%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM525+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.48s 0.65s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 55
% Syntax : Number of formulae : 156 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 1517 ( 486 equ)
% Maximal formula atoms : 32 ( 9 avg)
% Number of connectives : 2399 (1151 ~; 825 |; 199 &)
% ( 198 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 113 ( 113 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 : 392 ( 345 !; 15 ?; 392 :)
% 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(xn_type,type,
xn: $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( doDivides0(xp,xn)
<=> doDivides0(xp,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
tff(3,plain,
doDivides0(xp,xn),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
doDivides0(xp,xn),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( ( xp != sz00 )
<=> ( xp != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
tff(7,plain,
xp != sz00,
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
xp != sz00,
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 ) ),
inference(and_elim,[status(thm)],[6]) ).
tff(11,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 ) ),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[12]) ).
tff(17,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[17,15]) ).
tff(19,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(20,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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)],[22,20]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,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(28,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)],[27]) ).
tff(29,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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
tff(30,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)],[29,28]) ).
tff(31,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)],[30,26]) ).
tff(32,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)],[31]) ).
tff(33,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)],[32,25]) ).
tff(34,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[33,23]) ).
tff(35,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( 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(36,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(37,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W1)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) )
<=> ( W2 = sdtsldt0(W1,W0) ) ) )
| ( 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)],[36]) ).
tff(38,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)],[37,35]) ).
tff(39,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(40,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)],[39,38]) ).
tff(41,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xp,W2) ) )
<=> ( W2 = sdtsldt0(xn,xp) ) ),
inference(unit_resolution,[status(thm)],[40,34,18,14,8,4]) ).
tff(42,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(43,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)],[42,41]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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)],[47,45]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,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(53,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)],[52]) ).
tff(54,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
tff(55,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)],[54,53]) ).
tff(56,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)],[55,51]) ).
tff(57,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)],[56]) ).
tff(58,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)],[57,50]) ).
tff(59,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)],[58,48]) ).
tff(60,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(61,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(62,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)],[61]) ).
tff(63,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)],[62,60]) ).
tff(64,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(65,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)],[64,63]) ).
tff(66,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)],[65,59,18,14]) ).
tff(67,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(68,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)],[67,66]) ).
tff(69,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(70,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)],[69,4]) ).
tff(71,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( xn != sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) ) ),
inference(unit_resolution,[status(thm)],[70,68]) ).
tff(72,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(73,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)],[72,71]) ).
tff(74,plain,
tptp_fun_W2_1(xn,xp) = sdtsldt0(xn,xp),
inference(unit_resolution,[status(thm)],[73,43]) ).
tff(75,plain,
sdtasdt0(tptp_fun_W2_1(xn,xp),xn) = sdtasdt0(sdtsldt0(xn,xp),xn),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(tptp_fun_W2_1(xn,xp),xn),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( aNaturalNumber0(tptp_fun_W2_1(xn,xp))
<=> aNaturalNumber0(sdtsldt0(xn,xp)) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(78,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(79,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xp)),
inference(unit_resolution,[status(thm)],[78,71]) ).
tff(80,plain,
aNaturalNumber0(sdtsldt0(xn,xp)),
inference(modus_ponens,[status(thm)],[79,77]) ).
tff(81,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,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(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(89,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[92,82]) ).
tff(94,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp)) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) ) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ( sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
sdtasdt0(sdtsldt0(xn,xp),xn) = sdtasdt0(xn,sdtsldt0(xn,xp)),
inference(unit_resolution,[status(thm)],[99,93,18,80]) ).
tff(101,plain,
sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(sdtsldt0(xn,xp),xn),
inference(symmetry,[status(thm)],[100]) ).
tff(102,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(103,plain,
xn = sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),
inference(unit_resolution,[status(thm)],[102,71]) ).
tff(104,plain,
sdtasdt0(xp,tptp_fun_W2_1(xn,xp)) = xn,
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
sdtsldt0(xn,xp) = tptp_fun_W2_1(xn,xp),
inference(symmetry,[status(thm)],[74]) ).
tff(106,plain,
sdtasdt0(xp,sdtsldt0(xn,xp)) = sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
sdtasdt0(xp,sdtsldt0(xn,xp)) = xn,
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xn,sdtsldt0(xn,xp)),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,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(110,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)],[109]) ).
tff(111,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(112,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)],[111]) ).
tff(113,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(114,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(115,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)],[114]) ).
tff(116,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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
tff(117,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)],[116,115]) ).
tff(118,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)],[117,113]) ).
tff(119,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)],[118]) ).
tff(120,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)],[119,112]) ).
tff(121,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)],[120,110]) ).
tff(122,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(123,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(124,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)],[123]) ).
tff(125,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)],[124,122]) ).
tff(126,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(127,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)],[126,125]) ).
tff(128,plain,
sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(unit_resolution,[status(thm)],[127,121,14,80]) ).
tff(129,plain,
sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) = sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
( ( xq = sdtsldt0(xn,xp) )
<=> ( xq = sdtsldt0(xn,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,axiom,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
tff(132,plain,
xq = sdtsldt0(xn,xp),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
sdtsldt0(xn,xp) = xq,
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp)) = sdtasdt0(xq,xq),
inference(monotonicity,[status(thm)],[133,133]) ).
tff(135,plain,
sdtasdt0(xq,xq) = sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp)),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(tptp_fun_W2_1(xn,xp),xn),
inference(transitivity,[status(thm)],[136,129,108,101,76]) ).
tff(138,plain,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,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(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) ) )
<=> ( ~ ! [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(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ( ( sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ~ aNaturalNumber0(xp) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,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,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(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(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) ) ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,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,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(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(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) ) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,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,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ~ aNaturalNumber0(xp) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,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(xn)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xp))
| ( sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)) ) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xp,sdtasdt0(tptp_fun_W2_1(xn,xp),xn)),
inference(unit_resolution,[status(thm)],[145,121,18,14,79]) ).
tff(147,plain,
sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn) = sdtasdt0(xn,xn),
inference(monotonicity,[status(thm)],[104]) ).
tff(148,plain,
sdtasdt0(xn,xn) = sdtasdt0(sdtasdt0(xp,tptp_fun_W2_1(xn,xp)),xn),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( ( sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) )
<=> ( sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
tff(151,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(transitivity,[status(thm)],[151,148,146,139]) ).
tff(153,plain,
( ( sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) )
<=> ( sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(155,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
$false,
inference(unit_resolution,[status(thm)],[155,152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM525+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 01:22:39 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.48/0.65 % SZS status Theorem
% 0.48/0.65 % SZS output start Proof
% See solution above
% 0.48/0.67 % E exiting
%------------------------------------------------------------------------------