%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM474+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:21:06 AM UTC 2025
% Result : Theorem 225.70s 225.87s
% Output : Proof 225.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 94
% Syntax : Number of formulae : 249 ( 77 unt; 0 typ; 0 def)
% Number of atoms : 2721 ( 869 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 4619 (2331 ~;1547 |; 306 &)
% ( 392 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 184 ( 184 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 668 ( 589 !; 30 ?; 668 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xl_type,type,
xl: $i ).
tff(xr_type,type,
xr: $i ).
tff(xm_type,type,
xm: $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(tptp_fun_W2_0_type,type,
tptp_fun_W2_0: ( $i * $i ) > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xq_type,type,
xq: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(1,plain,
( ( xl != sz00 )
<=> ( xl != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
tff(3,plain,
xl != sz00,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( doDivides0(xl,xm)
<=> doDivides0(xl,xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
tff(6,plain,
doDivides0(xl,xm),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
doDivides0(xl,xm),
inference(modus_ponens,[status(thm)],[6,4]) ).
tff(8,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
tff(10,plain,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[11,8]) ).
tff(13,plain,
( aNaturalNumber0(xl)
<=> aNaturalNumber0(xl) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
aNaturalNumber0(xl),
inference(and_elim,[status(thm)],[10]) ).
tff(15,plain,
aNaturalNumber0(xl),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
rewrite(( ( ( W2 = sdtsldt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
rewrite(( ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
( ( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )),
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ~ ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
rewrite(( ~ ~ ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) ) )),
rewrite(( ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) ),
inference(unit_resolution,[status(thm)],[37,31,15,12,7,3]) ).
tff(39,plain,
( ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ( ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
<=> ( sdtsldt0(xm,xl) = sdtsldt0(xm,xl) ) )
<=> ~ ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
<=> ( sdtsldt0(xm,xl) = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) ) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
<=> ( sdtsldt0(xm,xl) = sdtsldt0(xm,xl) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) ) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
<=> ( sdtsldt0(xm,xl) = sdtsldt0(xm,xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xm != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(xm,xl) ) )
| ~ ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) ) ),
inference(unit_resolution,[status(thm)],[44,38]) ).
tff(46,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) )
| ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(47,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ( xp = sdtsldt0(xm,xl) )
<=> ( xp = sdtsldt0(xm,xl) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
tff(51,plain,
xp = sdtsldt0(xm,xl),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
sdtasdt0(xl,xp) = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
sdtasdt0(xl,xp) = xm,
inference(transitivity,[status(thm)],[52,48]) ).
tff(54,plain,
sdtpldt0(sdtasdt0(xl,xp),xn) = sdtpldt0(xm,xn),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
sdtpldt0(xm,xn) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[9]) ).
tff(58,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,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)],[61]) ).
tff(63,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(64,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(65,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)],[64]) ).
tff(66,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(67,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[70,60]) ).
tff(72,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(unit_resolution,[status(thm)],[77,71,12,58]) ).
tff(79,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
<=> ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )),
rewrite(( ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
tff(90,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[93,83]) ).
tff(95,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[100,95]) ).
tff(102,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ ( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
~ ( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ) ),
inference(unit_resolution,[status(thm)],[103,94,15,78]) ).
tff(105,plain,
( ~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) ) )
| ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(106,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
<=> doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(and_elim,[status(thm)],[5]) ).
tff(109,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(111,plain,
( ~ ( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ) ),
inference(unit_resolution,[status(thm)],[110,109]) ).
tff(112,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ),
inference(unit_resolution,[status(thm)],[111,106]) ).
tff(113,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(114,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) = sdtpldt0(xm,xn),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ( ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
<=> ( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(unit_resolution,[status(thm)],[121,31,15,109,3,78]) ).
tff(123,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,W2) ) )
<=> ( W2 = sdtsldt0(sdtpldt0(xm,xn),xl) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(unit_resolution,[status(thm)],[123,122]) ).
tff(125,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(tautology,[status(thm)],[]) ).
tff(126,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ) )
<=> ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) )
| ( tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(unit_resolution,[status(thm)],[125,112]) ).
tff(127,plain,
tptp_fun_W2_1(sdtpldt0(xm,xn),xl) = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(unit_resolution,[status(thm)],[126,124]) ).
tff(128,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
( ( xq = sdtsldt0(sdtpldt0(xm,xn),xl) )
<=> ( xq = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,axiom,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
tff(131,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
sdtsldt0(xm,xl) = xp,
inference(symmetry,[status(thm)],[51]) ).
tff(134,plain,
( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
<=> sdtlseqdt0(xp,xq) ),
inference(monotonicity,[status(thm)],[133,132]) ).
tff(135,plain,
( sdtlseqdt0(xp,xq)
<=> sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( sdtlseqdt0(xp,xq)
<=> sdtlseqdt0(xp,xq) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,axiom,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1395) ).
tff(138,plain,
sdtlseqdt0(xp,xq),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)),
inference(modus_ponens,[status(thm)],[138,135]) ).
tff(140,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ( xm != sdtasdt0(xl,sdtsldt0(xm,xl)) )
| aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(tautology,[status(thm)],[]) ).
tff(141,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(unit_resolution,[status(thm)],[140,45]) ).
tff(142,plain,
( aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
<=> aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(143,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl))
| ( sdtpldt0(xm,xn) != sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) )
| aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl)) ),
inference(tautology,[status(thm)],[]) ).
