TSTP Solution File: RNG077+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG077+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 03:18:14 EDT 2022
% Result : Theorem 18.50s 11.81s
% Output : Proof 18.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 76
% Syntax : Number of formulae : 160 ( 46 unt; 16 typ; 0 def)
% Number of atoms : 1222 ( 600 equ)
% Maximal formula atoms : 28 ( 8 avg)
% Number of connectives : 2099 (1067 ~; 801 |; 141 &)
% ( 81 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 46 ( 46 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 217 ( 202 !; 0 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
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(xE_type,type,
xE: $i ).
tff(xq_type,type,
xq: $i ).
tff(xp_type,type,
xp: $i ).
tff(xB_type,type,
xB: $i ).
tff(xA_type,type,
xA: $i ).
tff(xP_type,type,
xP: $i ).
tff(xH_type,type,
xH: $i ).
tff(1,plain,
( aScalar0(xE)
<=> aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aScalar0(xE)
<=> aScalar0(xE) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
tff(4,plain,
aScalar0(xE),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aScalar0(xE),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt)))
<=> aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs))) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( aScalar0(xB)
<=> aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt))) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( aScalar0(xB)
<=> aScalar0(xB) ),
inference(rewrite,[status(thm)],]) ).
tff(10,axiom,
( aScalar0(xB)
& ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
tff(11,plain,
aScalar0(xB),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
aScalar0(xB),
inference(modus_ponens,[status(thm)],[11,9]) ).
tff(13,plain,
aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(modus_ponens,[status(thm)],[13,7]) ).
tff(15,plain,
( aScalar0(xA)
<=> aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( aScalar0(xA)
<=> aScalar0(xA) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
( aScalar0(xA)
& ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
tff(18,plain,
aScalar0(xA),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
aScalar0(xA),
inference(modus_ponens,[status(thm)],[18,16]) ).
tff(20,plain,
aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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)],[23]) ).
tff(25,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(26,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(27,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)],[26]) ).
tff(28,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(29,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)],[28,27]) ).
tff(30,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)],[29,25]) ).
tff(31,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)],[30]) ).
tff(32,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)],[31,24]) ).
tff(33,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)],[32,22]) ).
tff(34,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) )
<=> ( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) )
<=> ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) )
<=> ( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) ) ),
inference(transitivity,[status(thm)],[39,34]) ).
tff(41,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ),
inference(unit_resolution,[status(thm)],[42,33,20,14,6]) ).
tff(44,plain,
( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(45,plain,
sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( ( sdtpldt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) )
| ( sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) ) ),
inference(tautology,[status(thm)],]) ).
tff(47,plain,
sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),
inference(unit_resolution,[status(thm)],[46,43]) ).
tff(48,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) = sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,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(51,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)],[50]) ).
tff(52,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(53,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)],[52]) ).
tff(54,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(55,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(56,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)],[55]) ).
tff(57,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
tff(58,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[61,51]) ).
tff(63,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))),
inference(unit_resolution,[status(thm)],[65,62,20,6]) ).
tff(67,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(68,plain,
( aScalar0(xP)
<=> aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( aScalar0(xP)
<=> aScalar0(xP) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
( aScalar0(xP)
& ( xP = sdtasdt0(xE,xH) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
tff(71,plain,
aScalar0(xP),
inference(and_elim,[status(thm)],[70]) ).
tff(72,plain,
aScalar0(xP),
inference(modus_ponens,[status(thm)],[71,69]) ).
tff(73,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(modus_ponens,[status(thm)],[73,67]) ).
tff(75,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(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),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(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,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(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,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(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(unit_resolution,[status(thm)],[77,33,14,74,66]) ).
tff(79,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) != sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtpldt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(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)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(80,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) ) ) )
<=> ( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
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) ) ) )
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
~ ( ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(unit_resolution,[status(thm)],[87,33,20,14,6]) ).
tff(89,plain,
( ( sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) )
| ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) = sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) = sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)))),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,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(92,plain,
( aScalar0(xH)
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( aScalar0(xH)
<=> aScalar0(xH) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
( aScalar0(xH)
& ( xH = sdtasdt0(xA,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
tff(95,plain,
aScalar0(xH),
inference(and_elim,[status(thm)],[94]) ).
tff(96,plain,
aScalar0(xH),
inference(modus_ponens,[status(thm)],[95,93]) ).
tff(97,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(modus_ponens,[status(thm)],[97,91]) ).
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(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(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,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(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ aScalar0(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(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) )
<=> ( ~ aScalar0(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(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ) ),
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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,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(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ) ),
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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,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(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ) ),
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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xt,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ),
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(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(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ),
inference(unit_resolution,[status(thm)],[107,33,20,14,98]) ).
tff(109,plain,
( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtpldt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtpldt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) != sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) != sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) )
| ( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ),
inference(tautology,[status(thm)],]) ).
tff(110,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))) = sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(unit_resolution,[status(thm)],[109,108]) ).
tff(111,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) = sdtasdt0(sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
sdtasdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) = sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(transitivity,[status(thm)],[111,90,81,49,45]) ).
tff(113,plain,
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)),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))))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
sdtpldt0(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(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)],[113]) ).
tff(115,plain,
sdtpldt0(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(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)),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(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ 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))))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ 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))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,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(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))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,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(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))))) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,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(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))))) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,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(121,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ 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))))) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,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)],[121,62,98]) ).
tff(123,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(xt)),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)))))
| ~ ( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),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)))))
| ~ ( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( ~ aScalar0(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(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(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)),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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ~ ( ( 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(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(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(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)),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(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))))) ) )
<=> ~ ( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( ~ aScalar0(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ( 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(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(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(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)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ) ) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ( ~ aScalar0(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ( 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(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(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(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)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(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)),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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ) ) ),
inference(transitivity,[status(thm)],[126,124]) ).
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(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ( 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(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(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(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)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ 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(xt)),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)))))
| ~ ( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ) ) ),
inference(monotonicity,[status(thm)],[127]) ).
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(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ( 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(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(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(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)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ 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(xt)),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)))))
| ~ ( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ) ) ),
inference(transitivity,[status(thm)],[128,123]) ).
tff(130,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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))
| ~ ( ( 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(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(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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),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)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(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)),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(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,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(xt)),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)))))
| ~ ( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,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(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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ) ),
inference(unit_resolution,[status(thm)],[131,33,74]) ).
tff(133,plain,
~ ( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(unit_resolution,[status(thm)],[132,122]) ).
tff(134,plain,
( ( 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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) )
| ( sdtasdt0(sdtasdt0(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))))) != sdtasdt0(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(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)),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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ) ),
inference(tautology,[status(thm)],]) ).
tff(135,plain,
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(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(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
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(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(transitivity,[status(thm)],[135,115]) ).
tff(137,plain,
( ( 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(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(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(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(rewrite,[status(thm)],]) ).
tff(138,plain,
( ( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) )
<=> ( 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(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)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) )
<=> ( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,axiom,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(141,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
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(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)))))),
inference(modus_ponens,[status(thm)],[141,138]) ).
tff(143,plain,
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(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(modus_ponens,[status(thm)],[142,137]) ).
tff(144,plain,
$false,
inference(unit_resolution,[status(thm)],[143,136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG077+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 22:16:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 18.50/11.81 % SZS status Theorem
% 18.50/11.81 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------