%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM493+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 49.08s 49.32s
% Output : Proof 49.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 98
% Syntax : Number of formulae : 273 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 4536 (1476 equ)
% Maximal formula atoms : 88 ( 16 avg)
% Number of connectives : 6950 (2944 ~;2753 |; 915 &)
% ( 245 <=>; 93 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 257 ( 257 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-6 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 802 ( 622 !; 121 ?; 802 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(xr_type,type,
xr: $i ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(tptp_fun_W3_5_type,type,
tptp_fun_W3_5: ( $i * $i ) > $i ).
tff(sz10_type,type,
sz10: $i ).
tff(tptp_fun_W3_6_type,type,
tptp_fun_W3_6: $i > $i ).
tff(tptp_fun_W4_7_type,type,
tptp_fun_W4_7: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(tptp_fun_W3_4_type,type,
tptp_fun_W3_4: ( $i * $i ) > $i ).
tff(1,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(3,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[2]) ).
tff(7,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[6]) ).
tff(11,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(17,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(18,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)],[17]) ).
tff(19,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(20,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)],[19,18]) ).
tff(21,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)],[20,16]) ).
tff(22,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)],[21]) ).
tff(23,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)],[22,15]) ).
tff(24,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)],[23,13]) ).
tff(25,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,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(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,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(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) ) ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,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(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) ) ) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,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(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)),
inference(unit_resolution,[status(thm)],[30,24,11,8,4]) ).
tff(32,plain,
sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ( xr = sdtmndt0(xn,xp) )
<=> ( xr = sdtmndt0(xn,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
( aNaturalNumber0(xr)
& ( sdtpldt0(xp,xr) = xn )
& ( xr = sdtmndt0(xn,xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
tff(35,plain,
xr = sdtmndt0(xn,xp),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
xr = sdtmndt0(xn,xp),
inference(modus_ponens,[status(thm)],[35,33]) ).
tff(37,plain,
sdtmndt0(xn,xp) = xr,
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
<=> aNaturalNumber0(xr) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( aNaturalNumber0(xr)
<=> aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( aNaturalNumber0(xr)
<=> aNaturalNumber0(xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( aNaturalNumber0(xr)
& ( sdtpldt0(xp,xr) = xn ) ),
inference(and_elim,[status(thm)],[34]) ).
tff(42,plain,
aNaturalNumber0(xr),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
aNaturalNumber0(xr),
inference(modus_ponens,[status(thm)],[42,40]) ).
tff(44,plain,
aNaturalNumber0(sdtmndt0(xn,xp)),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,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(xp)
| ~ aNaturalNumber0(sdtmndt0(xn,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(xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,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(xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,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(xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,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(xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,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(50,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(xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),
inference(unit_resolution,[status(thm)],[50,24,8,4,44]) ).
tff(52,plain,
sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(monotonicity,[status(thm)],[52,32]) ).
tff(54,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
<=> sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
<=> ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,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(62,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)],[61]) ).
tff(63,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(64,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[67,57]) ).
tff(69,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(70,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(71,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)],[70,69]) ).
tff(72,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(unit_resolution,[status(thm)],[71,68,11,8]) ).
tff(73,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(74,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(75,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)],[74]) ).
tff(76,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)],[75,73]) ).
tff(77,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(78,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)],[77,76]) ).
tff(79,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(unit_resolution,[status(thm)],[78,68,4]) ).
tff(80,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)),
inference(unit_resolution,[status(thm)],[86,68,8,44]) ).
tff(88,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(unit_resolution,[status(thm)],[93,68,4]) ).
tff(95,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)),
inference(unit_resolution,[status(thm)],[94,87]) ).
tff(96,plain,
( sdtlseqdt0(sdtmndt0(xn,xp),xn)
<=> sdtlseqdt0(xr,xn) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(97,plain,
( sdtlseqdt0(xr,xn)
<=> sdtlseqdt0(sdtmndt0(xn,xp),xn) ),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( sdtlseqdt0(xr,xn)
<=> sdtlseqdt0(xr,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
( ( xr != xn )
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xr,W0) = xn ) )
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1894) ).
tff(100,plain,
sdtlseqdt0(xr,xn),
inference(and_elim,[status(thm)],[99]) ).
