%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG049+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:24:00 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 85
% Syntax : Number of formulae : 220 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 2122 ( 763 equ)
% Maximal formula atoms : 34 ( 9 avg)
% Number of connectives : 2870 (1136 ~;1000 |; 485 &)
% ( 180 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 168 ( 168 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 387 ( 342 !; 0 ?; 387 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(xs_type,type,
xs: $i ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(1,plain,
( ( aDimensionOf0(xs) != sz00 )
<=> ( aDimensionOf0(xs) != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542_01) ).
tff(3,plain,
aDimensionOf0(xs) != sz00,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
aVector0(xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542) ).
tff(6,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
<=> ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) ) )),
( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
<=> ~ ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) ) )),
rewrite(( ~ ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) )
<=> ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) ) )),
( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
<=> ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) ) )),
trans(monotonicity(rewrite(( ( aVector0(W0)
& aVector0(W1) )
<=> ~ ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aVector0(W1) )
<=> ~ ~ ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
rewrite(( ~ ~ ( ~ aVector0(W1)
| ~ aVector0(W0) )
<=> ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aVector0(W1) )
<=> ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 )
| ~ aVector0(W1)
| ~ aVector0(W0) ) )),
rewrite(( ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 )
| ~ aVector0(W1)
| ~ aVector0(W0) )
<=> ( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
( ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) )
<=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )
<=> ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) ) )),
rewrite(( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
tff(15,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[18,8]) ).
tff(20,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| $false
| ~ aVector0(xs) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xs) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> $false ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| $false
| ~ aVector0(xs) ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(transitivity,[status(thm)],[26,21]) ).
tff(28,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(transitivity,[status(thm)],[28,20]) ).
tff(30,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[31,19,6,3]) ).
tff(33,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [W0: $i] :
refl(( ( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
<=> ( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [W0: $i] :
rewrite(( ( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )
<=> ( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 ) ) )),
rewrite(( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) ) )),
rewrite(( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 ) ) )),
rewrite(( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 ) ) )),
rewrite(( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )),
rewrite(( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )),
( ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) )
<=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )),
( ( aScalar0(W0)
=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )
<=> ( aScalar0(W0)
=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) ) )),
rewrite(( ( aScalar0(W0)
=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )
<=> ( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) ) )),
( ( aScalar0(W0)
=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )
<=> ( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [W0: $i] :
( aScalar0(W0)
=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [W0: $i] :
( aScalar0(W0)
=> ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
tff(42,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| ( ( sdtpldt0(W0,sz0z00) = W0 )
& ( sdtpldt0(sz0z00,W0) = W0 )
& ( sdtasdt0(W0,sz0z00) = sz0z00 )
& ( sdtasdt0(sz0z00,W0) = sz0z00 )
& ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
& ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
& ( smndt0(smndt0(W0)) = W0 )
& ( smndt0(sz0z00) = sz0z00 ) ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) ),
inference(modus_ponens,[status(thm)],[45,35]) ).
tff(47,plain,
( aScalar0(sz0z00)
<=> aScalar0(sz0z00) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
tff(49,plain,
aScalar0(sz0z00),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
| ~ aScalar0(sz0z00)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
| ~ aScalar0(sz0z00)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
<=> ( ~ aScalar0(sz0z00)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
| ~ aScalar0(sz0z00)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
| ~ aScalar0(sz0z00)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 )
| ( smndt0(sz0z00) != sz0z00 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| ~ ( ( sdtpldt0(W0,sz0z00) != W0 )
| ( sdtpldt0(sz0z00,W0) != W0 )
| ( sdtasdt0(W0,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,W0) != sz0z00 )
| ( sdtpldt0(W0,smndt0(W0)) != sz0z00 )
| ( sdtpldt0(smndt0(W0),W0) != sz0z00 )
| ( smndt0(smndt0(W0)) != W0 )
| ( smndt0(sz0z00) != sz0z00 ) ) )
| ~ aScalar0(sz0z00)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 ) ),
inference(unit_resolution,[status(thm)],[55,49,46]) ).
tff(57,plain,
( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
| ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
| ( smndt0(smndt0(sz0z00)) != sz0z00 )
| ( sdtpldt0(sz0z00,sz0z00) = sz0z00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(58,plain,
sdtpldt0(sz0z00,sz0z00) = sz0z00,
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
<=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(monotonicity,[status(thm)],[58,33]) ).
tff(60,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
<=> sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) ),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
<=> ~ sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
<=> ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(64,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
~ sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))),
inference(modus_ponens,[status(thm)],[64,61]) ).
tff(66,plain,
( aVector0(sziznziztdt0(xs))
<=> aVector0(sziznziztdt0(xs)) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) )
& aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1568) ).
tff(68,plain,
( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) )
& aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ) ),
inference(and_elim,[status(thm)],[67]) ).
tff(69,plain,
( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) )
& aVector0(sziznziztdt0(xs)) ),
inference(and_elim,[status(thm)],[68]) ).
tff(70,plain,
( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) ) ),
inference(and_elim,[status(thm)],[69]) ).
tff(71,plain,
( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ) ),
inference(and_elim,[status(thm)],[70]) ).
tff(72,plain,
aVector0(sziznziztdt0(xs)),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
aVector0(sziznziztdt0(xs)),
inference(modus_ponens,[status(thm)],[72,66]) ).
