%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM524+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:21:16 AM UTC 2025
% Result : Theorem 0.42s 0.62s
% Output : Proof 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 96
% Syntax : Number of formulae : 262 ( 73 unt; 0 typ; 0 def)
% Number of atoms : 3041 (1104 equ)
% Maximal formula atoms : 32 ( 11 avg)
% Number of connectives : 4790 (2219 ~;1885 |; 282 &)
% ( 318 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 208 ( 208 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 793 ( 725 !; 15 ?; 793 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xq_type,type,
xq: $i ).
tff(xp_type,type,
xp: $i ).
tff(xm_type,type,
xm: $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( ( xq = sdtsldt0(xn,xp) )
<=> ( xq = sdtsldt0(xn,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
tff(3,plain,
xq = sdtsldt0(xn,xp),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sdtsldt0(xn,xp) = xq,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp)) = sdtasdt0(xq,xq),
inference(monotonicity,[status(thm)],[4,4]) ).
tff(6,plain,
sdtasdt0(xq,xq) = sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( doDivides0(xp,xn)
<=> doDivides0(xp,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
tff(11,plain,
doDivides0(xp,xn),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
doDivides0(xp,xn),
inference(modus_ponens,[status(thm)],[11,9]) ).
tff(13,plain,
( ( xp != sz00 )
<=> ( xp != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
tff(15,plain,
xp != sz00,
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
xp != sz00,
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 ) ),
inference(and_elim,[status(thm)],[14]) ).
tff(19,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 ) ),
inference(and_elim,[status(thm)],[18]) ).
tff(20,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
inference(and_elim,[status(thm)],[19]) ).
tff(21,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[20]) ).
tff(22,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[20]) ).
tff(25,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[25,23]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(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) ) ) )
<=> ! [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)],[29]) ).
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) ) ) )
<=> ! [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)],[30,28]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,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(36,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)],[35]) ).
tff(37,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(38,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)],[37,36]) ).
tff(39,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)],[38,34]) ).
tff(40,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)],[39]) ).
tff(41,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)],[40,33]) ).
tff(42,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)],[41,31]) ).
tff(43,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) )
<=> ( ~ ! [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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) )
<=> ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) )
<=> ( ~ ! [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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) )
<=> ( ~ ! [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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[48,42,26,22,16,12]) ).
tff(50,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) )
<=> ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) )
<=> ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,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(53,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)],[52]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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)],[55,53]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,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)],[60]) ).
tff(62,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(63,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)],[62,61]) ).
tff(64,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)],[63,59]) ).
tff(65,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)],[64]) ).
tff(66,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)],[65,58]) ).
tff(67,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)],[66,56]) ).
tff(68,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(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) )
<=> ( ~ ! [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(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,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(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,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(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,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(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,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(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,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(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,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(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
~ ( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ) ),
inference(unit_resolution,[status(thm)],[73,67,26,22]) ).
tff(75,plain,
( ~ ( doDivides0(xp,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(76,plain,
( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
( ~ ( ~ doDivides0(xp,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ) ),
inference(unit_resolution,[status(thm)],[77,12]) ).
tff(79,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ),
inference(unit_resolution,[status(thm)],[78,76]) ).
tff(80,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) )
<=> ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) )
| ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(81,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) )
<=> ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) )
| ( tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp),
inference(unit_resolution,[status(thm)],[81,51]) ).
tff(83,plain,
( aNaturalNumber0(tptp_fun_W2_1(xn,xp))
<=> aNaturalNumber0(sdtsldt0(xn,xp)) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) )
| aNaturalNumber0(tptp_fun_W2_1(xn,xp)) ),
inference(tautology,[status(thm)],[]) ).
tff(85,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xp)),
inference(unit_resolution,[status(thm)],[84,79]) ).
tff(86,plain,
aNaturalNumber0(sdtsldt0(xn,xp)),
inference(modus_ponens,[status(thm)],[85,83]) ).
tff(87,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
tff(95,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[98,88]) ).
tff(100,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xp) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xp) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) ) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xp) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) ) ) ),
inference(transitivity,[status(thm)],[102,100]) ).
tff(104,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) )
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xp) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(unit_resolution,[status(thm)],[105,99,22,86]) ).
tff(107,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) )
| ( xn = sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(108,plain,
xn = sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),
inference(unit_resolution,[status(thm)],[107,79]) ).
