%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM492+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:09 AM UTC 2025
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 50
% Syntax : Number of formulae : 140 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 1047 ( 176 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 1486 ( 662 ~; 500 |; 131 &)
% ( 168 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 83 ( 83 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 253 ( 229 !; 0 ?; 253 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xr_type,type,
xr: $i ).
tff(xn_type,type,
xn: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(xm_type,type,
xm: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(1,plain,
( ( xn = sdtpldt0(xp,xr) )
<=> ( xn = sdtpldt0(xp,xr) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1924) ).
tff(3,plain,
xn = sdtpldt0(xp,xr),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sdtmndt0(xn,xp) = sdtmndt0(sdtpldt0(xp,xr),xp),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
sdtpldt0(xp,xr) = xn,
inference(symmetry,[status(thm)],[3]) ).
tff(6,plain,
( aNaturalNumber0(sdtpldt0(xp,xr))
<=> aNaturalNumber0(xn) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(sdtpldt0(xp,xr)) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(10,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[11,8]) ).
tff(13,plain,
aNaturalNumber0(sdtpldt0(xp,xr)),
inference(modus_ponens,[status(thm)],[12,7]) ).
tff(14,plain,
( sdtlseqdt0(xp,sdtpldt0(xp,xr))
<=> sdtlseqdt0(xp,xn) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(15,plain,
( sdtlseqdt0(xp,xn)
<=> sdtlseqdt0(xp,sdtpldt0(xp,xr)) ),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( sdtlseqdt0(xp,xn)
<=> sdtlseqdt0(xp,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
tff(18,plain,
sdtlseqdt0(xp,xn),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
sdtlseqdt0(xp,sdtpldt0(xp,xr)),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[9]) ).
tff(22,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,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(24,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)],[23]) ).
tff(25,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(26,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)],[25]) ).
tff(27,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)],[26,24]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(31,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(32,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)],[31]) ).
tff(33,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(34,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)],[33,32]) ).
tff(35,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)],[34,30]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36,29]) ).
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) ) ) ),
inference(modus_ponens,[status(thm)],[37,27]) ).
tff(39,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(xp)
| ~ aNaturalNumber0(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),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(xp)
| ~ aNaturalNumber0(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),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(xp)
| ~ aNaturalNumber0(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) ) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,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(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),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(xp)
| ~ aNaturalNumber0(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) ) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,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(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,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(xp)
| ~ aNaturalNumber0(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ aNaturalNumber0(sdtpldt0(xp,xr))
| ~ sdtlseqdt0(xp,sdtpldt0(xp,xr))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) ) ),
inference(unit_resolution,[status(thm)],[44,38,22]) ).
tff(46,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) ),
inference(unit_resolution,[status(thm)],[45,19,13]) ).
tff(47,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != sdtpldt0(xp,xr) ) )
<=> ( W2 = sdtmndt0(sdtpldt0(xp,xr),xp) ) )
| ~ ( ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != sdtpldt0(xp,xr) ) )
<=> ( sdtmndt0(xn,xp) = sdtmndt0(sdtpldt0(xp,xr),xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
~ ( ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != sdtpldt0(xp,xr) ) )
<=> ( sdtmndt0(xn,xp) = sdtmndt0(sdtpldt0(xp,xr),xp) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
( ( sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) )
<=> ( sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1978) ).
tff(51,plain,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( xr = sdtmndt0(xn,xp) )
<=> ( xr = sdtmndt0(xn,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
tff(54,plain,
xr = sdtmndt0(xn,xp),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
sdtmndt0(xn,xp) = xr,
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
sdtasdt0(sdtmndt0(xn,xp),xm) = sdtasdt0(xr,xm),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
sdtasdt0(sdtmndt0(xn,xp),xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(transitivity,[status(thm)],[56,51]) ).
tff(58,plain,
( aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm))
<=> aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
<=> aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
<=> ~ aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) )
<=> ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1951) ).
