TSTP Solution File: RNG071+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG071+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 03:18:11 EDT 2022
% Result : Theorem 0.62s 0.65s
% Output : Proof 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 129
% Syntax : Number of formulae : 257 ( 67 unt; 27 typ; 0 def)
% Number of atoms : 1438 ( 21 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 2140 (1013 ~; 781 |; 178 &)
% ( 133 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 81 ( 81 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 11 >; 5 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 23 ( 23 usr; 16 con; 0-2 aty)
% Number of variables : 261 ( 236 !; 0 ?; 261 :)
% Comments :
%------------------------------------------------------------------------------
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(xt_type,type,
xt: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(xs_type,type,
xs: $i ).
tff(xS_type,type,
xS: $i ).
tff(xD_type,type,
xD: $i ).
tff(xF_type,type,
xF: $i ).
tff(xR_type,type,
xR: $i ).
tff(xG_type,type,
xG: $i ).
tff(xC_type,type,
xC: $i ).
tff(xP_type,type,
xP: $i ).
tff(xH_type,type,
xH: $i ).
tff(xE_type,type,
xE: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(xq_type,type,
xq: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(xA_type,type,
xA: $i ).
tff(xp_type,type,
xp: $i ).
tff(xB_type,type,
xB: $i ).
tff(1,plain,
( aScalar0(xS)
<=> aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aScalar0(xS)
<=> aScalar0(xS) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aScalar0(xS)
& ( xS = sdtasdt0(xF,xD) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
tff(4,plain,
aScalar0(xS),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aScalar0(xS),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))
<=> aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( aScalar0(xR)
<=> aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( aScalar0(xR)
<=> aScalar0(xR) ),
inference(rewrite,[status(thm)],]) ).
tff(10,axiom,
( aScalar0(xR)
& ( xR = sdtasdt0(xC,xG) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
tff(11,plain,
aScalar0(xR),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
aScalar0(xR),
inference(modus_ponens,[status(thm)],[11,9]) ).
tff(13,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(modus_ponens,[status(thm)],[13,7]) ).
tff(15,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) )
<=> ( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
<=> ( ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))),
inference(unit_resolution,[status(thm)],[33,27,14,6]) ).
tff(35,plain,
( aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))
<=> aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( aScalar0(xP)
<=> aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( aScalar0(xP)
<=> aScalar0(xP) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
( aScalar0(xP)
& ( xP = sdtasdt0(xE,xH) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
tff(39,plain,
aScalar0(xP),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
aScalar0(xP),
inference(modus_ponens,[status(thm)],[39,37]) ).
tff(41,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(modus_ponens,[status(thm)],[41,35]) ).
tff(43,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
<=> ( ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(unit_resolution,[status(thm)],[48,27,42]) ).
tff(50,plain,
( aVector0(xq)
<=> aVector0(sziznziztdt0(xt)) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( aVector0(xq)
<=> aVector0(xq) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
( aVector0(xq)
& ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) ) )
& ( xq = sziznziztdt0(xt) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
tff(53,plain,
( aVector0(xq)
& ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) ) ) ),
inference(and_elim,[status(thm)],[52]) ).
tff(54,plain,
( aVector0(xq)
& ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) ) ),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
aVector0(xq),
inference(and_elim,[status(thm)],[54]) ).
tff(56,plain,
aVector0(xq),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
aVector0(sziznziztdt0(xt)),
inference(modus_ponens,[status(thm)],[56,50]) ).
tff(58,plain,
^ [W0: $i] :
refl(
( ( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [W0: $i] :
rewrite(
( ( aVector0(W0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [W0: $i] :
( aVector0(W0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [W0: $i] :
( aVector0(W0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
tff(64,plain,
! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(sziznziztdt0(xt))
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) )
<=> ( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(sziznziztdt0(xt))
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(sziznziztdt0(xt))
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(sziznziztdt0(xt))
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),
inference(unit_resolution,[status(thm)],[70,67,57]) ).
tff(72,plain,
( aScalar0(xA)
<=> aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( aScalar0(xA)
<=> aScalar0(xA) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
( aScalar0(xA)
& ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
tff(75,plain,
aScalar0(xA),
inference(and_elim,[status(thm)],[74]) ).
tff(76,plain,
aScalar0(xA),
inference(modus_ponens,[status(thm)],[75,73]) ).
tff(77,plain,
aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
^ [W0: $i] :
refl(
( ( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [W0: $i] :
rewrite(
( ( aScalar0(W0)
=> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
tff(84,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[90,87,77]) ).