tff(109,plain,
sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) = xn,
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
sdtsldt0(xn,xp) = tptp_fun_W2_1(xn,xp),
inference(symmetry,[status(thm)],[82]) ).
tff(111,plain,
sdtasdt0(xp,sdtsldt0(xn,xp)) = sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
sdtasdt0(xp,sdtsldt0(xn,xp)) = xn,
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,plain,
sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xn,sdtsldt0(xn,xp)),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ( W0 != 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) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( W0 = sz00 )
| ~ doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
rewrite(( ( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
<=> ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ))),
( ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
<=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )),
( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
rewrite(( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
( ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
<=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
tff(128,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ ( ( W0 != sz00 )
& doDivides0(W0,W1) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) )
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[131,121]) ).
tff(133,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
inference(modus_ponens,[status(thm)],[132,116]) ).
tff(134,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ doDivides0(xp,xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ doDivides0(xp,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) ) )
<=> ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ doDivides0(xp,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ doDivides0(xp,xn) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ doDivides0(xp,xn) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ doDivides0(xp,xn) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) ),
inference(unit_resolution,[status(thm)],[139,133,26,22,16,12]) ).
tff(141,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(xn,xn),xp) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(xn,xn),xp) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(W2,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(W2,xn),xp) ) )
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(xn,xn),xp) ) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(xn,xn),xp),
inference(unit_resolution,[status(thm)],[143,26,140]) ).
tff(145,plain,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,sdtsldt0(xn,xp)),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ( sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) )
<=> ( sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
tff(148,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
sdtasdt0(xn,xn) = sdtasdt0(xp,sdtasdt0(xm,xm)),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
<=> aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm))) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
<=> aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[24]) ).
tff(154,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
^ [W0: $i,W1: $i] :
refl(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(156,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(161,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(163,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[163,159]) ).
tff(165,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[164]) ).
tff(166,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[165,158]) ).
tff(167,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[166,156]) ).
tff(168,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) )
<=> ( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm) ) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm) ) ),
inference(transitivity,[status(thm)],[170,168]) ).
tff(172,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(unit_resolution,[status(thm)],[173,167,154]) ).
tff(175,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,plain,
( ( aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm))) ) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm))) ) ),
inference(transitivity,[status(thm)],[177,175]) ).
tff(179,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm))) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm))),
inference(unit_resolution,[status(thm)],[180,167,22,174]) ).
tff(182,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(modus_ponens,[status(thm)],[181,151]) ).
tff(183,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
<=> doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(and_elim,[status(thm)],[10]) ).
tff(185,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) )
<=> ( ~ ! [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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
( ( ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) )
<=> ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) )
<=> ( ~ ! [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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) ) ),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) )
<=> ( ~ ! [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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) ) ),
inference(transitivity,[status(thm)],[188,186]) ).
tff(190,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(191,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) ) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) ),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) ),
inference(unit_resolution,[status(thm)],[191,42,22,16,185]) ).
tff(193,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) ),
inference(unit_resolution,[status(thm)],[192,182]) ).
tff(194,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(sdtasdt0(xn,xn),xp) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtsldt0(sdtasdt0(xn,xn),xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtsldt0(sdtasdt0(xn,xn),xp) ) ),
inference(unit_resolution,[status(thm)],[194,193]) ).
tff(196,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(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) )
<=> ( ~ ! [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(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,plain,
( ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(199,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[199,197]) ).
tff(201,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(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,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(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,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(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,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(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[201,196]) ).
tff(203,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(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ ( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) )
| ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,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(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[204,67,22]) ).
tff(206,plain,
~ ( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ) ),
inference(unit_resolution,[status(thm)],[205,182]) ).
tff(207,plain,
( ~ ( doDivides0(xp,sdtasdt0(xn,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,W2) ) ) )
| ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) )
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(208,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ),
inference(unit_resolution,[status(thm)],[207,206]) ).
tff(209,plain,
( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) )
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(210,plain,
( ~ ( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ) ),
inference(unit_resolution,[status(thm)],[209,185]) ).
tff(211,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ),
inference(unit_resolution,[status(thm)],[210,208]) ).
tff(212,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtsldt0(sdtasdt0(xn,xn),xp) ) )
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) )
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtsldt0(sdtasdt0(xn,xn),xp) ) ),
inference(tautology,[status(thm)],[]) ).
