%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM495+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:10 AM UTC 2025
% Result : Theorem 1.75s 1.91s
% Output : Proof 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 80
% Syntax : Number of formulae : 215 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 2251 ( 381 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 3440 (1581 ~;1257 |; 278 &)
% ( 263 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 177 ( 177 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 525 ( 463 !; 15 ?; 525 :)
% 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(xr_type,type,
xr: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $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(isPrime0_type,type,
isPrime0: $i > $o ).
tff(1,plain,
( ( xr = sdtmndt0(xn,xp) )
<=> ( xr = sdtmndt0(xn,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
tff(3,plain,
xr = sdtmndt0(xn,xp),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sdtmndt0(xn,xp) = xr,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xr,xm),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
sdtpldt0(xr,xm) = sdtpldt0(sdtmndt0(xn,xp),xm),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
<=> iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
<=> ~ iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
sdtasdt0(sdtmndt0(xn,xp),xm) = sdtasdt0(xr,xm),
inference(monotonicity,[status(thm)],[4]) ).
tff(12,plain,
( doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
<=> doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
<=> doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
<=> doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1913) ).
tff(16,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
( doDivides0(xp,sdtmndt0(xn,xp))
<=> doDivides0(xp,xr) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(19,plain,
( doDivides0(xp,xr)
<=> doDivides0(xp,sdtmndt0(xn,xp)) ),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ~ doDivides0(xp,xr)
<=> ~ doDivides0(xp,sdtmndt0(xn,xp)) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ~ doDivides0(xp,xr)
<=> ~ doDivides0(xp,xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
~ ( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(23,plain,
~ doDivides0(xp,xr),
inference(or_elim,[status(thm)],[22]) ).
tff(24,plain,
~ doDivides0(xp,xr),
inference(modus_ponens,[status(thm)],[23,21]) ).
tff(25,plain,
~ doDivides0(xp,sdtmndt0(xn,xp)),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( sdtlseqdt0(xp,xn)
<=> sdtlseqdt0(xp,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
tff(28,plain,
sdtlseqdt0(xp,xn),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(31,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[31,29]) ).
tff(33,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[30]) ).
tff(35,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[35,33]) ).
tff(37,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
rewrite(( ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
rewrite(( ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(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) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
( ( ! [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] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,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] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,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(45,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(46,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)],[45]) ).
tff(47,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(48,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)],[47,46]) ).
tff(49,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)],[48,44]) ).
tff(50,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)],[49]) ).
tff(51,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[51,41]) ).
tff(53,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[58,52,36,32,28]) ).
tff(60,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) )
<=> ( W2 = 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(quant_inst,[status(thm)],[]) ).
tff(61,plain,
~ ( ( ~ 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)],[60,59]) ).
tff(62,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(63,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)],[62]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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)],[65,63]) ).
tff(67,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(68,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)],[67]) ).
tff(69,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(70,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(71,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)],[70]) ).
tff(72,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(73,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)],[72,71]) ).
tff(74,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)],[73,69]) ).
tff(75,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)],[74]) ).
tff(76,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)],[75,68]) ).
tff(77,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)],[76,66]) ).
tff(78,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)
| ! [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 ) ) ) ) )
<=> ( ~ ! [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)
| ! [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(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ 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 ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( 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(rewrite,[status(thm)],[]) ).
tff(80,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)
| ! [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(monotonicity,[status(thm)],[79]) ).
tff(81,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)
| ! [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(transitivity,[status(thm)],[80,78]) ).
tff(82,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(83,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)
| ! [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(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
~ ( ~ ( 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(unit_resolution,[status(thm)],[83,77,36,32]) ).
tff(85,plain,
( ~ ( 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 ) ) )
| ~ sdtlseqdt0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(86,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)],[85,84]) ).
tff(87,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(88,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)],[87,28]) ).
tff(89,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xp))
| ( sdtpldt0(xp,tptp_fun_W2_0(xn,xp)) != xn ) ),
inference(unit_resolution,[status(thm)],[88,86]) ).
tff(90,plain,
( ( ( ~ 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 )
| ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(91,plain,
( ( ( ~ 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) ) )
| ( tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
tptp_fun_W2_0(xn,xp) = sdtmndt0(xn,xp),
inference(unit_resolution,[status(thm)],[91,61]) ).
tff(93,plain,
( aNaturalNumber0(tptp_fun_W2_0(xn,xp))
<=> aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,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(95,plain,
aNaturalNumber0(tptp_fun_W2_0(xn,xp)),
inference(unit_resolution,[status(thm)],[94,89]) ).
