TSTP Solution File: RNG078+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG078+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 03:18:15 EDT 2022
% Result : Theorem 9.98s 6.62s
% Output : Proof 10.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 131
% Syntax : Number of formulae : 283 ( 86 unt; 23 typ; 0 def)
% Number of atoms : 1757 ( 677 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 2876 (1440 ~;1125 |; 163 &)
% ( 136 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 61 ( 61 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 15 con; 0-2 aty)
% Number of variables : 335 ( 314 !; 0 ?; 335 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(xs_type,type,
xs: $i ).
tff(xt_type,type,
xt: $i ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(xD_type,type,
xD: $i ).
tff(xq_type,type,
xq: $i ).
tff(xC_type,type,
xC: $i ).
tff(xp_type,type,
xp: $i ).
tff(xG_type,type,
xG: $i ).
tff(xB_type,type,
xB: $i ).
tff(xF_type,type,
xF: $i ).
tff(xA_type,type,
xA: $i ).
tff(xS_type,type,
xS: $i ).
tff(xR_type,type,
xR: $i ).
tff(xH_type,type,
xH: $i ).
tff(xE_type,type,
xE: $i ).
tff(xP_type,type,
xP: $i ).
tff(1,plain,
( aScalar0(xD)
<=> aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aScalar0(xD)
<=> aScalar0(xD) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aScalar0(xD)
& ( xD = sdtasasdt0(xq,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
tff(4,plain,
aScalar0(xD),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aScalar0(xD),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aScalar0(xC)
<=> aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( aScalar0(xC)
<=> aScalar0(xC) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
( aScalar0(xC)
& ( xC = sdtasasdt0(xp,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
tff(10,plain,
aScalar0(xC),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aScalar0(xC),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
tff(21,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[24,14]) ).
tff(26,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(unit_resolution,[status(thm)],[28,25,12,6]) ).
tff(30,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(31,plain,
( aScalar0(xG)
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( aScalar0(xG)
<=> aScalar0(xG) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
( aScalar0(xG)
& ( xG = sdtasdt0(xB,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
tff(34,plain,
aScalar0(xG),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
aScalar0(xG),
inference(modus_ponens,[status(thm)],[34,32]) ).
tff(36,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(modus_ponens,[status(thm)],[36,30]) ).
tff(38,plain,
( aScalar0(xF)
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( aScalar0(xF)
<=> aScalar0(xF) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
( aScalar0(xF)
& ( xF = sdtasdt0(xA,xA) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(41,plain,
aScalar0(xF),
inference(and_elim,[status(thm)],[40]) ).
tff(42,plain,
aScalar0(xF),
inference(modus_ponens,[status(thm)],[41,39]) ).
tff(43,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
<=> ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(unit_resolution,[status(thm)],[49,25,43,37]) ).
tff(51,plain,
( aScalar0(xS)
<=> aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( aScalar0(xS)
<=> aScalar0(xS) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
( aScalar0(xS)
& ( xS = sdtasdt0(xF,xD) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
tff(54,plain,
aScalar0(xS),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
aScalar0(xS),
inference(modus_ponens,[status(thm)],[54,52]) ).
tff(56,plain,
aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,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(63,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)],[62]) ).
tff(64,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
tff(65,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[68,58]) ).
tff(70,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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(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(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))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(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)))) )
<=> ( ~ ! [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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(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)))) )
<=> ( ~ ! [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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(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)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(unit_resolution,[status(thm)],[75,69,56]) ).
tff(77,plain,
aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(unit_resolution,[status(thm)],[76,50]) ).
tff(78,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(79,plain,
( aScalar0(xR)
<=> aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( aScalar0(xR)
<=> aScalar0(xR) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
( aScalar0(xR)
& ( xR = sdtasdt0(xC,xG) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
tff(82,plain,
aScalar0(xR),
inference(and_elim,[status(thm)],[81]) ).
tff(83,plain,
aScalar0(xR),
inference(modus_ponens,[status(thm)],[82,80]) ).
tff(84,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(modus_ponens,[status(thm)],[84,78]) ).
tff(86,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,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) ) )),
rewrite(
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
rewrite(
( ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) ) )),
trans(
monotonicity(
rewrite(
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
rewrite(
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) )),
rewrite(
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
tff(94,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[97,87]) ).