tff(92,plain,
( aScalar0(xF)
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( aScalar0(xF)
<=> aScalar0(xF) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
( aScalar0(xF)
& ( xF = sdtasdt0(xA,xA) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(95,plain,
aScalar0(xF),
inference(and_elim,[status(thm)],[94]) ).
tff(96,plain,
aScalar0(xF),
inference(modus_ponens,[status(thm)],[95,93]) ).
tff(97,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
( aScalar0(xD)
<=> aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( aScalar0(xD)
<=> aScalar0(xD) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
( aScalar0(xD)
& ( xD = sdtasasdt0(xq,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
tff(101,plain,
aScalar0(xD),
inference(and_elim,[status(thm)],[100]) ).
tff(102,plain,
aScalar0(xD),
inference(modus_ponens,[status(thm)],[101,99]) ).
tff(103,plain,
aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,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(105,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)],[104]) ).
tff(106,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(107,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)],[106]) ).
tff(108,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(109,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(110,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)],[109]) ).
tff(111,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(112,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)],[111,110]) ).
tff(113,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)],[112,108]) ).
tff(114,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)],[113]) ).
tff(115,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)],[114,107]) ).
tff(116,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)],[115,105]) ).
tff(117,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) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(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) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) )
<=> ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
<=> ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) )
<=> ( ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( ( ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) )
<=> ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,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(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(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) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,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(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(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) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ),
inference(transitivity,[status(thm)],[122,117]) ).
tff(124,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(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,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) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ),
inference(unit_resolution,[status(thm)],[125,116,103,97,91]) ).
tff(127,plain,
~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ),
inference(unit_resolution,[status(thm)],[126,71]) ).
tff(128,plain,
( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ),
inference(tautology,[status(thm)],]) ).
tff(129,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
( aVector0(xp)
<=> aVector0(sziznziztdt0(xs)) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( aVector0(xp)
<=> aVector0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(132,axiom,
( aVector0(xp)
& ( szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) ) )
& ( xp = sziznziztdt0(xs) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
tff(133,plain,
( aVector0(xp)
& ( szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) ) ) ),
inference(and_elim,[status(thm)],[132]) ).
tff(134,plain,
( aVector0(xp)
& ( szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs) ) ),
inference(and_elim,[status(thm)],[133]) ).
tff(135,plain,
aVector0(xp),
inference(and_elim,[status(thm)],[134]) ).
tff(136,plain,
aVector0(xp),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
aVector0(sziznziztdt0(xs)),
inference(modus_ponens,[status(thm)],[136,130]) ).
tff(138,plain,
( ( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(sziznziztdt0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(sziznziztdt0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(sziznziztdt0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [W0: $i] :
( ~ aVector0(W0)
| sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
| ~ aVector0(sziznziztdt0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[140,67,137]) ).
tff(142,plain,
( aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
<=> aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs))) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( aScalar0(xB)
<=> aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt))) ),
inference(rewrite,[status(thm)],]) ).
tff(144,plain,
( aScalar0(xB)
<=> aScalar0(xB) ),
inference(rewrite,[status(thm)],]) ).
tff(145,axiom,
( aScalar0(xB)
& ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
tff(146,plain,
aScalar0(xB),
inference(and_elim,[status(thm)],[145]) ).
tff(147,plain,
aScalar0(xB),
inference(modus_ponens,[status(thm)],[146,144]) ).
tff(148,plain,
aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(modus_ponens,[status(thm)],[148,142]) ).
tff(150,plain,
( ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(151,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[152,87,149]) ).
tff(154,plain,
( aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ),
inference(rewrite,[status(thm)],]) ).
tff(155,plain,
( aScalar0(xG)
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( aScalar0(xG)
<=> aScalar0(xG) ),
inference(rewrite,[status(thm)],]) ).
tff(157,axiom,
( aScalar0(xG)
& ( xG = sdtasdt0(xB,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
tff(158,plain,
aScalar0(xG),
inference(and_elim,[status(thm)],[157]) ).
tff(159,plain,
aScalar0(xG),
inference(modus_ponens,[status(thm)],[158,156]) ).
tff(160,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(modus_ponens,[status(thm)],[159,155]) ).
tff(161,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(modus_ponens,[status(thm)],[160,154]) ).
tff(162,plain,
( aScalar0(xC)
<=> aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
( aScalar0(xC)
<=> aScalar0(xC) ),
inference(rewrite,[status(thm)],]) ).