tff(101,plain,
sdtlseqdt0(xr,xn),
inference(modus_ponens,[status(thm)],[100,98]) ).
tff(102,plain,
sdtlseqdt0(sdtmndt0(xn,xp),xn),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
( ( sdtmndt0(xn,xp) = xn )
<=> ( xr = xn ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(104,plain,
( ( xr = xn )
<=> ( sdtmndt0(xn,xp) = xn ) ),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ( xr != xn )
<=> ( sdtmndt0(xn,xp) != xn ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( xr != xn )
<=> ( xr != xn ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ( xr != xn )
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xr,W0) = xn ) ) ),
inference(and_elim,[status(thm)],[99]) ).
tff(108,plain,
xr != xn,
inference(and_elim,[status(thm)],[107]) ).
tff(109,plain,
xr != xn,
inference(modus_ponens,[status(thm)],[108,106]) ).
tff(110,plain,
sdtmndt0(xn,xp) != xn,
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,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) ) )),
quant_intro(proof_bind(^ [W2: $i] :
rewrite(( ( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ))),
( ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
<=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )),
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) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) ) )
<=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) ) ) )),
( ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) )
<=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )),
rewrite(( ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) )
<=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )),
( ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) )
<=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )),
( ( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
<=> ( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )),
rewrite(( ( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
<=> ( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )),
( ( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
<=> ( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ))),
( ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
<=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )),
( ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
<=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )),
rewrite(( ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
<=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )),
( ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
<=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
tff(122,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[125,115]) ).
tff(127,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) = xn )
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) = xn )
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ( ( sdtmndt0(xn,xp) = xn )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) = xn )
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
| ( sdtmndt0(xn,xp) = xn )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) = xn )
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) ) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
| ( sdtmndt0(xn,xp) = xn )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) = xn )
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) ) ),
inference(transitivity,[status(thm)],[129,127]) ).
tff(131,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
| ( sdtmndt0(xn,xp) = xn )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W0,W2) = sdtpldt0(W1,W2) )
| ( sdtpldt0(W2,W0) = sdtpldt0(W2,W1) )
| ~ sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
| ~ sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) = xn )
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) = xn )
| ~ sdtlseqdt0(sdtmndt0(xn,xp),xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ) ),
inference(unit_resolution,[status(thm)],[132,126,11]) ).
tff(134,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) ),
inference(unit_resolution,[status(thm)],[133,110,102,44]) ).
tff(135,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ( sdtpldt0(xm,sdtmndt0(xn,xp)) = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,sdtmndt0(xn,xp)),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),xm),sdtpldt0(xn,xm)) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ( sdtpldt0(xm,sdtmndt0(xn,xp)) = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,sdtmndt0(xn,xp)),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),xm),sdtpldt0(xn,xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ( sdtpldt0(xm,sdtmndt0(xn,xp)) = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,sdtmndt0(xn,xp)),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),xm),sdtpldt0(xn,xm)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ( sdtpldt0(xm,sdtmndt0(xn,xp)) = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,sdtmndt0(xn,xp)),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),xm),sdtpldt0(xn,xm)) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
~ ( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ( sdtpldt0(xm,sdtmndt0(xn,xp)) = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,sdtmndt0(xn,xp)),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),xm),sdtpldt0(xn,xm)) ),
inference(unit_resolution,[status(thm)],[137,8,134]) ).
tff(139,plain,
( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ( sdtpldt0(xm,sdtmndt0(xn,xp)) = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,sdtmndt0(xn,xp)),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),xm),sdtpldt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xn,xp),xm) != sdtpldt0(xn,xm) ) ),
inference(tautology,[status(thm)],[]) ).
tff(140,plain,
sdtpldt0(sdtmndt0(xn,xp),xm) != sdtpldt0(xn,xm),
inference(unit_resolution,[status(thm)],[139,138]) ).
tff(141,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) )),
rewrite(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(144,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
trans(monotonicity(rewrite(( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
<=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )),
( ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
=> ( W1 = W2 ) ) )),
rewrite(( ( ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ( W1 = W2 ) ) )),
( ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ( W1 = W2 ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ( W1 = W2 ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(147,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
tff(149,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ),
inference(skolemize,[status(sab)],[150]) ).
tff(152,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[151,144]) ).
tff(153,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[152,142]) ).