tff(99,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) )
<=> ( ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ( ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ) ),
inference(transitivity,[status(thm)],[102,100]) ).
tff(104,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ) ),
inference(transitivity,[status(thm)],[104,99]) ).
tff(106,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
( ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ) ),
inference(unit_resolution,[status(thm)],[107,98,85]) ).
tff(109,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ) ),
inference(unit_resolution,[status(thm)],[108,77,29]) ).
tff(110,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) ) ),
inference(tautology,[status(thm)],]) ).
tff(111,plain,
sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),
inference(unit_resolution,[status(thm)],[110,109]) ).
tff(112,plain,
sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
( aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
<=> aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs))) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( aScalar0(xB)
<=> aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt))) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( aScalar0(xB)
<=> aScalar0(xB) ),
inference(rewrite,[status(thm)],]) ).
tff(116,axiom,
( aScalar0(xB)
& ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
tff(117,plain,
aScalar0(xB),
inference(and_elim,[status(thm)],[116]) ).
tff(118,plain,
aScalar0(xB),
inference(modus_ponens,[status(thm)],[117,115]) ).
tff(119,plain,
aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(modus_ponens,[status(thm)],[119,113]) ).
tff(121,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ) ),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ) ),
inference(transitivity,[status(thm)],[124,122]) ).
tff(126,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ) ),
inference(transitivity,[status(thm)],[126,121]) ).
tff(128,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(unit_resolution,[status(thm)],[129,98,120,43]) ).
tff(131,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(132,plain,
sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
( aScalar0(xA)
<=> aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( aScalar0(xA)
<=> aScalar0(xA) ),
inference(rewrite,[status(thm)],]) ).
tff(135,axiom,
( aScalar0(xA)
& ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
tff(136,plain,
aScalar0(xA),
inference(and_elim,[status(thm)],[135]) ).
tff(137,plain,
aScalar0(xA),
inference(modus_ponens,[status(thm)],[136,134]) ).
tff(138,plain,
aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(transitivity,[status(thm)],[144,139]) ).
tff(146,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(unit_resolution,[status(thm)],[147,98,138,120]) ).
tff(149,plain,
( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(150,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[149,148]) ).
tff(151,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ),
inference(rewrite,[status(thm)],]) ).
tff(153,plain,
( aScalar0(xH)
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ),
inference(rewrite,[status(thm)],]) ).
tff(154,plain,
( aScalar0(xH)
<=> aScalar0(xH) ),
inference(rewrite,[status(thm)],]) ).
tff(155,axiom,
( aScalar0(xH)
& ( xH = sdtasdt0(xA,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
tff(156,plain,
aScalar0(xH),
inference(and_elim,[status(thm)],[155]) ).
tff(157,plain,
aScalar0(xH),
inference(modus_ponens,[status(thm)],[156,154]) ).
tff(158,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(modus_ponens,[status(thm)],[157,153]) ).
tff(159,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(modus_ponens,[status(thm)],[158,152]) ).
tff(160,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(transitivity,[status(thm)],[163,161]) ).
tff(165,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ) ),
inference(transitivity,[status(thm)],[165,160]) ).
tff(167,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(unit_resolution,[status(thm)],[168,98,138,120,159]) ).
tff(170,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(171,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[170,169]) ).
tff(172,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(transitivity,[status(thm)],[171,151]) ).
tff(173,plain,
sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(175,plain,
sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[174,169]) ).
tff(176,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) = sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(transitivity,[status(thm)],[176,173,132]) ).
tff(178,plain,
sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) = sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) = sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(183,plain,
( ( aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(transitivity,[status(thm)],[184,182]) ).
tff(186,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(187,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ),
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(unit_resolution,[status(thm)],[187,25,159]) ).
tff(189,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,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)))))
| ~ ( ( sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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)))) != sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,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)))))
| ~ ( ( sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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)))) != sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,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)))))
| ~ ( ( sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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)))) != sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,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)))))
| ~ ( ( sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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)))) != sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
( ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ( sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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)))) != sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ),
inference(unit_resolution,[status(thm)],[191,98,85,56]) ).
tff(193,plain,
~ ( ( sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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)))) != sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ),
inference(unit_resolution,[status(thm)],[192,188]) ).