tff(213,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) )
<=> ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtsldt0(sdtasdt0(xn,xn),xp) ) )
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtsldt0(sdtasdt0(xn,xn),xp) ) ),
inference(unit_resolution,[status(thm)],[212,211]) ).
tff(214,plain,
tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtsldt0(sdtasdt0(xn,xn),xp),
inference(unit_resolution,[status(thm)],[213,195]) ).
tff(215,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) )
| ( sdtasdt0(xn,xn) = sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(216,plain,
sdtasdt0(xn,xn) = sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)),
inference(unit_resolution,[status(thm)],[215,211]) ).
tff(217,plain,
sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xn,xn),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)),
inference(transitivity,[status(thm)],[217,149]) ).
tff(219,plain,
( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) )
| ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) != sdtasdt0(xp,sdtasdt0(xm,xm)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(220,plain,
( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ),
inference(unit_resolution,[status(thm)],[219,218]) ).
tff(221,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( sdtasdt0(xn,xn) != sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) )
| aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) ),
inference(tautology,[status(thm)],[]) ).
tff(222,plain,
aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp)),
inference(unit_resolution,[status(thm)],[221,211]) ).
tff(223,plain,
^ [W0: $i] :
refl(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(224,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[223]) ).
tff(225,plain,
^ [W0: $i] :
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(226,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[225]) ).
tff(227,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(transitivity,[status(thm)],[226,224]) ).
tff(228,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
( ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
( ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
rewrite(( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
<=> ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )),
rewrite(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ))),
( ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )),
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(229,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[228]) ).
tff(230,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )),
( ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )),
rewrite(( ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) )),
( ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) )),
( ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )),
( ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ))),
( ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )),
( ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) )
<=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
rewrite(( ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
( ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) )
<=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) )
<=> ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) ) )),
rewrite(( ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(232,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[231]) ).
tff(233,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
tff(234,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[234,230]) ).
tff(236,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ),
inference(skolemize,[status(sab)],[235]) ).
tff(237,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[236,229]) ).
tff(238,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[237,227]) ).
tff(239,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(240,plain,
( ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) )
<=> ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(241,plain,
^ [W1: $i,W2: $i] :
rewrite(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) )
| ~ aNaturalNumber0(W1) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(242,plain,
( ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) )
| ~ aNaturalNumber0(W1) )
<=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) ),
inference(quant_intro,[status(thm)],[241]) ).
tff(243,plain,
( ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) ) ),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
( ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) ) ),
inference(transitivity,[status(thm)],[243,240]) ).
tff(245,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) ) ),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) ) ),
inference(transitivity,[status(thm)],[245,239]) ).
tff(247,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) )
| ~ aNaturalNumber0(W1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ) ),
inference(modus_ponens,[status(thm)],[247,246]) ).
tff(249,plain,
! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) ),
inference(unit_resolution,[status(thm)],[248,238,22,16]) ).
tff(250,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(251,plain,
( ( ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) )
<=> ( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(252,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) )
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) ) ),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) )
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) ) ),
inference(transitivity,[status(thm)],[252,250]) ).
tff(254,plain,
( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) )
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(255,plain,
( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xp,W1) = sdtasdt0(xp,W2) )
| ( sdtasdt0(W1,xp) = sdtasdt0(W2,xp) ) ) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp))
| ( tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ ( ( sdtasdt0(xp,tptp_fun_W2_1(sdtasdt0(xn,xn),xp)) = sdtasdt0(xp,sdtasdt0(xm,xm)) )
| ( sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn,xn),xp),xp) = sdtasdt0(sdtasdt0(xm,xm),xp) ) ) ),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
tptp_fun_W2_1(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm),
inference(unit_resolution,[status(thm)],[255,174,249,222,220]) ).
tff(257,plain,
sdtasdt0(xm,xm) = tptp_fun_W2_1(sdtasdt0(xn,xn),xp),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(transitivity,[status(thm)],[257,214,145,114,106,8]) ).
tff(259,plain,
( ( sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)) )
<=> ( sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,axiom,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(261,plain,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
$false,
inference(unit_resolution,[status(thm)],[261,258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : NUM524+1 : TPTP v9.0.0. Released v4.0.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:24:16 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.42/0.62 % SZS status Theorem
% 0.42/0.62 % SZS output start Proof
% See solution above
% 0.50/0.67 % E exiting
%------------------------------------------------------------------------------