TSTP Solution File: RNG081+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Tue Sep 20 03:18:18 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 74
% Syntax : Number of formulae : 163 ( 37 unt; 16 typ; 0 def)
% Number of atoms : 1779 ( 861 equ)
% Maximal formula atoms : 80 ( 12 avg)
% Number of connectives : 2446 ( 943 ~; 772 |; 551 &)
% ( 130 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 55 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 129 ( 129 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 12 >; 5 *; 0 +; 0 <<)
% Number of predicates : 13 ( 10 usr; 2 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 276 ( 195 !; 56 ?; 276 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(xt_type,type,
xt: $i ).
tff(xs_type,type,
xs: $i ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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)],[3]) ).
tff(5,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(6,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(7,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)],[6]) ).
tff(8,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(9,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)],[8,7]) ).
tff(10,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)],[9,5]) ).
tff(11,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)],[10]) ).
tff(12,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)],[11,4]) ).
tff(13,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)],[12,2]) ).
tff(14,plain,
( aScalar0(sz0z00)
<=> aScalar0(sz0z00) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
tff(16,plain,
aScalar0(sz0z00),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,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(18,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(19,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)],[18]) ).
tff(20,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)],[19,17]) ).
tff(21,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(22,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)],[21,20]) ).
tff(23,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)],[22,16,13]) ).
tff(24,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 )
| ( sdtasdt0(sz0z00,sz0z00) = sz0z00 ) ),
inference(tautology,[status(thm)],]) ).
tff(25,plain,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xt) )
<=> ( aDimensionOf0(xs) = aDimensionOf0(xt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
tff(28,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( aVector0(xt)
<=> aVector0(xt) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
tff(32,plain,
aVector0(xt),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
aVector0(xt),
inference(modus_ponens,[status(thm)],[32,30]) ).
tff(34,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
aVector0(xs),
inference(and_elim,[status(thm)],[31]) ).
tff(36,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,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) ) )),
trans(
monotonicity(
rewrite(
( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) )
<=> ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) )
<=> ~ ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
rewrite(
( ~ ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) ) )
<=> ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) )
<=> ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
rewrite(
( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) ) )),
( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
<=> ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )),
( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ) )),
rewrite(
( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ) )),
( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) )
<=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
| ( sdtasasdt0(W0,W1) = sz0z00 ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
<=> ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
| ( sdtasasdt0(W0,W1) = sz0z00 ) ) ) )),
rewrite(
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
| ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
tff(47,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ),
inference(modus_ponens,[status(thm)],[48,42]) ).
tff(50,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[50,40]) ).
tff(52,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[51,38]) ).
tff(53,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xt) = sz0z00 )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xt) = sz0z00 )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( ( sdtasasdt0(xs,xt) = sz0z00 )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xt) = sz0z00 )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
| ( sdtasasdt0(xs,xt) = sz0z00 )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xt) = sz0z00 )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
| ( sdtasasdt0(xs,xt) = sz0z00 )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xt) = sz0z00 )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
| ( sdtasasdt0(xs,xt) = sz0z00 )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) != aDimensionOf0(xs) )
| ~ aVector0(W0) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xt) = sz0z00 )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
sdtasasdt0(xs,xt) = sz0z00,
inference(unit_resolution,[status(thm)],[58,52,36,33,28,29]) ).
tff(60,plain,
sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)) = sdtasdt0(sz0z00,sz0z00),
inference(monotonicity,[status(thm)],[59,59]) ).
tff(61,plain,
sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)) = sz0z00,
inference(transitivity,[status(thm)],[60,25]) ).
tff(62,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
<=> sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
<=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
^ [W0: $i] :
refl(
( ( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
^ [W0: $i] :
rewrite(
( ( aVector0(W0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [W0: $i] :
( aVector0(W0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [W0: $i] :
( aVector0(W0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
tff(70,plain,
! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(xt)
| sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) )
<=> ( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(xt)
| sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(xt)
| sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(xt)
| sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)),
inference(unit_resolution,[status(thm)],[76,73,33]) ).
tff(78,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(79,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)],[78]) ).
tff(80,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(81,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)],[80]) ).
tff(82,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(83,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(84,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)],[83]) ).
tff(85,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(86,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[88,81]) ).
tff(90,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[89,79]) ).
tff(91,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs)
| $false
| ~ aVector0(xs) )
<=> ( aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xs) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> $false ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ( aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs)
| $false
| ~ aVector0(xs) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs) ) ),
inference(transitivity,[status(thm)],[97,92]) ).
tff(99,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs) ) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs) ) ),
inference(transitivity,[status(thm)],[99,91]) ).
