%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG052+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:24:01 AM UTC 2025
% Result : Theorem 1.16s 1.34s
% Output : Proof 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 50
% Syntax : Number of formulae : 155 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 805 ( 279 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1015 ( 425 ~; 386 |; 78 &)
% ( 84 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 60 ( 60 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 138 ( 122 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(xq_type,type,
xq: $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(xs_type,type,
xs: $i ).
tff(xt_type,type,
xt: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xp_type,type,
xp: $i ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(xD_type,type,
xD: $i ).
tff(xC_type,type,
xC: $i ).
tff(xE_type,type,
xE: $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
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/sandbox/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(xs) != sz00 )
<=> ( aDimensionOf0(xs) != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1692) ).
tff(7,plain,
aDimensionOf0(xs) != sz00,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
( aVector0(xt)
<=> aVector0(xt) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
tff(10,plain,
aVector0(xt),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aVector0(xt),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
aVector0(xs),
inference(and_elim,[status(thm)],[9]) ).
tff(14,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,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) ) )),
( ( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 )
| ~ aVector0(W1)
| ~ aVector0(W0) ) )),
rewrite(( ( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ( aDimensionOf0(W1) = sz00 )
| ~ aVector0(W1)
| ~ aVector0(W0) )
<=> ( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
( ( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i,W1: $i] :
( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) )
<=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) )
<=> ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) ) )),
rewrite(( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) )
<=> ( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) )
<=> ( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEqInit) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
| ~ ( aVector0(W0)
& aVector0(W1) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(xs)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ~ aVector0(xt) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(xs)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ~ aVector0(xt) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(xs)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ~ aVector0(xt) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(xs)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ~ aVector0(xt) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != aDimensionOf0(xs) )
| ( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)),
inference(unit_resolution,[status(thm)],[33,27,14,11,7,4]) ).
tff(35,plain,
( ( xq = sziznziztdt0(xt) )
<=> ( xq = sziznziztdt0(xt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
( aVector0(xq)
& ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) ) )
& ( xq = sziznziztdt0(xt) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
tff(37,plain,
xq = sziznziztdt0(xt),
inference(and_elim,[status(thm)],[36]) ).
tff(38,plain,
xq = sziznziztdt0(xt),
inference(modus_ponens,[status(thm)],[37,35]) ).
tff(39,plain,
aDimensionOf0(xq) = aDimensionOf0(sziznziztdt0(xt)),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
aDimensionOf0(xq) = aDimensionOf0(sziznziztdt0(xs)),
inference(transitivity,[status(thm)],[39,34]) ).
tff(41,plain,
( aNaturalNumber0(aDimensionOf0(xq))
<=> aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
<=> aNaturalNumber0(aDimensionOf0(xq)) ),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ( xp = sziznziztdt0(xs) )
<=> ( xp = sziznziztdt0(xs) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
( aVector0(xp)
& ( szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) ) )
& ( xp = sziznziztdt0(xs) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).
tff(45,plain,
xp = sziznziztdt0(xs),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
xp = sziznziztdt0(xs),
inference(modus_ponens,[status(thm)],[45,43]) ).
tff(47,plain,
sziznziztdt0(xs) = xp,
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( aVector0(sziznziztdt0(xs))
<=> aVector0(xp) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( aVector0(xp)
<=> aVector0(sziznziztdt0(xs)) ),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
( aVector0(xp)
<=> aVector0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( aVector0(xp)
& ( szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) ) ) ),
inference(and_elim,[status(thm)],[44]) ).
tff(52,plain,
( aVector0(xp)
& ( szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs) ) ),
inference(and_elim,[status(thm)],[51]) ).
tff(53,plain,
aVector0(xp),
inference(and_elim,[status(thm)],[52]) ).
tff(54,plain,
aVector0(xp),
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
aVector0(sziznziztdt0(xs)),
inference(modus_ponens,[status(thm)],[54,49]) ).
tff(56,plain,
^ [W0: $i] :
refl(( ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
^ [W0: $i] :
rewrite(( ( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
tff(62,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(unit_resolution,[status(thm)],[68,65]) ).
tff(70,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[69,55]) ).
tff(71,plain,
aNaturalNumber0(aDimensionOf0(xq)),
inference(modus_ponens,[status(thm)],[70,42]) ).
tff(72,plain,
( ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) )
<=> ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( aVector0(xq)
& ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) ) ) ),
inference(and_elim,[status(thm)],[36]) ).
tff(74,plain,
( aVector0(xq)
& ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) ) ),
inference(and_elim,[status(thm)],[73]) ).
tff(75,plain,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt),
inference(and_elim,[status(thm)],[74]) ).
tff(76,plain,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt),
inference(modus_ponens,[status(thm)],[75,72]) ).
tff(77,plain,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xs),
inference(transitivity,[status(thm)],[76,4]) ).
tff(78,plain,
( iLess0(aDimensionOf0(xq),szszuzczcdt0(aDimensionOf0(xq)))
<=> iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) ),
inference(monotonicity,[status(thm)],[40,77]) ).
tff(79,plain,
( iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
<=> iLess0(aDimensionOf0(xq),szszuzczcdt0(aDimensionOf0(xq))) ),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
<=> ~ iLess0(aDimensionOf0(xq),szszuzczcdt0(aDimensionOf0(xq))) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( xD = sdtasasdt0(xq,xq) )
<=> ( xD = sdtasasdt0(xq,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
( aScalar0(xD)
& ( xD = sdtasasdt0(xq,xq) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
tff(83,plain,
xD = sdtasasdt0(xq,xq),
inference(and_elim,[status(thm)],[82]) ).
