%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG080+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:08 AM UTC 2025
% Result : Theorem 0.22s 0.45s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 48
% Syntax : Number of formulae : 152 ( 77 unt; 0 typ; 0 def)
% Number of atoms : 642 ( 391 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 769 ( 308 ~; 325 |; 57 &)
% ( 66 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-2 aty)
% Number of variables : 84 ( 78 !; 0 ?; 84 :)
% 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(xG_type,type,
xG: $i ).
tff(xD_type,type,
xD: $i ).
tff(xF_type,type,
xF: $i ).
tff(xC_type,type,
xC: $i ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(xt_type,type,
xt: $i ).
tff(xs_type,type,
xs: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(xB_type,type,
xB: $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(xq_type,type,
xq: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xA_type,type,
xA: $i ).
tff(xp_type,type,
xp: $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) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( 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) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( 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) )
<=> ( ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( 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) )
<=> ( ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( 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) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( 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) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( 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) )
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( 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,
( ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
<=> ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
( aScalar0(xB)
& ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
tff(46,plain,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(and_elim,[status(thm)],[45]) ).
tff(47,plain,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(modus_ponens,[status(thm)],[46,44]) ).
tff(48,plain,
sdtlbdtrb0(xt,aDimensionOf0(xt)) = xB,
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(xB,xB),
inference(monotonicity,[status(thm)],[48,48]) ).
tff(50,plain,
sdtasdt0(xB,xB) = sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
( ( xG = sdtasdt0(xB,xB) )
<=> ( xG = sdtasdt0(xB,xB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
( aScalar0(xG)
& ( xG = sdtasdt0(xB,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
tff(53,plain,
xG = sdtasdt0(xB,xB),
inference(and_elim,[status(thm)],[52]) ).
tff(54,plain,
xG = sdtasdt0(xB,xB),
inference(modus_ponens,[status(thm)],[53,51]) ).
tff(55,plain,
xG = sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(transitivity,[status(thm)],[54,50]) ).
tff(56,plain,
( ( xq = sziznziztdt0(xt) )
<=> ( xq = sziznziztdt0(xt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
( aVector0(xq)
& ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) ) )
& ( xq = sziznziztdt0(xt) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
tff(58,plain,
xq = sziznziztdt0(xt),
inference(and_elim,[status(thm)],[57]) ).
tff(59,plain,
xq = sziznziztdt0(xt),
inference(modus_ponens,[status(thm)],[58,56]) ).
tff(60,plain,
sziznziztdt0(xt) = xq,
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)) = sdtasasdt0(xq,xq),
inference(monotonicity,[status(thm)],[60,60]) ).
tff(62,plain,
sdtasasdt0(xq,xq) = sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ( xD = sdtasasdt0(xq,xq) )
<=> ( xD = sdtasasdt0(xq,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
( aScalar0(xD)
& ( xD = sdtasasdt0(xq,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
tff(65,plain,
xD = sdtasasdt0(xq,xq),
inference(and_elim,[status(thm)],[64]) ).
tff(66,plain,
xD = sdtasasdt0(xq,xq),
inference(modus_ponens,[status(thm)],[65,63]) ).
tff(67,plain,
xD = sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),
inference(transitivity,[status(thm)],[66,62]) ).
tff(68,plain,
sdtpldt0(xD,xG) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(monotonicity,[status(thm)],[67,55]) ).
tff(69,plain,
sdtpldt0(xD,xG) = sdtasasdt0(xt,xt),
inference(transitivity,[status(thm)],[68,43]) ).
tff(70,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
aVector0(xs),
inference(and_elim,[status(thm)],[13]) ).
tff(72,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[71,70]) ).
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) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(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 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,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 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xs) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> $false ),
inference(transitivity,[status(thm)],[76,31]) ).
tff(78,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)],[77]) ).
tff(79,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 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(transitivity,[status(thm)],[78,74]) ).
tff(80,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 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,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 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ) ),
inference(transitivity,[status(thm)],[80,73]) ).
tff(82,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(83,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 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[83,28,72,10]) ).
tff(85,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ( xF = sdtasdt0(xA,xA) )
<=> ( xF = sdtasdt0(xA,xA) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
( aScalar0(xF)
& ( xF = sdtasdt0(xA,xA) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(88,plain,
xF = sdtasdt0(xA,xA),
inference(and_elim,[status(thm)],[87]) ).
tff(89,plain,
xF = sdtasdt0(xA,xA),
inference(modus_ponens,[status(thm)],[88,86]) ).
tff(90,plain,
sdtasdt0(xA,xA) = xF,
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
( ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
<=> ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
( aScalar0(xA)
& ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
tff(93,plain,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(and_elim,[status(thm)],[92]) ).
tff(94,plain,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(modus_ponens,[status(thm)],[93,91]) ).
tff(95,plain,
sdtlbdtrb0(xs,aDimensionOf0(xs)) = xA,
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sdtasdt0(xA,xA),
inference(monotonicity,[status(thm)],[95,95]) ).