tff(96,plain,
aNaturalNumber0(sdtmndt0(xn,xp)),
inference(modus_ponens,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ doDivides0(xp,xm)
<=> ~ doDivides0(xp,xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
~ doDivides0(xp,xm),
inference(or_elim,[status(thm)],[22]) ).
tff(99,plain,
~ doDivides0(xp,xm),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( isPrime0(xp)
<=> isPrime0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(102,plain,
isPrime0(xp),
inference(and_elim,[status(thm)],[101]) ).
tff(103,plain,
isPrime0(xp),
inference(modus_ponens,[status(thm)],[102,100]) ).
tff(104,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(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)) )
<=> ! [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)],[104]) ).
tff(106,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(107,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)],[106]) ).
tff(108,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(109,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(110,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)],[109]) ).
tff(111,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(112,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)],[111,110]) ).
tff(113,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)],[112,108]) ).
tff(114,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)],[113]) ).
tff(115,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)],[114,107]) ).
tff(116,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)],[115,105]) ).
tff(117,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[34]) ).
tff(119,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,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)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(xn,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)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(xn,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(121,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)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(xn,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(122,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)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(xn,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)],[121]) ).
tff(123,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)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(xn,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)],[122,120]) ).
tff(124,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(125,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)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(xn,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)],[124,123]) ).
tff(126,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(unit_resolution,[status(thm)],[125,119,32,116,103,99]) ).
tff(127,plain,
~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[126,96,25,17]) ).
tff(128,plain,
~ iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(modus_ponens,[status(thm)],[127,10]) ).
tff(129,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(132,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,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) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(135,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
tff(137,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[139,132]) ).
tff(141,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[140,130]) ).
tff(142,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ) ),
inference(transitivity,[status(thm)],[144,142]) ).
tff(146,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),
inference(unit_resolution,[status(thm)],[147,141,119,32,96]) ).
tff(149,plain,
sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(sdtpldt0(xr,xm),xp),
inference(transitivity,[status(thm)],[149,8]) ).
tff(151,plain,
( aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)))
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,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(153,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)],[152]) ).
tff(154,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(155,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)],[154]) ).
tff(156,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(157,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(158,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)],[157]) ).
tff(159,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(160,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[162,155]) ).
tff(164,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[163,153]) ).
tff(165,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(xm,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(xm,xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
( ( aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(xm,xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(xm,xp)) ) ),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(xm,xp)) ) ),
inference(transitivity,[status(thm)],[167,165]) ).
tff(169,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(xm,xp)) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
aNaturalNumber0(sdtpldt0(xm,xp)),
inference(unit_resolution,[status(thm)],[170,164,119,32]) ).
tff(172,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ( aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp))) ) ),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp))) ) ),
inference(transitivity,[status(thm)],[174,172]) ).
tff(176,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp))) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp))),
inference(unit_resolution,[status(thm)],[177,164,96,171]) ).
tff(179,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)),
inference(modus_ponens,[status(thm)],[178,151]) ).
tff(180,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(181,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(182,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)],[181,180]) ).
tff(183,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(unit_resolution,[status(thm)],[182,164,36,119]) ).
tff(184,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(185,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(186,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)],[185]) ).
tff(187,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)],[186,184]) ).
tff(188,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(189,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)],[188,187]) ).
tff(190,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[189,164,32,183]) ).
tff(191,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(192,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(193,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(and_elim,[status(thm)],[192]) ).
tff(194,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(modus_ponens,[status(thm)],[193,191]) ).
tff(195,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(196,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(and_elim,[status(thm)],[192]) ).
tff(197,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,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(199,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)],[198]) ).
tff(200,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(201,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)],[200]) ).
tff(202,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(203,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(204,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)],[203]) ).
tff(205,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(206,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[206,202]) ).
tff(208,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(skolemize,[status(sab)],[207]) ).
tff(209,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[208,201]) ).
tff(210,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[209,199]) ).
tff(211,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(212,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
( iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(unit_resolution,[status(thm)],[213,210,197,194,190]) ).
tff(215,plain,
$false,
inference(unit_resolution,[status(thm)],[214,179,128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM495+1 : TPTP v9.0.0. Released v4.0.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:18:11 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.75/1.91 % SZS status Theorem
% 1.75/1.91 % SZS output start Proof
% See solution above
% 1.75/1.95 % E exiting
%------------------------------------------------------------------------------