tff(154,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) )
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xp) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
( ( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) )
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xp) )
<=> ( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) )
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xp) ) ),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
( ( ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) )
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xp) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ) ) ),
inference(transitivity,[status(thm)],[157,155]) ).
tff(159,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) )
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xp) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ) ) ),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) )
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xp) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ) ) ),
inference(transitivity,[status(thm)],[159,154]) ).
tff(161,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) )
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(xp) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ( sdtpldt0(sdtmndt0(xn,xp),xm) = sdtpldt0(xn,xm) )
| ~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ) ),
inference(unit_resolution,[status(thm)],[162,153,4]) ).
tff(164,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ) ),
inference(unit_resolution,[status(thm)],[163,87,140,72]) ).
tff(165,plain,
( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ( sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(166,plain,
sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(unit_resolution,[status(thm)],[165,164]) ).
tff(167,plain,
sdtasdt0(sdtmndt0(xn,xp),xm) = sdtasdt0(xr,xm),
inference(monotonicity,[status(thm)],[37]) ).
tff(168,plain,
( doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
<=> doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
<=> doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
<=> doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xr,xm) = sdtasdt0(xp,W0) ) )
& doDivides0(xp,sdtasdt0(xr,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1913) ).
tff(172,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(and_elim,[status(thm)],[171]) ).
tff(173,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(modus_ponens,[status(thm)],[172,170]) ).
tff(174,plain,
doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)),
inference(modus_ponens,[status(thm)],[173,169]) ).
tff(175,plain,
( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(tautology,[status(thm)],[]) ).
tff(176,plain,
( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ),
inference(unit_resolution,[status(thm)],[175,174]) ).
tff(177,plain,
( doDivides0(xp,sdtmndt0(xn,xp))
<=> doDivides0(xp,xr) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(178,plain,
( doDivides0(xp,xr)
<=> doDivides0(xp,sdtmndt0(xn,xp)) ),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ~ doDivides0(xp,xr)
<=> ~ doDivides0(xp,sdtmndt0(xn,xp)) ),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
( ~ doDivides0(xp,xr)
<=> ~ doDivides0(xp,xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,axiom,
~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xr = sdtasdt0(xp,W0) ) )
| doDivides0(xp,xr)
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xp,W0) ) )
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(182,plain,
~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xr = sdtasdt0(xp,W0) ) )
| doDivides0(xp,xr)
| ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xp,W0) ) ) ),
inference(or_elim,[status(thm)],[181]) ).
tff(183,plain,
~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( xr = sdtasdt0(xp,W0) ) )
| doDivides0(xp,xr) ),
inference(or_elim,[status(thm)],[182]) ).
tff(184,plain,
~ doDivides0(xp,xr),
inference(or_elim,[status(thm)],[183]) ).
tff(185,plain,
~ doDivides0(xp,xr),
inference(modus_ponens,[status(thm)],[184,180]) ).
tff(186,plain,
~ doDivides0(xp,sdtmndt0(xn,xp)),
inference(modus_ponens,[status(thm)],[185,179]) ).
tff(187,plain,
( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp)))
| doDivides0(xp,sdtmndt0(xn,xp)) ),
inference(tautology,[status(thm)],[]) ).
tff(188,plain,
( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) ),
inference(unit_resolution,[status(thm)],[187,186]) ).
tff(189,plain,
( isPrime0(xp)
<=> isPrime0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,axiom,
( ( xp != sz00 )
& ( xp != sz10 )
& ! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xp = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xp) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& isPrime0(xp)
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,W0) ) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(191,plain,
( ( xp != sz00 )
& ( xp != sz10 )
& ! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xp = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xp) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& isPrime0(xp)
& ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,W0) ) ) ),
inference(and_elim,[status(thm)],[190]) ).
tff(192,plain,
( ( xp != sz00 )
& ( xp != sz10 )
& ! [W0: $i] :
( ( aNaturalNumber0(W0)
& ( ? [W1: $i] :
( aNaturalNumber0(W1)
& ( xp = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xp) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& isPrime0(xp) ),
inference(and_elim,[status(thm)],[191]) ).
tff(193,plain,
isPrime0(xp),
inference(and_elim,[status(thm)],[192]) ).
tff(194,plain,
isPrime0(xp),
inference(modus_ponens,[status(thm)],[193,189]) ).