tff(194,plain,
( ( sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( 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)))) != sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(tautology,[status(thm)],]) ).
tff(195,plain,
sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(unit_resolution,[status(thm)],[194,193]) ).
tff(196,plain,
sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(transitivity,[status(thm)],[195,181]) ).
tff(197,plain,
sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(transitivity,[status(thm)],[197,112]) ).
tff(199,plain,
( aScalar0(xE)
<=> aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
( aScalar0(xE)
<=> aScalar0(xE) ),
inference(rewrite,[status(thm)],]) ).
tff(201,axiom,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
tff(202,plain,
aScalar0(xE),
inference(and_elim,[status(thm)],[201]) ).
tff(203,plain,
aScalar0(xE),
inference(modus_ponens,[status(thm)],[202,200]) ).
tff(204,plain,
aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),
inference(modus_ponens,[status(thm)],[203,199]) ).
tff(205,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(206,plain,
( ( aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
<=> ( aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(207,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ),
inference(transitivity,[status(thm)],[207,205]) ).
tff(209,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))),
inference(unit_resolution,[status(thm)],[210,25,204]) ).
tff(212,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
( ( aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(214,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(transitivity,[status(thm)],[214,212]) ).
tff(216,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(217,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))),
inference(unit_resolution,[status(thm)],[217,25,204,159]) ).
tff(219,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(220,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
( aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ),
inference(unit_resolution,[status(thm)],[221,69]) ).
tff(223,plain,
aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(unit_resolution,[status(thm)],[222,188,218]) ).
tff(224,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(225,plain,
( aScalar0(xP)
<=> aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))) ),
inference(rewrite,[status(thm)],]) ).
tff(226,plain,
( aScalar0(xP)
<=> aScalar0(xP) ),
inference(rewrite,[status(thm)],]) ).
tff(227,axiom,
( aScalar0(xP)
& ( xP = sdtasdt0(xE,xH) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
tff(228,plain,
aScalar0(xP),
inference(and_elim,[status(thm)],[227]) ).
tff(229,plain,
aScalar0(xP),
inference(modus_ponens,[status(thm)],[228,226]) ).
tff(230,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),
inference(modus_ponens,[status(thm)],[229,225]) ).
tff(231,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(modus_ponens,[status(thm)],[230,224]) ).
tff(232,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(233,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(234,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
( ~ aScalar0(sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ),
inference(unit_resolution,[status(thm)],[234,98,231]) ).
tff(236,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(unit_resolution,[status(thm)],[235,223,211]) ).
tff(237,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) ) ),
inference(tautology,[status(thm)],]) ).
tff(238,plain,
sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) = sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),
inference(unit_resolution,[status(thm)],[237,236]) ).
tff(239,plain,
sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))))
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) ),
inference(monotonicity,[status(thm)],[239,198]) ).
tff(241,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) ),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))))
<=> ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) ),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))),sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))))
<=> ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(244,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))))
<=> ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))),sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(245,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG))))
<=> ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))) ),
inference(rewrite,[status(thm)],]) ).
tff(246,axiom,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(247,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
inference(modus_ponens,[status(thm)],[246,245]) ).
tff(248,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))),sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))))),
inference(modus_ponens,[status(thm)],[247,244]) ).
tff(249,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),
inference(modus_ponens,[status(thm)],[248,243]) ).
tff(250,plain,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),
inference(modus_ponens,[status(thm)],[249,242]) ).
tff(251,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(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))))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(252,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(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))))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(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))))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(253,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(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))))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(254,plain,
( sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))) ),
inference(rewrite,[status(thm)],]) ).
tff(255,axiom,
sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2796) ).
tff(256,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(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))))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))))),
inference(modus_ponens,[status(thm)],[256,253]) ).
tff(258,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(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))))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),
inference(modus_ponens,[status(thm)],[257,252]) ).
tff(259,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),sdtpldt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))),sdtpldt0(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)))),sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))),
inference(modus_ponens,[status(thm)],[258,251]) ).
tff(260,plain,
$false,
inference(unit_resolution,[status(thm)],[259,250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : RNG078+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 22:21:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 9.98/6.62 % SZS status Theorem
% 9.98/6.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------