%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM468+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:21:05 AM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 58
% Syntax : Number of formulae : 160 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 1724 ( 600 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 3019 (1555 ~;1030 |; 189 &)
% ( 220 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 100 ( 100 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 390 ( 349 !; 15 ?; 390 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xl_type,type,
xl: $i ).
tff(xn_type,type,
xn: $i ).
tff(xm_type,type,
xm: $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn) )
<=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240) ).
tff(4,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
( aNaturalNumber0(xl)
<=> aNaturalNumber0(xl) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[3]) ).
tff(8,plain,
aNaturalNumber0(xl),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
aNaturalNumber0(xl),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(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(quant_intro,[status(thm)],[12]) ).
tff(14,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)],[13,11]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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(19,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)],[18]) ).
tff(20,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(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)],[20,19]) ).
tff(22,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)],[21,17]) ).
tff(23,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)],[22]) ).
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)],[23,16]) ).
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) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,14]) ).
tff(26,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)
| ! [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(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(rewrite,[status(thm)],[]) ).
tff(27,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(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(rewrite,[status(thm)],[]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(transitivity,[status(thm)],[29,27]) ).
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(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(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)],[30]) ).
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(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(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(transitivity,[status(thm)],[31,26]) ).
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(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(34,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)
| ! [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)],[33,32]) ).
tff(35,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)],[34,25,9,5]) ).
tff(36,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)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(37,plain,
( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( doDivides0(xl,xn)
<=> doDivides0(xl,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
( doDivides0(xl,xm)
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240_04) ).
tff(40,plain,
doDivides0(xl,xn),
inference(and_elim,[status(thm)],[39]) ).
tff(41,plain,
doDivides0(xl,xn),
inference(modus_ponens,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) )
| ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(43,plain,
( ~ ( ~ doDivides0(xl,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ) ),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ),
inference(unit_resolution,[status(thm)],[43,37]) ).
tff(45,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) )
| ( xn = sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(46,plain,
xn = sdtasdt0(xl,tptp_fun_W2_1(xn,xl)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) = xn,
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ( xl != sz00 )
<=> ( xl != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ( ( xl != sz00 )
=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) )
<=> ~ ( ( xl = sz00 )
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
~ ( ( xl != sz00 )
=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(51,plain,
~ ( ( xl = sz00 )
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
xl != sz00,
inference(or_elim,[status(thm)],[51]) ).
tff(53,plain,
xl != sz00,
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
rewrite(( ( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
rewrite(( ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ~ ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
rewrite(( ~ ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
rewrite(( ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
tff(65,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[68,58]) ).
tff(70,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ( ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xl,xn)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xl,xn)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xl,xn)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xl,xn)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) ),
inference(unit_resolution,[status(thm)],[75,69,9,5,41,53]) ).
tff(77,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xn,xl) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) )
<=> ( tptp_fun_W2_1(xn,xl) = sdtsldt0(xn,xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) )
<=> ( tptp_fun_W2_1(xn,xl) = sdtsldt0(xn,xl) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) )
<=> ( tptp_fun_W2_1(xn,xl) = sdtsldt0(xn,xl) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) )
| ( tptp_fun_W2_1(xn,xl) = sdtsldt0(xn,xl) ) ),
inference(tautology,[status(thm)],[]) ).
tff(80,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) ) )
<=> ( tptp_fun_W2_1(xn,xl) = sdtsldt0(xn,xl) ) )
| ( tptp_fun_W2_1(xn,xl) = sdtsldt0(xn,xl) ) ),
inference(unit_resolution,[status(thm)],[79,44]) ).
tff(81,plain,
tptp_fun_W2_1(xn,xl) = sdtsldt0(xn,xl),
inference(unit_resolution,[status(thm)],[80,78]) ).
tff(82,plain,
sdtsldt0(xn,xl) = tptp_fun_W2_1(xn,xl),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
sdtasdt0(xl,sdtsldt0(xn,xl)) = sdtasdt0(xl,tptp_fun_W2_1(xn,xl)),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
sdtasdt0(xl,sdtsldt0(xn,xl)) = xn,
inference(transitivity,[status(thm)],[83,47]) ).