tff(195,plain,
( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) )
| ~ isPrime0(xp) ),
inference(tautology,[status(thm)],[]) ).
tff(196,plain,
( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) ),
inference(unit_resolution,[status(thm)],[195,194]) ).
tff(197,plain,
( ~ doDivides0(xp,xm)
<=> ~ doDivides0(xp,xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,plain,
~ doDivides0(xp,xm),
inference(or_elim,[status(thm)],[181]) ).
tff(199,plain,
~ doDivides0(xp,xm),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) )
| doDivides0(xp,xm) ),
inference(tautology,[status(thm)],[]) ).
tff(201,plain,
( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) ),
inference(unit_resolution,[status(thm)],[200,199]) ).
tff(202,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
<=> ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )),
rewrite(( ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) ) )),
monotonicity(monotonicity(rewrite(( ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) )
<=> ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )),
( ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
( ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) ) )),
( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(203,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) ) ),
inference(quant_intro,[status(thm)],[202]) ).
tff(204,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(205,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,plain,
^ [W0: $i,W1: $i,W2: $i] :
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(207,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[206]) ).
tff(208,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[207,205]) ).
tff(209,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(quant_intro(proof_bind(^ [W3: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
<=> ~ ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )),
( ~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
<=> ~ ~ ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) )
<=> ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )),
( ~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
<=> ( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ))),
( ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
<=> ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )),
( ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
<=> ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )),
rewrite(( ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
<=> ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )),
( ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
<=> ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )),
rewrite(( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
<=> ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) ) )),
rewrite(( ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
<=> ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) ) )),
trans(monotonicity(trans(monotonicity(rewrite(( ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) )
<=> ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) )),
( ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) )
<=> ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )),
rewrite(( ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) )
<=> ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )),
( ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) )
<=> ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )),
( ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
rewrite(( ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
( ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
<=> ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(210,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[209]) ).
tff(211,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
<=> ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) ) )),
rewrite(( ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
<=> ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) ) )),
rewrite(( ( ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ( ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) )),
( ( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
( ( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(212,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[211]) ).
tff(213,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
trans(monotonicity(rewrite(( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
<=> ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) )),
trans(monotonicity(trans(monotonicity(rewrite(( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
<=> ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) )),
rewrite(( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
<=> ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) )),
( ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) )),
rewrite(( ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) ) )),
( ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) ) )),
( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) )
<=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) ) ) )),
rewrite(( ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& 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))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )),
( ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) )
<=> ( ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ) )),
rewrite(( ( ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) )
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )),
( ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) ) )
<=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(215,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[214]) ).
tff(216,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| isPrime0(W2) )
& ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) )
| doDivides0(W2,sdtasdt0(W0,W1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
tff(217,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
| ( ? [W3: $i] :
( aNaturalNumber0(W3)
& ( W0 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ( isPrime0(W2)
| ( ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3: $i] :
( ( W3 = W2 )
| ( W3 = sz10 )
| ~ ( aNaturalNumber0(W3)
& ? [W4: $i] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
& doDivides0(W3,W2) ) ) ) )
& ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3: $i] :
( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[217,213]) ).
tff(219,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) ) ),
inference(skolemize,[status(sab)],[218]) ).
tff(220,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3: $i] :
~ ( aNaturalNumber0(W3)
& ( sdtasdt0(W0,W1) = sdtasdt0(W2,W3) ) ) )
| ( aNaturalNumber0(tptp_fun_W3_4(W2,W1))
& ( W1 = sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) )
& doDivides0(W2,W1) )
| ( aNaturalNumber0(tptp_fun_W3_5(W2,W0))
& ( W0 = sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
& doDivides0(W2,W0) )
| ( ~ isPrime0(W2)
& ( ( W2 = sz00 )
| ( W2 = sz10 )
| ( ( tptp_fun_W3_6(W2) != W2 )
& ( tptp_fun_W3_6(W2) != sz10 )
& aNaturalNumber0(tptp_fun_W3_6(W2))
& aNaturalNumber0(tptp_fun_W4_7(W2))
& ( W2 = sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
& doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[219,212]) ).
tff(221,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[220,210]) ).
tff(222,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) )
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[221,208]) ).