tff(164,axiom,
( aScalar0(xC)
& ( xC = sdtasasdt0(xp,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
tff(165,plain,
aScalar0(xC),
inference(and_elim,[status(thm)],[164]) ).
tff(166,plain,
aScalar0(xC),
inference(modus_ponens,[status(thm)],[165,163]) ).
tff(167,plain,
aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(modus_ponens,[status(thm)],[166,162]) ).
tff(168,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) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
<=> ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
( ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
( ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ),
inference(transitivity,[status(thm)],[171,169]) ).
tff(173,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(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,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(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ),
inference(transitivity,[status(thm)],[173,168]) ).
tff(175,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(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,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) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ),
inference(unit_resolution,[status(thm)],[176,116,167,161,153]) ).
tff(178,plain,
~ ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ),
inference(unit_resolution,[status(thm)],[177,141]) ).
tff(179,plain,
( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ),
inference(tautology,[status(thm)],]) ).
tff(180,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(unit_resolution,[status(thm)],[179,178]) ).
tff(181,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(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(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(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(182,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(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,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(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ),
inference(unit_resolution,[status(thm)],[183,116,14,6]) ).
tff(185,plain,
~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) ),
inference(unit_resolution,[status(thm)],[184,180,129]) ).
tff(186,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) ),
inference(tautology,[status(thm)],]) ).
tff(187,plain,
sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))),
inference(unit_resolution,[status(thm)],[186,185]) ).
tff(188,plain,
( ~ ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
<=> ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(189,plain,
( ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
& sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
<=> ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
( ~ ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
& sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
<=> ~ ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
( ~ ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
& sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
<=> ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(transitivity,[status(thm)],[190,188]) ).
tff(192,plain,
( ~ ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
& sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))) )
<=> ~ ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
& sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(193,plain,
( ~ ( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
& sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) )
<=> ~ ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
& sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
( ~ ( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
& sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) )
<=> ~ ( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
& sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,axiom,
~ ( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
& sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(196,plain,
~ ( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
& sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
~ ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
& sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))) ),
inference(modus_ponens,[status(thm)],[196,193]) ).
tff(198,plain,
~ ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
& sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(modus_ponens,[status(thm)],[197,192]) ).
tff(199,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(modus_ponens,[status(thm)],[198,191]) ).
tff(200,plain,
~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(unit_resolution,[status(thm)],[199,187]) ).
tff(201,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))) ),
inference(rewrite,[status(thm)],]) ).
tff(203,plain,
( sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP))
<=> sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)) ),
inference(rewrite,[status(thm)],]) ).
tff(204,axiom,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2610) ).
tff(205,plain,
sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))),
inference(modus_ponens,[status(thm)],[205,202]) ).
tff(207,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(modus_ponens,[status(thm)],[206,201]) ).
tff(208,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
<=> ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],]) ).
tff(209,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[208]) ).
tff(210,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ~ ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ~ ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
<=> ~ ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
<=> ~ ~ ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(
( ~ ~ ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
<=> ( ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) )
<=> ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(
( ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
<=> ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) )
<=> ( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],]) ).
tff(211,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[210]) ).
tff(212,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) ) )),
rewrite(
( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
| sdtlseqdt0(W0,W2) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
| sdtlseqdt0(W0,W2) ) ) )),
rewrite(
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
| sdtlseqdt0(W0,W2) ) )
<=> ( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) )
<=> ( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ) )),
inference(bind,[status(th)],]) ).
tff(214,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ) ),
inference(quant_intro,[status(thm)],[213]) ).
tff(215,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETrn) ).
tff(216,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ),
inference(modus_ponens,[status(thm)],[216,212]) ).
tff(218,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) ) ),
inference(skolemize,[status(sab)],[217]) ).
tff(219,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[218,211]) ).
tff(220,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[219,209]) ).
tff(221,plain,
( aScalar0(sz0z00)
<=> aScalar0(sz0z00) ),
inference(rewrite,[status(thm)],]) ).
tff(222,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
tff(223,plain,
aScalar0(sz0z00),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(225,plain,
( ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) )
<=> ( sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(226,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(monotonicity,[status(thm)],[225]) ).
tff(227,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(transitivity,[status(thm)],[226,224]) ).
tff(228,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(229,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( sdtlseqdt0(W0,W2)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1) )
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))))
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
$false,
inference(unit_resolution,[status(thm)],[229,223,220,207,187,200,49,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG071+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.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 22:18:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.62/0.65 % SZS status Theorem
% 0.62/0.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------