tff(63,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) = sdtasdt0(xr,xm),
inference(symmetry,[status(thm)],[51]) ).
tff(66,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))) = sdtasdt0(xn,xm),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))))
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
<=> doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) ),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(72,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(modus_ponens,[status(thm)],[72,70]) ).
tff(74,plain,
doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[10]) ).
tff(77,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
^ [W0: $i,W1: $i] :
refl(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(86,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[88,81]) ).
tff(90,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[89,79]) ).
tff(91,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(unit_resolution,[status(thm)],[93,90,77,22]) ).
tff(95,plain,
( doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
<=> doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(96,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
<=> doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))) ),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ doDivides0(xp,sdtasdt0(xr,xm))
<=> ~ doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ~ doDivides0(xp,sdtasdt0(xr,xm))
<=> ~ doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
~ doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(100,plain,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
~ doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))),
inference(modus_ponens,[status(thm)],[100,97]) ).
tff(102,plain,
( doDivides0(xp,sdtasdt0(xp,xm))
<=> doDivides0(xp,sdtasdt0(xp,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& doDivides0(xp,sdtasdt0(xp,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2001) ).
tff(104,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(and_elim,[status(thm)],[103]) ).
tff(105,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(modus_ponens,[status(thm)],[104,102]) ).
tff(106,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
<=> ( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,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(( ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
<=> ~ ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) )),
( ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
<=> ~ ~ ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) )),
rewrite(( ~ ~ ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
<=> ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) )),
( ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
<=> ( ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) )),
( ( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) )
<=> ( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) )),
rewrite(( ( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
<=> ( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) )),
( ( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) )
<=> ( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
rewrite(( ( ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
=> doDivides0(W0,W2) )
<=> ( ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
| doDivides0(W0,W2) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
=> doDivides0(W0,W2) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
| doDivides0(W0,W2) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
| doDivides0(W0,W2) ) )
<=> ( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
=> doDivides0(W0,W2) ) )
<=> ( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
=> doDivides0(W0,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
tff(114,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) ) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,plain,
! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) ),
inference(modus_ponens,[status(thm)],[117,107]) ).
tff(119,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ( doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) )
<=> ( ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
| doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) ) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
| doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) ) ),
inference(transitivity,[status(thm)],[121,119]) ).
tff(123,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
| doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( doDivides0(W0,W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ doDivides0(W0,W1)
| ~ doDivides0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
( doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)))) ),
inference(unit_resolution,[status(thm)],[124,118,22,105]) ).
tff(126,plain,
~ aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))),
inference(unit_resolution,[status(thm)],[125,101,94,74]) ).
tff(127,plain,
~ aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)),
inference(modus_ponens,[status(thm)],[126,60]) ).
tff(128,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
( ( aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(transitivity,[status(thm)],[130,128]) ).
tff(132,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(unit_resolution,[status(thm)],[133,90,77]) ).
tff(135,plain,
~ aNaturalNumber0(sdtmndt0(xn,xp)),
inference(unit_resolution,[status(thm)],[134,127]) ).
tff(136,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != sdtpldt0(xp,xr) )
| aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(tautology,[status(thm)],[]) ).
tff(137,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != sdtpldt0(xp,xr) ) ),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
( ( ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != sdtpldt0(xp,xr) ) )
<=> ( sdtmndt0(xn,xp) = sdtmndt0(sdtpldt0(xp,xr),xp) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != sdtpldt0(xp,xr) ) )
| ( sdtmndt0(xn,xp) != sdtmndt0(sdtpldt0(xp,xr),xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(139,plain,
sdtmndt0(xn,xp) != sdtmndt0(sdtpldt0(xp,xr),xp),
inference(unit_resolution,[status(thm)],[138,137,48]) ).
tff(140,plain,
$false,
inference(unit_resolution,[status(thm)],[139,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM492+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:17:18 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% See solution above
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------