tff(97,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = xF,
inference(transitivity,[status(thm)],[96,90]) ).
tff(98,plain,
( ( xC = sdtasasdt0(xp,xp) )
<=> ( xC = sdtasasdt0(xp,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
( aScalar0(xC)
& ( xC = sdtasasdt0(xp,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
tff(100,plain,
xC = sdtasasdt0(xp,xp),
inference(and_elim,[status(thm)],[99]) ).
tff(101,plain,
xC = sdtasasdt0(xp,xp),
inference(modus_ponens,[status(thm)],[100,98]) ).
tff(102,plain,
sdtasasdt0(xp,xp) = xC,
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ( xp = sziznziztdt0(xs) )
<=> ( xp = sziznziztdt0(xs) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,axiom,
( aVector0(xp)
& ( szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) ) )
& ( xp = sziznziztdt0(xs) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
tff(105,plain,
xp = sziznziztdt0(xs),
inference(and_elim,[status(thm)],[104]) ).
tff(106,plain,
xp = sziznziztdt0(xs),
inference(modus_ponens,[status(thm)],[105,103]) ).
tff(107,plain,
sziznziztdt0(xs) = xp,
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sdtasasdt0(xp,xp),
inference(monotonicity,[status(thm)],[107,107]) ).
tff(109,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = xC,
inference(transitivity,[status(thm)],[108,102]) ).
tff(110,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtpldt0(xC,xF),
inference(monotonicity,[status(thm)],[109,97]) ).
tff(111,plain,
sdtpldt0(xC,xF) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
sdtpldt0(xC,xF) = sdtasasdt0(xs,xs),
inference(transitivity,[status(thm)],[111,85]) ).
tff(113,plain,
sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)) = sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)),
inference(monotonicity,[status(thm)],[112,69]) ).
tff(114,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
<=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,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(sdtpldt0(xC,xF),sdtpldt0(xD,xG))) ),
inference(symmetry,[status(thm)],[114]) ).
tff(116,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(sdtpldt0(xC,xF),sdtpldt0(xD,xG))) ),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,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(118,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(119,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(modus_ponens,[status(thm)],[119,116]) ).
tff(121,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)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(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)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,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)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,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)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ) ),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,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)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ) ),
inference(transitivity,[status(thm)],[123,121]) ).
tff(125,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(126,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)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) = sz00 )
| ( sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) )
| ( aDimensionOf0(xs) != aDimensionOf0(xt) ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,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)],[126,28,72,15,3]) ).
tff(128,plain,
sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(unit_resolution,[status(thm)],[127,11]) ).
tff(129,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) = sdtasasdt0(xs,xt),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))) = sdtasdt0(xA,xB),
inference(monotonicity,[status(thm)],[95,48]) ).
tff(131,plain,
sdtasdt0(xA,xB) = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ( xH = sdtasdt0(xA,xB) )
<=> ( xH = sdtasdt0(xA,xB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,axiom,
( aScalar0(xH)
& ( xH = sdtasdt0(xA,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
tff(134,plain,
xH = sdtasdt0(xA,xB),
inference(and_elim,[status(thm)],[133]) ).
tff(135,plain,
xH = sdtasdt0(xA,xB),
inference(modus_ponens,[status(thm)],[134,132]) ).
tff(136,plain,
xH = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))),
inference(transitivity,[status(thm)],[135,131]) ).
tff(137,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)) = sdtasasdt0(xp,xq),
inference(monotonicity,[status(thm)],[107,60]) ).
tff(138,plain,
sdtasasdt0(xp,xq) = sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ( xE = sdtasasdt0(xp,xq) )
<=> ( xE = sdtasasdt0(xp,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,axiom,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
tff(141,plain,
xE = sdtasasdt0(xp,xq),
inference(and_elim,[status(thm)],[140]) ).
tff(142,plain,
xE = sdtasasdt0(xp,xq),
inference(modus_ponens,[status(thm)],[141,139]) ).
tff(143,plain,
xE = sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),
inference(transitivity,[status(thm)],[142,138]) ).
tff(144,plain,
sdtpldt0(xE,xH) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt)))),
inference(monotonicity,[status(thm)],[143,136]) ).
tff(145,plain,
sdtpldt0(xE,xH) = sdtasasdt0(xs,xt),
inference(transitivity,[status(thm)],[144,129]) ).
tff(146,plain,
sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)) = sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),
inference(monotonicity,[status(thm)],[145,145]) ).
tff(147,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
<=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,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(149,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(150,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(modus_ponens,[status(thm)],[150,147]) ).
tff(152,plain,
$false,
inference(unit_resolution,[status(thm)],[151,120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG080+2 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 03:19:17 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.45 % SZS status Theorem
% 0.22/0.45 % SZS output start Proof
% See solution above
% 0.22/0.48 % E exiting
%------------------------------------------------------------------------------