> $false ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ( ~ aNaturalNumber0(xm)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,xm) ) )
<=> ( ~ aNaturalNumber0(xm)
| $false ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ aNaturalNumber0(xm)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,xm) ) )
<=> ~ aNaturalNumber0(xm) ),
inference(transitivity,[status(thm)],[66,61]) ).
tff(68,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,xm) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(xm) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,xm) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(xm) ) ),
inference(transitivity,[status(thm)],[68,60]) ).
tff(70,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,xm) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xp,xm) != sdtasdt0(xp,W2) ) )
| ~ aNaturalNumber0(xm) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
$false,
inference(unit_resolution,[status(thm)],[71,8,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM491+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:16:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 % SZS output start Proof
% See solution above
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------