tff(84,plain,
xD = sdtasasdt0(xq,xq),
inference(modus_ponens,[status(thm)],[83,81]) ).
tff(85,plain,
sdtasasdt0(xq,xq) = xD,
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
sziznziztdt0(xt) = xq,
inference(symmetry,[status(thm)],[38]) ).
tff(87,plain,
sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)) = sdtasasdt0(xq,xq),
inference(monotonicity,[status(thm)],[86,86]) ).
tff(88,plain,
sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)) = xD,
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
( ( xC = sdtasasdt0(xp,xp) )
<=> ( xC = sdtasasdt0(xp,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
( aScalar0(xC)
& ( xC = sdtasasdt0(xp,xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
tff(91,plain,
xC = sdtasasdt0(xp,xp),
inference(and_elim,[status(thm)],[90]) ).
tff(92,plain,
xC = sdtasasdt0(xp,xp),
inference(modus_ponens,[status(thm)],[91,89]) ).
tff(93,plain,
sdtasasdt0(xp,xp) = xC,
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sdtasasdt0(xp,xp),
inference(monotonicity,[status(thm)],[47,47]) ).
tff(95,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = xC,
inference(transitivity,[status(thm)],[94,93]) ).
tff(96,plain,
sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) = sdtasdt0(xC,xD),
inference(monotonicity,[status(thm)],[95,88]) ).
tff(97,plain,
( ( xE = sdtasasdt0(xp,xq) )
<=> ( xE = sdtasasdt0(xp,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,axiom,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).
tff(99,plain,
xE = sdtasasdt0(xp,xq),
inference(and_elim,[status(thm)],[98]) ).
tff(100,plain,
xE = sdtasasdt0(xp,xq),
inference(modus_ponens,[status(thm)],[99,97]) ).
tff(101,plain,
sdtasasdt0(xp,xq) = xE,
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)) = sdtasasdt0(xp,xq),
inference(monotonicity,[status(thm)],[47,86]) ).
tff(103,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)) = xE,
inference(transitivity,[status(thm)],[102,101]) ).
tff(104,plain,
sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) = sdtasdt0(xE,xE),
inference(monotonicity,[status(thm)],[103,103]) ).
tff(105,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
<=> sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(monotonicity,[status(thm)],[104,96]) ).
tff(106,plain,
( sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
<=> sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
<=> ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
<=> ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(110,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(modus_ponens,[status(thm)],[110,107]) ).
tff(112,plain,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
inference(symmetry,[status(thm)],[34]) ).
tff(113,plain,
( aVector0(sziznziztdt0(xt))
<=> aVector0(xq) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(114,plain,
( aVector0(xq)
<=> aVector0(sziznziztdt0(xt)) ),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
( aVector0(xq)
<=> aVector0(xq) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
aVector0(xq),
inference(and_elim,[status(thm)],[74]) ).
tff(117,plain,
aVector0(xq),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
aVector0(sziznziztdt0(xt)),
inference(modus_ponens,[status(thm)],[117,114]) ).
tff(119,plain,
^ [W0: $i,W1: $i] :
refl(( ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
<=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(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) ) )),
( ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
<=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) )),
rewrite(( ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
<=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) ) )),
( ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
<=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) )
<=> ( ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) )),
( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) )
<=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) ) )),
rewrite(( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) )
<=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) )),
( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) )
<=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) ) )
<=> ( ( aVector0(W0)
& aVector0(W1) )
=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) ) )),
rewrite(( ( ( aVector0(W0)
& aVector0(W1) )
=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) )
<=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) ) )
<=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) )),
inference(bind,[status(th)],[]) ).
tff(125,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1652) ).
tff(127,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[129,122]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[130,120]) ).
tff(132,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xt))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xt))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
( ( sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aVector0(sziznziztdt0(xt))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) )
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xt))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aVector0(sziznziztdt0(xt))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) )
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xt))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aVector0(sziznziztdt0(xt))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) )
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xt))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ~ aVector0(sziznziztdt0(xt))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) )
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1)))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
| ~ aVector0(W0) )
| ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xt))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xt))
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(unit_resolution,[status(thm)],[137,131]) ).
tff(139,plain,
~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)),
inference(unit_resolution,[status(thm)],[138,118,112,55,111]) ).
tff(140,plain,
~ iLess0(aDimensionOf0(xq),szszuzczcdt0(aDimensionOf0(xq))),
inference(modus_ponens,[status(thm)],[139,80]) ).
tff(141,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) )
<=> ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
tff(147,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(xq))
| iLess0(aDimensionOf0(xq),szszuzczcdt0(aDimensionOf0(xq))) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(xq))
| iLess0(aDimensionOf0(xq),szszuzczcdt0(aDimensionOf0(xq))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(xq))
| iLess0(aDimensionOf0(xq),szszuzczcdt0(aDimensionOf0(xq))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(xq))
| iLess0(aDimensionOf0(xq),szszuzczcdt0(aDimensionOf0(xq))) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
( ~ aNaturalNumber0(aDimensionOf0(xq))
| iLess0(aDimensionOf0(xq),szszuzczcdt0(aDimensionOf0(xq))) ),
inference(unit_resolution,[status(thm)],[153,150]) ).
tff(155,plain,
$false,
inference(unit_resolution,[status(thm)],[154,140,71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG052+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 03:16:05 EDT 2025
% 0.19/0.33 % CPUTime :
% 1.16/1.34 % SZS status Theorem
% 1.16/1.34 % SZS output start Proof
% See solution above
% 1.16/1.36 % E exiting
%------------------------------------------------------------------------------