tff(74,plain,
^ [W0: $i,W1: $i] :
refl(( ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aVector0(W0)
& aVector0(W1) )
<=> ~ ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aVector0(W1) )
<=> ~ ~ ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
rewrite(( ~ ~ ( ~ aVector0(W1)
| ~ aVector0(W0) )
<=> ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aVector0(W1) )
<=> ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
rewrite(( ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
( ( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) ) )
<=> ( ( aVector0(W0)
& aVector0(W1) )
=> ( aScalar0(sdtasasdt0(W0,W1))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) ) )),
rewrite(( ( ( aVector0(W0)
& aVector0(W1) )
=> ( aScalar0(sdtasasdt0(W0,W1))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
tff(82,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[85,75]) ).
tff(87,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| $false
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ aVector0(sziznziztdt0(xs))
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xs)) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
<=> $false ),
inference(transitivity,[status(thm)],[90,22]) ).
tff(92,plain,
( ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| $false
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ aVector0(sziznziztdt0(xs))
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(transitivity,[status(thm)],[92,88]) ).
tff(94,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(transitivity,[status(thm)],[94,87]) ).
tff(96,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[97,86,73]) ).
tff(99,plain,
( ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
<=> ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(and_elim,[status(thm)],[71]) ).
tff(101,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
<=> iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))))
<=> iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) ),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
^ [W0: $i] :
refl(( ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(106,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
^ [W0: $i] :
rewrite(( ( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
tff(111,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
( ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[117,114,73]) ).
tff(119,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) )
<=> ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
tff(125,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[127,120]) ).
tff(129,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ),
inference(unit_resolution,[status(thm)],[131,128]) ).
tff(133,plain,
iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))),
inference(unit_resolution,[status(thm)],[132,118]) ).
tff(134,plain,
iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)),
inference(modus_ponens,[status(thm)],[133,104]) ).
tff(135,plain,
^ [W0: $i] :
refl(( ( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
<=> ( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) )),
inference(bind,[status(th)],[]) ).
tff(136,plain,
( ! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
<=> ! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
<=> ! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ( ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )),
( ( aVector0(W0)
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )
<=> ( aVector0(W0)
=> ( ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ) )),
rewrite(( ( aVector0(W0)
=> ( ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )
<=> ( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) )),
( ( aVector0(W0)
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )
<=> ( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [W0: $i] :
( aVector0(W0)
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )
<=> ! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,axiom,
! [W0: $i] :
( aVector0(W0)
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1516) ).
tff(141,plain,
! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ),
inference(modus_ponens,[status(thm)],[143,136]) ).
tff(145,plain,
( ( ~ ! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) )
<=> ( ~ ! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
( ~ ! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
( ~ ! [W0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))
| ~ aVector0(W0)
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) ),
inference(unit_resolution,[status(thm)],[147,144,73]) ).
tff(149,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[148,134]) ).
tff(150,plain,
( ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
aNaturalNumber0(aDimensionOf0(xs)),
inference(unit_resolution,[status(thm)],[152,114,6]) ).
tff(154,plain,
^ [W0: $i,W1: $i] :
refl(( ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(155,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aVector0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
( ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
rewrite(( ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
( ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(157,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aVector0(W0)
& aNaturalNumber0(W1) )
=> aScalar0(sdtlbdtrb0(W0,W1)) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(160,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aNaturalNumber0(W1) )
=> aScalar0(sdtlbdtrb0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aNaturalNumber0(W1) )
=> aScalar0(sdtlbdtrb0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
tff(162,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[164,157]) ).
tff(166,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[165,155]) ).
tff(167,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,plain,
( ( aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) )
<=> ( aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ) ),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ) ),
inference(transitivity,[status(thm)],[169,167]) ).
tff(171,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(unit_resolution,[status(thm)],[172,166,6,153]) ).
tff(174,plain,
^ [W0: $i,W1: $i] :
refl(( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(175,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[174]) ).
tff(176,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(177,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[176]) ).
tff(178,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(179,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(180,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
tff(182,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[182,178]) ).
tff(184,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[183]) ).
tff(185,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[184,177]) ).
tff(186,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[185,175]) ).
tff(187,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,plain,
( ( aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) )
<=> ( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(transitivity,[status(thm)],[189,187]) ).
tff(191,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(unit_resolution,[status(thm)],[192,186]) ).
tff(194,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[193,173]) ).
tff(195,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
<=> sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,axiom,
( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) )
& aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) )
& sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1590) ).
tff(197,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(and_elim,[status(thm)],[196]) ).
tff(198,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(modus_ponens,[status(thm)],[197,195]) ).
tff(199,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
refl(( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(200,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[199]) ).
tff(201,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ~ ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ~ ~ ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
<=> ~ ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
<=> ~ ~ ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
<=> ( ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(202,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(204,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) ) )),
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) ) )),
rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) ) )),
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) ) )),
rewrite(( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ) )),
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
| sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )
<=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ) )),
inference(bind,[status(th)],[]) ).
tff(205,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,axiom,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
tff(207,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ),
inference(modus_ponens,[status(thm)],[207,203]) ).
tff(209,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) ) ),
inference(skolemize,[status(sab)],[208]) ).
tff(210,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[209,202]) ).
tff(211,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[210,200]) ).
tff(212,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,plain,
( ( sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) )
<=> ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(transitivity,[status(thm)],[214,212]) ).
tff(216,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
( sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(unit_resolution,[status(thm)],[217,49,211,198,194]) ).
tff(219,plain,
sdtlseqdt0(sdtpldt0(sz0z00,sz0z00),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))),
inference(unit_resolution,[status(thm)],[218,149,98]) ).
tff(220,plain,
$false,
inference(unit_resolution,[status(thm)],[219,65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG049+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 03:16:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% See solution above
% 0.18/0.44 % E exiting
%------------------------------------------------------------------------------