TSTP Solution File: RNG080+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG080+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 03:18:17 EDT 2022
% Result : Theorem 10.03s 6.73s
% Output : Proof 10.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 47
% Syntax : Number of formulae : 110 ( 37 unt; 17 typ; 0 def)
% Number of atoms : 558 ( 316 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 744 ( 308 ~; 325 |; 43 &)
% ( 57 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 82 ( 76 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $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(sz00_type,type,
sz00: $i ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(xG_type,type,
xG: $i ).
tff(xD_type,type,
xD: $i ).
tff(xF_type,type,
xF: $i ).
tff(xC_type,type,
xC: $i ).
tff(xH_type,type,
xH: $i ).
tff(xE_type,type,
xE: $i ).
tff(1,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xt) )
<=> ( aDimensionOf0(xs) = aDimensionOf0(xt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
tff(3,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( aDimensionOf0(xt) = sz00 )
<=> ( aDimensionOf0(xs) = sz00 ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ( aDimensionOf0(xs) = sz00 )
<=> ( aDimensionOf0(xt) = sz00 ) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ( aDimensionOf0(xs) != sz00 )
<=> ( aDimensionOf0(xt) != sz00 ) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ( aDimensionOf0(xs) != sz00 )
<=> ( aDimensionOf0(xs) != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
tff(10,plain,
aDimensionOf0(xs) != sz00,
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
aDimensionOf0(xt) != sz00,
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( aVector0(xt)
<=> aVector0(xt) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
tff(14,plain,
aVector0(xt),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aVector0(xt),
inference(modus_ponens,[status(thm)],[14,12]) ).
tff(16,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
<=> ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) ) )),
( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
<=> ~ ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) ) )),
rewrite(
( ~ ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) )
<=> ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) ) )),
( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
<=> ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 ) ) )),
trans(
monotonicity(
rewrite(
( ( aVector0(W0)
& aVector0(W1) )
<=> ~ ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aVector0(W1) )
<=> ~ ~ ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
rewrite(
( ~ ~ ( ~ aVector0(W1)
| ~ aVector0(W0) )
<=> ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aVector0(W1) )
<=> ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 )
| ~ aVector0(W1)
| ~ aVector0(W0) ) )),
rewrite(
( ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 )
| ~ aVector0(W1)
| ~ aVector0(W0) )
<=> ( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
( ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) )
<=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )
<=> ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) ) )),
rewrite(
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[27,17]) ).
tff(29,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| $false
| ~ aVector0(xt) )
<=> ( ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( aDimensionOf0(xt) = aDimensionOf0(xt) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( aDimensionOf0(xt) != aDimensionOf0(xt) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( aDimensionOf0(xt) != aDimensionOf0(xt) )
<=> $false ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ( ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) )
<=> ( ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| $false
| ~ aVector0(xt) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) )
<=> ( ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ),
inference(transitivity,[status(thm)],[35,30]) ).
tff(37,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ) ),
inference(transitivity,[status(thm)],[37,29]) ).
tff(39,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xt) )
| ~ aVector0(xt) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ),
inference(unit_resolution,[status(thm)],[40,28,15]) ).
tff(42,plain,
sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(unit_resolution,[status(thm)],[41,11]) ).
tff(43,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) = sdtasasdt0(xt,xt),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
sdtlbdtrb0(xt,aDimensionOf0(xt)) = sdtlbdtrb0(xt,aDimensionOf0(xs)),
inference(monotonicity,[status(thm)],[4]) ).
tff(45,plain,
sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(monotonicity,[status(thm)],[44,44]) ).
tff(46,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))) = sdtasasdt0(xt,xt),
inference(transitivity,[status(thm)],[47,43]) ).
tff(49,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
aVector0(xs),
inference(and_elim,[status(thm)],[13]) ).
tff(51,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| $false
| ~ aVector0(xs) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xs) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> $false ),
inference(transitivity,[status(thm)],[55,31]) ).
tff(57,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| $false
| ~ aVector0(xs) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs) ) ),
inference(transitivity,[status(thm)],[57,53]) ).
tff(59,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs) ) ),
inference(transitivity,[status(thm)],[59,52]) ).
tff(61,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ~ aVector0(xs) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[62,28,51,10]) ).
tff(64,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) = sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)),
inference(monotonicity,[status(thm)],[64,48]) ).
tff(66,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))),
inference(monotonicity,[status(thm)],[44]) ).
tff(67,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(xs)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(xs)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs) )
<=> ( ~ aVector0(xs)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(xs)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(xs)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) )
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1)))) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ~ aVector0(xs)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ~ aVector0(xt)
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) ) ),
inference(unit_resolution,[status(thm)],[73,28,51,15,3]) ).
tff(75,plain,
sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(unit_resolution,[status(thm)],[74,11]) ).
tff(76,plain,
sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),
inference(transitivity,[status(thm)],[75,67]) ).
tff(77,plain,
sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)) = sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),
inference(monotonicity,[status(thm)],[76,76]) ).
tff(78,plain,
sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))) = sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))))
<=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(monotonicity,[status(thm)],[78,65]) ).
tff(80,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
<=> sdtlseqdt0(sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
<=> ~ sdtlseqdt0(sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
<=> ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(84,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(modus_ponens,[status(thm)],[84,81]) ).
tff(86,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))))
<=> sdtlseqdt0(sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
<=> sdtlseqdt0(sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
<=> sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2733) ).
tff(90,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))),sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))))),
inference(modus_ponens,[status(thm)],[90,87]) ).
tff(92,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs))))),sdtasdt0(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xs)))))),
inference(modus_ponens,[status(thm)],[91,86]) ).
tff(93,plain,
$false,
inference(unit_resolution,[status(thm)],[92,85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG080+2 : 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 : n017.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 21:44:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 10.03/6.73 % SZS status Theorem
% 10.03/6.73 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------