tff(223,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) ),
inference(modus_ponens,[status(thm)],[222,203]) ).
tff(224,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,plain,
( ( ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) )
<=> ( ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,plain,
( ~ ( doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) ) )
<=> ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(227,plain,
( ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ( tptp_fun_W3_6(xp) = sz10 )
| ( tptp_fun_W3_6(xp) = xp )
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ doDivides0(tptp_fun_W3_6(xp),xp) ) ) )
<=> ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,plain,
( ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp)))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ doDivides0(xp,sdtmndt0(xn,xp)) )
<=> ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(229,plain,
( ( ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp)))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ doDivides0(xp,sdtmndt0(xn,xp)) )
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ( tptp_fun_W3_6(xp) = sz10 )
| ( tptp_fun_W3_6(xp) = xp )
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ doDivides0(tptp_fun_W3_6(xp),xp) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ) ),
inference(monotonicity,[status(thm)],[228,227,226]) ).
tff(230,plain,
( ( ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp)))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ doDivides0(xp,sdtmndt0(xn,xp)) )
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ( tptp_fun_W3_6(xp) = sz10 )
| ( tptp_fun_W3_6(xp) = xp )
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ doDivides0(tptp_fun_W3_6(xp),xp) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) ) ) )
<=> ( ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ) ),
inference(transitivity,[status(thm)],[229,225]) ).
tff(231,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp)))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ doDivides0(xp,sdtmndt0(xn,xp)) )
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ( tptp_fun_W3_6(xp) = sz10 )
| ( tptp_fun_W3_6(xp) = xp )
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ doDivides0(tptp_fun_W3_6(xp),xp) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ) ),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp)))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ doDivides0(xp,sdtmndt0(xn,xp)) )
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ( tptp_fun_W3_6(xp) = sz10 )
| ( tptp_fun_W3_6(xp) = xp )
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ doDivides0(tptp_fun_W3_6(xp),xp) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ) ),
inference(transitivity,[status(thm)],[231,224]) ).
tff(233,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp)))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ doDivides0(xp,sdtmndt0(xn,xp)) )
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ( tptp_fun_W3_6(xp) = sz10 )
| ( tptp_fun_W3_6(xp) = xp )
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ doDivides0(tptp_fun_W3_6(xp),xp) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ doDivides0(W2,W1)
| ~ aNaturalNumber0(tptp_fun_W3_4(W2,W1))
| ( W1 != sdtasdt0(W2,tptp_fun_W3_4(W2,W1)) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W3_5(W2,W0))
| ( W0 != sdtasdt0(W2,tptp_fun_W3_5(W2,W0)) )
| ~ doDivides0(W2,W0) )
| ~ ( isPrime0(W2)
| ~ ( ( W2 = sz00 )
| ( W2 = sz10 )
| ~ ( ( tptp_fun_W3_6(W2) = sz10 )
| ( tptp_fun_W3_6(W2) = W2 )
| ~ aNaturalNumber0(tptp_fun_W3_6(W2))
| ~ aNaturalNumber0(tptp_fun_W4_7(W2))
| ( W2 != sdtasdt0(tptp_fun_W3_6(W2),tptp_fun_W4_7(W2)) )
| ~ doDivides0(tptp_fun_W3_6(W2),W2) ) ) )
| ~ ( doDivides0(W2,sdtasdt0(W0,W1))
| ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(W0,W1) != sdtasdt0(W2,W3) ) ) ) )
| ~ ( ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(tptp_fun_W3_4(xp,xm))
| ( xm != sdtasdt0(xp,tptp_fun_W3_4(xp,xm)) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( isPrime0(xp)
| ~ ( ( xp = sz00 )
| ( xp = sz10 )
| ~ ( ~ doDivides0(tptp_fun_W3_6(xp),xp)
| ( xp != sdtasdt0(tptp_fun_W3_6(xp),tptp_fun_W4_7(xp)) )
| ~ aNaturalNumber0(tptp_fun_W4_7(xp))
| ~ aNaturalNumber0(tptp_fun_W3_6(xp))
| ( tptp_fun_W3_6(xp) = xp )
| ( tptp_fun_W3_6(xp) = sz10 ) ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ ( ~ doDivides0(xp,sdtmndt0(xn,xp))
| ( sdtmndt0(xn,xp) != sdtasdt0(xp,tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ aNaturalNumber0(tptp_fun_W3_5(xp,sdtmndt0(xn,xp))) )
| ~ ( ~ ! [W3: $i] :
( ~ aNaturalNumber0(W3)
| ( sdtasdt0(sdtmndt0(xn,xp),xm) != sdtasdt0(xp,W3) ) )
| doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
inference(unit_resolution,[status(thm)],[234,8,4,223,201,196]) ).