tff(85,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[7]) ).
tff(87,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ 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)) ) ) ) ) )
<=> ( ~ ! [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)
| ! [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(89,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(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(rewrite,[status(thm)],[]) ).
tff(90,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(91,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)],[90]) ).
tff(92,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(transitivity,[status(thm)],[91,89]) ).
tff(93,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(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)],[92]) ).
tff(94,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(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(transitivity,[status(thm)],[93,88]) ).
tff(95,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(96,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)
| ! [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)],[95,94]) ).
tff(97,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)],[96,25,9,87]) ).
tff(98,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(99,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)],[98,97]) ).
tff(100,plain,
( doDivides0(xl,xm)
<=> doDivides0(xl,xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
doDivides0(xl,xm),
inference(and_elim,[status(thm)],[39]) ).
tff(102,plain,
doDivides0(xl,xm),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,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(104,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)],[103,102]) ).
tff(105,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) ),
inference(unit_resolution,[status(thm)],[104,99]) ).
tff(106,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(107,plain,
xm = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) = xm,
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ),
inference(unit_resolution,[status(thm)],[114,69,9,87,102,53]) ).
tff(116,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) )
<=> ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) )
<=> ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) ),
inference(unit_resolution,[status(thm)],[116,115]) ).
tff(118,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) )
<=> ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) )
| ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) ),
inference(tautology,[status(thm)],[]) ).
tff(119,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xm,xl))
| ( xm != sdtasdt0(xl,tptp_fun_W2_1(xm,xl)) ) )
<=> ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) )
| ( tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl) ) ),
inference(unit_resolution,[status(thm)],[118,105]) ).
tff(120,plain,
tptp_fun_W2_1(xm,xl) = sdtsldt0(xm,xl),
inference(unit_resolution,[status(thm)],[119,117]) ).
tff(121,plain,
sdtsldt0(xm,xl) = tptp_fun_W2_1(xm,xl),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
sdtasdt0(xl,sdtsldt0(xm,xl)) = sdtasdt0(xl,tptp_fun_W2_1(xm,xl)),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(transitivity,[status(thm)],[122,108]) ).
tff(124,plain,
sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) = sdtpldt0(xm,xn),
inference(monotonicity,[status(thm)],[123,84]) ).
tff(125,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
<=> ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
<=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
inference(transitivity,[status(thm)],[125,1]) ).
tff(127,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) )
<=> ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) ) ),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) )
<=> ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) )
<=> ( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(or_elim,[status(thm)],[51]) ).
tff(131,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))),
inference(modus_ponens,[status(thm)],[131,128]) ).
tff(133,plain,
( aNaturalNumber0(tptp_fun_W2_1(xm,xl))
<=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(134,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(135,plain,
aNaturalNumber0(tptp_fun_W2_1(xm,xl)),
inference(unit_resolution,[status(thm)],[134,105]) ).
tff(136,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(modus_ponens,[status(thm)],[135,133]) ).
tff(137,plain,
( aNaturalNumber0(tptp_fun_W2_1(xn,xl))
<=> aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(138,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xl))
| ( xn != sdtasdt0(xl,tptp_fun_W2_1(xn,xl)) )
| aNaturalNumber0(tptp_fun_W2_1(xn,xl)) ),
inference(tautology,[status(thm)],[]) ).
tff(139,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xl)),
inference(unit_resolution,[status(thm)],[138,44]) ).
tff(140,plain,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(modus_ponens,[status(thm)],[139,137]) ).
tff(141,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,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) ) )),
rewrite(( ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
<=> ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(144,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,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(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(147,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
tff(149,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(skolemize,[status(sab)],[150]) ).
tff(152,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[151,144]) ).
tff(153,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[152,142]) ).
tff(154,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ) ),
inference(unit_resolution,[status(thm)],[156,153,9]) ).
tff(158,plain,
~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ),
inference(unit_resolution,[status(thm)],[157,140,136]) ).
tff(159,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) )
| ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(160,plain,
$false,
inference(unit_resolution,[status(thm)],[159,158,132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM468+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.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 01:14:46 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% See solution above
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------