%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG046+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:23:59 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 29
% Syntax : Number of formulae : 74 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 843 ( 629 equ)
% Maximal formula atoms : 36 ( 11 avg)
% Number of connectives : 1174 ( 463 ~; 349 |; 297 &)
% ( 53 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 58 ( 58 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 73 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xy_type,type,
xy: $i ).
tff(xx_type,type,
xx: $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(1,plain,
( aScalar0(xx)
<=> aScalar0(xx) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aScalar0(xx)
& aScalar0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
tff(3,plain,
aScalar0(xx),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aScalar0(xx),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,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(6,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)],[5]) ).
tff(7,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(8,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)],[7]) ).
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 ) ) )
<=> ! [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(10,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(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 ) ) )
<=> ! [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)],[10]) ).
tff(12,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/sandbox/benchmark/theBenchmark.p',mScZero) ).
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)],[12,11]) ).
tff(14,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)],[13,9]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15,8]) ).
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 ) ) ),
inference(modus_ponens,[status(thm)],[16,6]) ).
tff(18,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(xx)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx ) ) )
<=> ( ~ ! [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(xx)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ aScalar0(xx)
| ~ ( ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx )
| ( smndt0(sz0z00) != sz0z00 ) ) )
<=> ( ~ aScalar0(xx)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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(xx)
| ~ ( ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx )
| ( 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(xx)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx ) ) ) ),
inference(monotonicity,[status(thm)],[19]) ).
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(xx)
| ~ ( ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx )
| ( 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(xx)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx ) ) ) ),
inference(transitivity,[status(thm)],[20,18]) ).
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(xx)
| ~ ( ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx )
| ( smndt0(sz0z00) != sz0z00 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,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(xx)
| ~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx ) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
~ ( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx ) ),
inference(unit_resolution,[status(thm)],[23,17,4]) ).
tff(25,plain,
( ( smndt0(sz0z00) != sz0z00 )
| ( sdtpldt0(xx,sz0z00) != xx )
| ( sdtpldt0(sz0z00,xx) != xx )
| ( sdtasdt0(xx,sz0z00) != sz0z00 )
| ( sdtasdt0(sz0z00,xx) != sz0z00 )
| ( sdtpldt0(xx,smndt0(xx)) != sz0z00 )
| ( sdtpldt0(smndt0(xx),xx) != sz0z00 )
| ( smndt0(smndt0(xx)) != xx )
| ( smndt0(smndt0(xx)) = xx ) ),
inference(tautology,[status(thm)],[]) ).
tff(26,plain,
smndt0(smndt0(xx)) = xx,
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
xx = smndt0(smndt0(xx)),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
sdtasdt0(xx,xy) = sdtasdt0(smndt0(smndt0(xx)),xy),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
sdtasdt0(smndt0(smndt0(xx)),xy) = sdtasdt0(xx,xy),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
^ [W0: $i] :
refl(( ( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
<=> ( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
<=> ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
<=> ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [W0: $i] :
rewrite(( ( aScalar0(W0)
=> aScalar0(smndt0(W0)) )
<=> ( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [W0: $i] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) )
<=> ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [W0: $i] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
tff(36,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(xx))
| ~ aScalar0(xx) )
<=> ( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(xx))
| ~ aScalar0(xx) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(xx))
| ~ aScalar0(xx) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(xx))
| ~ aScalar0(xx) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
aScalar0(smndt0(xx)),
inference(unit_resolution,[status(thm)],[42,39,4]) ).
tff(44,plain,
( aScalar0(xy)
<=> aScalar0(xy) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
aScalar0(xy),
inference(and_elim,[status(thm)],[2]) ).
tff(46,plain,
aScalar0(xy),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,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) ) )),
rewrite(( ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) )
<=> ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) )),
rewrite(( ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).
tff(55,plain,
! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[58,48]) ).
tff(60,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(xy)
| ~ aScalar0(smndt0(xx))
| ~ ( ( sdtasdt0(smndt0(xx),smndt0(xy)) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(smndt0(xx)),xy) != smndt0(sdtasdt0(smndt0(xx),xy)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(xy)
| ~ aScalar0(smndt0(xx))
| ~ ( ( sdtasdt0(smndt0(xx),smndt0(xy)) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(smndt0(xx)),xy) != smndt0(sdtasdt0(smndt0(xx),xy)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(xy)
| ~ aScalar0(smndt0(xx))
| ~ ( ( sdtasdt0(smndt0(xx),smndt0(xy)) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(smndt0(xx)),xy) != smndt0(sdtasdt0(smndt0(xx),xy)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(xy)
| ~ aScalar0(smndt0(xx))
| ~ ( ( sdtasdt0(smndt0(xx),smndt0(xy)) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(smndt0(xx)),xy) != smndt0(sdtasdt0(smndt0(xx),xy)) ) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( ~ aScalar0(smndt0(xx))
| ~ ( ( sdtasdt0(smndt0(xx),smndt0(xy)) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(smndt0(xx)),xy) != smndt0(sdtasdt0(smndt0(xx),xy)) ) ) ),
inference(unit_resolution,[status(thm)],[62,59,46]) ).
tff(64,plain,
~ ( ( sdtasdt0(smndt0(xx),smndt0(xy)) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(smndt0(xx)),xy) != smndt0(sdtasdt0(smndt0(xx),xy)) ) ),
inference(unit_resolution,[status(thm)],[63,43]) ).
tff(65,plain,
( ( sdtasdt0(smndt0(xx),smndt0(xy)) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(smndt0(xx)),xy) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(smndt0(xx)),xy) = smndt0(sdtasdt0(smndt0(xx),xy)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(66,plain,
sdtasdt0(smndt0(smndt0(xx)),xy) = smndt0(sdtasdt0(smndt0(xx),xy)),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
smndt0(sdtasdt0(smndt0(xx),xy)) = sdtasdt0(smndt0(smndt0(xx)),xy),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ( sdtasdt0(smndt0(xx),smndt0(xy)) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(smndt0(xx)),xy) != smndt0(sdtasdt0(smndt0(xx),xy)) )
| ( sdtasdt0(smndt0(xx),smndt0(xy)) = smndt0(sdtasdt0(smndt0(xx),xy)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(69,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) = smndt0(sdtasdt0(smndt0(xx),xy)),
inference(unit_resolution,[status(thm)],[68,64]) ).
tff(70,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy),
inference(transitivity,[status(thm)],[69,67,29]) ).
tff(71,plain,
( ( sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy) )
<=> ( sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(73,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG046+1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n010.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 Jun 20 03:17:41 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------