tff(236,plain,
~ iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[235,188,44,176]) ).
tff(237,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(238,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)],[237]) ).
tff(239,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(240,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)],[239]) ).
tff(241,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(242,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(243,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)],[242]) ).
tff(244,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(245,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[244,243]) ).
tff(246,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[245,241]) ).
tff(247,plain,
! [W0: $i,W1: $i] :
( iLess0(W0,W1)
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) ) ),
inference(skolemize,[status(sab)],[246]) ).
tff(248,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[247,240]) ).
tff(249,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[248,238]) ).
tff(250,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(251,plain,
( ( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) )
<=> ( iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(252,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ) ),
inference(transitivity,[status(thm)],[252,250]) ).
tff(254,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(255,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0) )
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
( ( sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
inference(unit_resolution,[status(thm)],[255,249,236]) ).
tff(257,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(unit_resolution,[status(thm)],[256,166,95,80]) ).
tff(258,plain,
~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))),
inference(modus_ponens,[status(thm)],[257,55]) ).
tff(259,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(260,plain,
( ( aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(xm,xp)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(261,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)],[260]) ).
tff(262,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)],[261,259]) ).
tff(263,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(264,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)],[263,262]) ).
tff(265,plain,
aNaturalNumber0(sdtpldt0(xm,xp)),
inference(unit_resolution,[status(thm)],[264,68,8,4]) ).
tff(266,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ( sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)) = sdtpldt0(sdtpldt0(xm,xp),xn) )
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)),sdtpldt0(sdtpldt0(xm,xp),xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ( sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)) = sdtpldt0(sdtpldt0(xm,xp),xn) )
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)),sdtpldt0(sdtpldt0(xm,xp),xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(267,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ( sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)) = sdtpldt0(sdtpldt0(xm,xp),xn) )
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)),sdtpldt0(sdtpldt0(xm,xp),xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(268,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),W2) = sdtpldt0(xn,W2) )
| ( sdtpldt0(W2,sdtmndt0(xn,xp)) = sdtpldt0(W2,xn) )
| ~ sdtlseqdt0(sdtpldt0(W2,sdtmndt0(xn,xp)),sdtpldt0(W2,xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),W2),sdtpldt0(xn,W2)) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ( sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)) = sdtpldt0(sdtpldt0(xm,xp),xn) )
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)),sdtpldt0(sdtpldt0(xm,xp),xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ) ),
inference(modus_ponens,[status(thm)],[267,266]) ).
tff(269,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ ( ( sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ( sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)) = sdtpldt0(sdtpldt0(xm,xp),xn) )
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)),sdtpldt0(sdtpldt0(xm,xp),xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ) ),
inference(unit_resolution,[status(thm)],[268,134]) ).
tff(270,plain,
~ ( ( sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ( sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)) = sdtpldt0(sdtpldt0(xm,xp),xn) )
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)),sdtpldt0(sdtpldt0(xm,xp),xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(unit_resolution,[status(thm)],[269,265]) ).
tff(271,plain,
( ( sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) )
| ( sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)) = sdtpldt0(sdtpldt0(xm,xp),xn) )
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xp),sdtmndt0(xn,xp)),sdtpldt0(sdtpldt0(xm,xp),xn))
| ~ sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
| sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(tautology,[status(thm)],[]) ).
tff(272,plain,
sdtlseqdt0(sdtpldt0(sdtmndt0(xn,xp),sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))),
inference(unit_resolution,[status(thm)],[271,270]) ).
tff(273,plain,
$false,
inference(unit_resolution,[status(thm)],[272,258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM493+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.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 01:18:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 49.08/49.32 % SZS status Theorem
% 49.08/49.32 % SZS output start Proof
% See solution above
% 49.25/49.43 % E exiting
%------------------------------------------------------------------------------