%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM466+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:21:04 AM UTC 2025
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 55
% Syntax : Number of formulae : 141 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 1437 ( 317 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 2680 (1452 ~; 981 |; 125 &)
% ( 105 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 68 ( 68 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 350 ( 312 !; 15 ?; 350 :)
% Comments :
%------------------------------------------------------------------------------
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(xl_type,type,
xl: $i ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(1,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1218) ).
tff(3,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( aNaturalNumber0(xl)
& 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(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[12,10]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
<=> ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )),
rewrite(( ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
tff(20,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,13]) ).
tff(25,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[30,25]) ).
tff(32,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ),
inference(unit_resolution,[status(thm)],[33,24,8,4]) ).
tff(35,plain,
( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( doDivides0(xm,xn)
<=> doDivides0(xm,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ( ( doDivides0(xl,xm)
& doDivides0(xm,xn) )
=> doDivides0(xl,xn) )
<=> ~ ( ~ ( doDivides0(xl,xm)
& doDivides0(xm,xn) )
| doDivides0(xl,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
~ ( ( doDivides0(xl,xm)
& doDivides0(xm,xn) )
=> doDivides0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(40,plain,
~ ( ~ ( doDivides0(xl,xm)
& doDivides0(xm,xn) )
| doDivides0(xl,xn) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( doDivides0(xl,xm)
& doDivides0(xm,xn) ),
inference(or_elim,[status(thm)],[40]) ).
tff(42,plain,
doDivides0(xm,xn),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
doDivides0(xm,xn),
inference(modus_ponens,[status(thm)],[42,37]) ).
tff(44,plain,
( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(45,plain,
( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ),
inference(unit_resolution,[status(thm)],[45,36]) ).
tff(47,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) )
| aNaturalNumber0(tptp_fun_W2_1(xn,xm)) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xm)),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
( aNaturalNumber0(xl)
<=> aNaturalNumber0(xl) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
aNaturalNumber0(xl),
inference(and_elim,[status(thm)],[6]) ).
tff(51,plain,
aNaturalNumber0(xl),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[57,52]) ).
tff(59,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
~ ( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ) ),
inference(unit_resolution,[status(thm)],[60,24,51,8]) ).
tff(62,plain,
( ~ ( doDivides0(xl,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(63,plain,
( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
( doDivides0(xl,xm)
<=> doDivides0(xl,xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
doDivides0(xl,xm),
inference(and_elim,[status(thm)],[41]) ).
tff(66,plain,
doDivides0(xl,xm),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(68,plain,
( ~ ( ~ doDivides0(xl,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ),
inference(unit_resolution,[status(thm)],[68,63]) ).
tff(70,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| aNaturalNumber0(tptp_fun_W2_1(xm,xl)) ),
inference(tautology,[status(thm)],[]) ).
tff(71,plain,
aNaturalNumber0(tptp_fun_W2_1(xm,xl)),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
tff(80,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[83,73]) ).
tff(85,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ( ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(xl) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(xl) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(xl) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ) ),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(xl) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))),
inference(unit_resolution,[status(thm)],[90,84,51,71,48]) ).
tff(92,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( xm = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(93,plain,
xm = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),
inference(unit_resolution,[status(thm)],[92,69]) ).
tff(94,plain,
sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) = xm,
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)) = sdtasdt0(xm,tptp_fun_W2_1(xn,xm)),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) = sdtasdt0(sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),tptp_fun_W2_1(xn,xm)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) )
| ( xn = sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(98,plain,
xn = sdtasdt0(xm,tptp_fun_W2_1(xn,xm)),
inference(unit_resolution,[status(thm)],[97,46]) ).
tff(99,plain,
xn = sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))),
inference(transitivity,[status(thm)],[98,96,91]) ).
tff(100,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ~ ( ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) )
| ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) )
| ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) )
| ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[103,101]) ).
tff(105,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) )
| ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) )
| ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[105,100]) ).
tff(107,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) )
| ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
~ ( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ) ),
inference(unit_resolution,[status(thm)],[108,24,51,4]) ).
tff(110,plain,
( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) )
| doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(111,plain,
( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ),
inference(unit_resolution,[status(thm)],[110,109]) ).
tff(112,plain,
( ~ doDivides0(xl,xn)
<=> ~ doDivides0(xl,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
~ doDivides0(xl,xn),
inference(or_elim,[status(thm)],[40]) ).
tff(114,plain,
~ doDivides0(xl,xn),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(116,plain,
( ~ ( doDivides0(xl,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ) ),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) ),
inference(unit_resolution,[status(thm)],[116,111]) ).
tff(118,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
| ~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm)))
| ( xn != sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
| ~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm)))
| ( xn != sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
| ~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm)))
| ( xn != sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
| ~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm)))
| ( xn != sdtasdt0(xl,sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))),
inference(unit_resolution,[status(thm)],[120,117,99]) ).
tff(122,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(123,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)],[122]) ).
tff(124,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(125,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)],[124]) ).
tff(126,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(127,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(128,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)],[127]) ).
tff(129,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[132,125]) ).
tff(134,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[133,123]) ).
tff(135,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ( aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm)))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl)) )
<=> ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm)))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm)))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ) ),
inference(transitivity,[status(thm)],[137,135]) ).
tff(139,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm)))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| aNaturalNumber0(sdtasdt0(tptp_fun_W2_1(xm,xl),tptp_fun_W2_1(xn,xm))) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,134,71,48,121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM466+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:13:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% See solution above
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------