TSTP Solution File: NUM495+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM495+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:03 EDT 2022
% Result : Theorem 0.53s 0.58s
% Output : Proof 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 86
% Syntax : Number of formulae : 192 ( 50 unt; 13 typ; 0 def)
% Number of atoms : 1893 ( 287 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 2891 (1323 ~;1060 |; 231 &)
% ( 222 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 146 ( 146 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 432 ( 379 !; 15 ?; 432 :)
% Comments :
%------------------------------------------------------------------------------
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(tptp_fun_W2_0_type,type,
tptp_fun_W2_0: ( $i * $i ) > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(xr_type,type,
xr: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(1,plain,
( sdtlseqdt0(xp,xn)
<=> sdtlseqdt0(xp,xn) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
tff(3,plain,
sdtlseqdt0(xp,xn),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(6,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[6,4]) ).
tff(8,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[5]) ).
tff(10,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i] :
rewrite(
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
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) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ),
inference(unit_resolution,[status(thm)],[33,27,11,7,3]) ).
tff(35,plain,
( ~ ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ( ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,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(
( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) ) )),
rewrite(
( ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
( ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
rewrite(
( ( ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
rewrite(
( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
tff(48,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[51,41]) ).
tff(53,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ ( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ),
inference(unit_resolution,[status(thm)],[55,52,11,7]) ).
tff(57,plain,
( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(tautology,[status(thm)],]) ).
tff(58,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(tautology,[status(thm)],]) ).
tff(60,plain,
( ~ ( ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(unit_resolution,[status(thm)],[59,3]) ).
tff(61,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ),
inference(unit_resolution,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ( ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ),
inference(tautology,[status(thm)],]) ).
tff(63,plain,
( ~ ( ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) )
| ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp),
inference(unit_resolution,[status(thm)],[63,36]) ).
tff(65,plain,
( aNaturalNumber0(tptp_fun_W2_0(xn,xp))
<=> aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn )
| aNaturalNumber0(tptp_fun_W2_0(xn,xp)) ),
inference(tautology,[status(thm)],]) ).
tff(67,plain,
aNaturalNumber0(tptp_fun_W2_0(xn,xp)),
inference(unit_resolution,[status(thm)],[66,61]) ).
tff(68,plain,
aNaturalNumber0(sdtmndt0(xn,xp)),
inference(modus_ponens,[status(thm)],[67,65]) ).
tff(69,plain,
( ~ doDivides0(xp,xm)
<=> ~ doDivides0(xp,xm) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
~ ( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(71,plain,
~ doDivides0(xp,xm),
inference(or_elim,[status(thm)],[70]) ).
tff(72,plain,
~ doDivides0(xp,xm),
inference(modus_ponens,[status(thm)],[71,69]) ).
tff(73,plain,
( ~ doDivides0(xp,xr)
<=> ~ doDivides0(xp,sdtmndt0(xn,xp)) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ~ doDivides0(xp,xr)
<=> ~ doDivides0(xp,xr) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
~ doDivides0(xp,xr),
inference(or_elim,[status(thm)],[70]) ).
tff(76,plain,
~ doDivides0(xp,xr),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
~ doDivides0(xp,sdtmndt0(xn,xp)),
inference(modus_ponens,[status(thm)],[76,73]) ).
tff(78,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
<=> doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
<=> doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1913) ).
tff(81,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)),
inference(modus_ponens,[status(thm)],[81,78]) ).
tff(83,plain,
( isPrime0(xp)
<=> isPrime0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(85,plain,
isPrime0(xp),
inference(and_elim,[status(thm)],[84]) ).
tff(86,plain,
isPrime0(xp),
inference(modus_ponens,[status(thm)],[85,83]) ).
tff(87,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,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) ) )),
trans(
monotonicity(
rewrite(
( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ~ ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
( ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ~ ~ ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
rewrite(
( ~ ~ ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
( ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ( ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
( ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
rewrite(
( ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
( ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( doDivides0(W2,W0)
| doDivides0(W2,W1) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) )),
( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) )
<=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) ) )),
rewrite(
( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )),
( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )),
( ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) )
<=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ) )),
rewrite(
( ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )),
( ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ) )
<=> ( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
tff(95,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) ),
inference(modus_ponens,[status(thm)],[98,88]) ).
tff(100,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[9]) ).
tff(102,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) )
<=> ( doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1)) )
| doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(unit_resolution,[status(thm)],[108,102,7,99,86,82,77,72]) ).
tff(110,plain,
~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[109,68]) ).
tff(111,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,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(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(119,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[122,112]) ).
tff(124,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ( aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ) ),
inference(transitivity,[status(thm)],[126,124]) ).
tff(128,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ),
inference(unit_resolution,[status(thm)],[129,123,102]) ).
tff(131,plain,
aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)),
inference(unit_resolution,[status(thm)],[130,68]) ).
tff(132,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ( aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(unit_resolution,[status(thm)],[137,123,7]) ).
tff(139,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)),
inference(unit_resolution,[status(thm)],[138,131]) ).
tff(140,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(unit_resolution,[status(thm)],[142,123,11,102]) ).
tff(144,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
( ( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(transitivity,[status(thm)],[146,144]) ).
tff(148,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[149,123,7,143]) ).
tff(151,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(rewrite,[status(thm)],]) ).
tff(153,axiom,
( ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) )
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2062) ).
tff(154,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(and_elim,[status(thm)],[153]) ).
tff(155,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(modus_ponens,[status(thm)],[154,152]) ).
tff(156,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
( ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) )
<=> ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) )
<=> ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(and_elim,[status(thm)],[153]) ).
tff(160,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(modus_ponens,[status(thm)],[160,157]) ).
tff(162,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(163,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,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(
( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
<=> ~ ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
<=> ~ ~ ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(
( ~ ~ ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
( ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ( iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(
( ( iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
( ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(165,plain,
( ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,plain,
( ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) )
<=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| iLess0(W0,W1) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| iLess0(W0,W1) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| iLess0(W0,W1) ) )
<=> ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) )
<=> ( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(168,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) ),
inference(quant_intro,[status(thm)],[167]) ).
tff(169,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
tff(170,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[170,166]) ).
tff(172,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(skolemize,[status(sab)],[171]) ).
tff(173,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[172,165]) ).
tff(174,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[173,163]) ).
tff(175,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
( iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(unit_resolution,[status(thm)],[177,174,161,156,150]) ).
tff(179,plain,
$false,
inference(unit_resolution,[status(thm)],[178,139,110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM495+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 11:08:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.53/0.58 % SZS status Theorem
% 0.53/0.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------