tff(101,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
aScalar0(sdtasasdt0(xs,xs)),
inference(unit_resolution,[status(thm)],[102,90,36]) ).
tff(104,plain,
( ( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(xs)
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
<=> ( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(xs)
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(xs)
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(xs)
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(unit_resolution,[status(thm)],[106,73,36]) ).
tff(108,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt)
| $false
| ~ aVector0(xt) )
<=> ( aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( aDimensionOf0(xt) = aDimensionOf0(xt) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( aDimensionOf0(xt) != aDimensionOf0(xt) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( aDimensionOf0(xt) != aDimensionOf0(xt) )
<=> $false ),
inference(transitivity,[status(thm)],[111,93]) ).
tff(113,plain,
( ( aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) )
<=> ( aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt)
| $false
| ~ aVector0(xt) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) )
<=> ( aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt) ) ),
inference(transitivity,[status(thm)],[113,109]) ).
tff(115,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt) ) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt) ) ),
inference(transitivity,[status(thm)],[115,108]) ).
tff(117,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(xt,xt))
| ~ aVector0(xt) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
aScalar0(sdtasasdt0(xt,xt)),
inference(unit_resolution,[status(thm)],[118,90,33]) ).
tff(120,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
<=> ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
<=> ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) )),
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) ) )),
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
<=> ~ ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
<=> ~ ~ ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
rewrite(
( ~ ~ ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) )
<=> ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
<=> ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
( ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) )
<=> ( ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
rewrite(
( ( ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) )),
( ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) )
<=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
| ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
| ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ) )),
rewrite(
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
| ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
<=> ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
<=> ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
tff(128,plain,
! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ),
inference(modus_ponens,[status(thm)],[131,121]) ).
tff(133,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ aScalar0(sdtasasdt0(xt,xt))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ aScalar0(sdtasasdt0(xt,xt))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ aScalar0(sdtasasdt0(xt,xt))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ aScalar0(sdtasasdt0(xt,xt))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
( ~ aScalar0(sdtasasdt0(xt,xt))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
inference(unit_resolution,[status(thm)],[135,132]) ).
tff(137,plain,
~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(unit_resolution,[status(thm)],[136,119,107,103,77]) ).
tff(138,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(tautology,[status(thm)],]) ).
tff(139,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(unit_resolution,[status(thm)],[138,137]) ).
tff(140,plain,
sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(modus_ponens,[status(thm)],[139,63]) ).
tff(141,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
<=> ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ~ ( ( ( aDimensionOf0(xs) != sz00 )
=> ? [W0: $i] :
( aVector0(W0)
& ( szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs) )
& ! [W1: $i] :
( aNaturalNumber0(W1)
=> ( sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) ) )
& ( W0 = sziznziztdt0(xs) )
& ? [W1: $i] :
( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) )
& ( W1 = sziznziztdt0(xt) )
& ? [W2: $i] :
( aScalar0(W2)