tff(144,plain,
aNaturalNumber0(tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),
inference(unit_resolution,[status(thm)],[143,112]) ).
tff(145,plain,
aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)),
inference(modus_ponens,[status(thm)],[144,142]) ).
tff(146,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(147,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(149,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[149,147]) ).
tff(151,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) ) )),
rewrite(( ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
( ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
rewrite(( ( ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(152,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[151]) ).
tff(153,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(155,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
tff(157,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[157,153]) ).
tff(159,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(skolemize,[status(sab)],[158]) ).
tff(160,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[159,152]) ).
tff(161,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[160,150]) ).
tff(162,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
( ( ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ~ ( ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) )
<=> ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
( ( ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( ( ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[165,163]) ).
tff(167,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[167,162]) ).
tff(169,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[170,161]) ).
tff(172,plain,
~ ( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ) ),
inference(unit_resolution,[status(thm)],[171,145,141]) ).
tff(173,plain,
( ~ ( sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(174,plain,
( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ),
inference(unit_resolution,[status(thm)],[173,172]) ).
tff(175,plain,
( ~ ( ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) )
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(176,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(unit_resolution,[status(thm)],[175,174,139]) ).
tff(177,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) )
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
inference(tautology,[status(thm)],[]) ).
tff(178,plain,
sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(unit_resolution,[status(thm)],[177,176]) ).
tff(179,plain,
sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) = tptp_fun_W2_1(sdtpldt0(xm,xn),xl),
inference(transitivity,[status(thm)],[178,128]) ).
tff(180,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) = sdtasdt0(xl,tptp_fun_W2_1(sdtpldt0(xm,xn),xl)),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) )
| aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) ),
inference(tautology,[status(thm)],[]) ).
tff(182,plain,
aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),
inference(unit_resolution,[status(thm)],[181,176]) ).
tff(183,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(184,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[183]) ).
tff(185,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
<=> ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(186,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[185]) ).
tff(187,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(189,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[188]) ).
tff(190,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
tff(191,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[191,187]) ).
tff(193,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(skolemize,[status(sab)],[192]) ).
tff(194,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[193,186]) ).
tff(195,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[194,184]) ).
tff(196,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,plain,
( ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) ) ),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) ) ),
inference(transitivity,[status(thm)],[198,196]) ).
tff(200,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ) ),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,plain,
~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) ) ),
inference(unit_resolution,[status(thm)],[201,195,15,141,182]) ).
tff(203,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),xl)) )
| ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(204,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))),
inference(unit_resolution,[status(thm)],[203,202]) ).
tff(205,plain,
sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
( ( xr = sdtmndt0(xq,xp) )
<=> ( xr = sdtmndt0(xq,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,axiom,
xr = sdtmndt0(xq,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1422) ).
tff(208,plain,
xr = sdtmndt0(xq,xp),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
sdtmndt0(xq,xp) = xr,
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
sdtmndt0(xq,xp) = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),
inference(monotonicity,[status(thm)],[131,51]) ).
tff(211,plain,
sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) = sdtmndt0(xq,xp),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(213,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[212]) ).
tff(214,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(215,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[214]) ).
tff(216,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(transitivity,[status(thm)],[215,213]) ).
tff(217,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
rewrite(( ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
rewrite(( ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(218,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[217]) ).
tff(219,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(221,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[220]) ).
tff(222,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
tff(223,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[223,219]) ).
tff(225,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(skolemize,[status(sab)],[224]) ).
tff(226,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[225,218]) ).
tff(227,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[226,216]) ).
tff(228,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(229,plain,
( ( ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) )
<=> ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(230,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ) ),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ) ),
inference(transitivity,[status(thm)],[230,228]) ).
tff(232,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(unit_resolution,[status(thm)],[233,227]) ).
tff(235,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ),
inference(unit_resolution,[status(thm)],[234,145,139,141]) ).
tff(236,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sdtsldt0(xm,xl),W2) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( W2 = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ),
inference(unit_resolution,[status(thm)],[236,235]) ).
tff(238,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) )
| ( tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(239,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ( sdtpldt0(sdtsldt0(xm,xl),tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) != sdtsldt0(sdtpldt0(xm,xn),xl) ) )
<=> ( tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) )
| ( tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) ) ),
inference(unit_resolution,[status(thm)],[238,176]) ).
tff(240,plain,
tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) = sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)),
inference(unit_resolution,[status(thm)],[239,237]) ).
tff(241,plain,
tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)) = xr,
inference(transitivity,[status(thm)],[240,211,209]) ).
tff(242,plain,
sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))) = sdtasdt0(xl,xr),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
sdtasdt0(xl,xr) = sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,tptp_fun_W2_0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))),
inference(monotonicity,[status(thm)],[52,243]) ).
tff(245,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(transitivity,[status(thm)],[244,205,180,115,55]) ).
tff(246,plain,
( ( sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn) )
<=> ( sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(247,axiom,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(248,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(modus_ponens,[status(thm)],[247,246]) ).
tff(249,plain,
$false,
inference(unit_resolution,[status(thm)],[248,245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM474+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 01:13:48 EDT 2025
% 0.14/0.35 % CPUTime :
% 225.70/225.87 % SZS status Theorem
% 225.70/225.87 % SZS output start Proof
% See solution above
% 225.77/225.91 % E exiting
%------------------------------------------------------------------------------