& ( W2 = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
& ? [W3: $i] :
( aScalar0(W3)
& ( W3 = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
& ? [W4: $i] :
( aScalar0(W4)
& ( W4 = sdtasasdt0(W0,W0) )
& ? [W5: $i] :
( aScalar0(W5)
& ( W5 = sdtasasdt0(W1,W1) )
& ? [W6: $i] :
( aScalar0(W6)
& ( W6 = sdtasasdt0(W0,W1) )
& ? [W7: $i] :
( aScalar0(W7)
& ( W7 = sdtasdt0(W2,W2) )
& ? [W8: $i] :
( aScalar0(W8)
& ( W8 = sdtasdt0(W3,W3) )
& ? [W9: $i] :
( aScalar0(W9)
& ( W9 = sdtasdt0(W2,W3) )
& ? [W10: $i] :
( aScalar0(W10)
& ( W10 = sdtasdt0(W4,W8) )
& ? [W11: $i] :
( aScalar0(W11)
& ( W11 = sdtasdt0(W6,W9) )
& ? [W12: $i] :
( aScalar0(W12)
& ( W12 = sdtasdt0(W7,W5) )
& ? [W13: $i] :
( aScalar0(W13)
& ( W13 = sdtasdt0(W10,W12) )
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
<=> ~ ( ~ ( ( aDimensionOf0(xs) = sz00 )
| ? [W0: $i] :
( aVector0(W0)
& ( szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs) )
& ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) ) )
& ( W0 = sziznziztdt0(xs) )
& ? [W1: $i] :
( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) )
& ( W1 = sziznziztdt0(xt) )
& ? [W2: $i] :
( aScalar0(W2)
& ( W2 = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
& ? [W3: $i] :
( aScalar0(W3)
& ( W3 = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
& ? [W4: $i] :
( aScalar0(W4)
& ( W4 = sdtasasdt0(W0,W0) )
& ? [W5: $i] :
( aScalar0(W5)
& ( W5 = sdtasasdt0(W1,W1) )
& ? [W6: $i] :
( aScalar0(W6)
& ( W6 = sdtasasdt0(W0,W1) )
& ? [W7: $i] :
( aScalar0(W7)
& ( W7 = sdtasdt0(W2,W2) )
& ? [W8: $i] :
( aScalar0(W8)
& ( W8 = sdtasdt0(W3,W3) )
& ? [W9: $i] :
( aScalar0(W9)
& ( W9 = sdtasdt0(W2,W3) )
& ? [W10: $i] :
( aScalar0(W10)
& ( W10 = sdtasdt0(W4,W8) )
& ? [W11: $i] :
( aScalar0(W11)
& ( W11 = sdtasdt0(W6,W9) )
& ? [W12: $i] :
( aScalar0(W12)
& ( W12 = sdtasdt0(W7,W5) )
& ? [W13: $i] :
( aScalar0(W13)
& ( W13 = sdtasdt0(W10,W12) )
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,axiom,
~ ( ( ( aDimensionOf0(xs) != sz00 )
=> ? [W0: $i] :
( aVector0(W0)
& ( szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs) )
& ! [W1: $i] :
( aNaturalNumber0(W1)
=> ( sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) ) )
& ( W0 = sziznziztdt0(xs) )
& ? [W1: $i] :
( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) )
& ( W1 = sziznziztdt0(xt) )
& ? [W2: $i] :
( aScalar0(W2)
& ( W2 = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
& ? [W3: $i] :
( aScalar0(W3)
& ( W3 = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
& ? [W4: $i] :
( aScalar0(W4)
& ( W4 = sdtasasdt0(W0,W0) )
& ? [W5: $i] :
( aScalar0(W5)
& ( W5 = sdtasasdt0(W1,W1) )
& ? [W6: $i] :
( aScalar0(W6)
& ( W6 = sdtasasdt0(W0,W1) )
& ? [W7: $i] :
( aScalar0(W7)
& ( W7 = sdtasdt0(W2,W2) )
& ? [W8: $i] :
( aScalar0(W8)
& ( W8 = sdtasdt0(W3,W3) )
& ? [W9: $i] :
( aScalar0(W9)
& ( W9 = sdtasdt0(W2,W3) )
& ? [W10: $i] :
( aScalar0(W10)
& ( W10 = sdtasdt0(W4,W8) )
& ? [W11: $i] :
( aScalar0(W11)
& ( W11 = sdtasdt0(W6,W9) )
& ? [W12: $i] :
( aScalar0(W12)
& ( W12 = sdtasdt0(W7,W5) )
& ? [W13: $i] :
( aScalar0(W13)
& ( W13 = sdtasdt0(W10,W12) )
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(144,plain,
~ ( ~ ( ( aDimensionOf0(xs) = sz00 )
| ? [W0: $i] :
( aVector0(W0)
& ( szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs) )
& ! [W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) ) )
& ( W0 = sziznziztdt0(xs) )
& ? [W1: $i] :
( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) )
& ( W1 = sziznziztdt0(xt) )
& ? [W2: $i] :
( aScalar0(W2)
& ( W2 = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
& ? [W3: $i] :
( aScalar0(W3)
& ( W3 = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
& ? [W4: $i] :
( aScalar0(W4)
& ( W4 = sdtasasdt0(W0,W0) )
& ? [W5: $i] :
( aScalar0(W5)
& ( W5 = sdtasasdt0(W1,W1) )
& ? [W6: $i] :
( aScalar0(W6)
& ( W6 = sdtasasdt0(W0,W1) )
& ? [W7: $i] :
( aScalar0(W7)
& ( W7 = sdtasdt0(W2,W2) )
& ? [W8: $i] :
( aScalar0(W8)
& ( W8 = sdtasdt0(W3,W3) )
& ? [W9: $i] :
( aScalar0(W9)
& ( W9 = sdtasdt0(W2,W3) )
& ? [W10: $i] :
( aScalar0(W10)
& ( W10 = sdtasdt0(W4,W8) )
& ? [W11: $i] :
( aScalar0(W11)
& ( W11 = sdtasdt0(W6,W9) )
& ? [W12: $i] :
( aScalar0(W12)
& ( W12 = sdtasdt0(W7,W5) )
& ? [W13: $i] :
( aScalar0(W13)
& ( W13 = sdtasdt0(W10,W12) )
& sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
& sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(or_elim,[status(thm)],[144]) ).
tff(146,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
$false,
inference(unit_resolution,[status(thm)],[146,140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 22:35:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------