%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG052+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 1.30s 1.47s
% Output : Proof 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 65
% Syntax : Number of formulae : 183 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 2069 (1005 equ)
% Maximal formula atoms : 48 ( 11 avg)
% Number of connectives : 3430 (1661 ~;1378 |; 178 &)
% ( 153 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 117 ( 117 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 403 ( 376 !; 0 ?; 403 :)
% Comments :
%------------------------------------------------------------------------------
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(xs_type,type,
xs: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xt_type,type,
xt: $i ).
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(xq_type,type,
xq: $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(xp_type,type,
xp: $i ).
tff(1,plain,
( ( aDimensionOf0(xs) != sz00 )
<=> ( aDimensionOf0(xs) != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
tff(3,plain,
aDimensionOf0(xs) != sz00,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
tff(6,plain,
aVector0(xs),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[6,4]) ).
tff(8,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )
<=> ~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ))),
( ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )
<=> ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )),
( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ) )),
rewrite(( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ) )),
( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
refl(( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
trans(monotonicity(rewrite(( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
<=> ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) )),
rewrite(( ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
<=> ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )),
( ( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )
<=> ( ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )),
rewrite(( ( ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )
<=> ~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )),
( ( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )
<=> ~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ))),
( ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )
<=> ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )),
( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) )),
rewrite(( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) )),
( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )
<=> ( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ))),
( ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )
<=> ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )),
( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) )),
rewrite(( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) )),
( ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) )
<=> ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
<=> ( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ))),
( ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
<=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) )),
( ( ( aDimensionOf0(W0) != sz00 )
=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) != sz00 )
=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ( aDimensionOf0(W0) != sz00 )
=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )),
( ( ( aDimensionOf0(W0) != sz00 )
=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )),
( ( aVector0(W0)
=> ( ( aDimensionOf0(W0) != sz00 )
=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
<=> ( aVector0(W0)
=> ( ( aDimensionOf0(W0) = sz00 )
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ) )),
rewrite(( ( aVector0(W0)
=> ( ( aDimensionOf0(W0) = sz00 )
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )),
( ( aVector0(W0)
=> ( ( aDimensionOf0(W0) != sz00 )
=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [W0: $i] :
( aVector0(W0)
=> ( ( aDimensionOf0(W0) != sz00 )
=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
<=> ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [W0: $i] :
( aVector0(W0)
=> ( ( aDimensionOf0(W0) != sz00 )
=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
tff(23,plain,
! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
( ( ( W1 != sziznziztdt0(W0) )
| ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
& ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,14]) ).
tff(29,plain,
! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[28,9]) ).
tff(30,plain,
( ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [W1: $i] :
rewrite(( ~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
<=> ~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
<=> ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[34,31]) ).
tff(36,plain,
( ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[36,30]) ).
tff(38,plain,
( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[39,29,7,3]) ).
tff(41,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
<=> ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ),
inference(unit_resolution,[status(thm)],[46,40]) ).
tff(48,plain,
( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ) ),
inference(tautology,[status(thm)],[]) ).
tff(49,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
( iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))))
<=> iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
<=> iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
<=> ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( xD = sdtasasdt0(xq,xq) )
<=> ( xD = sdtasasdt0(xq,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
( aScalar0(xD)
& ( xD = sdtasasdt0(xq,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
tff(55,plain,
xD = sdtasasdt0(xq,xq),
inference(and_elim,[status(thm)],[54]) ).
tff(56,plain,
xD = sdtasasdt0(xq,xq),
inference(modus_ponens,[status(thm)],[55,53]) ).
tff(57,plain,
sdtasasdt0(xq,xq) = xD,
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ( xq = sziznziztdt0(xt) )
<=> ( xq = sziznziztdt0(xt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
( aVector0(xq)
& ( xq = sziznziztdt0(xt) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
tff(60,plain,
xq = sziznziztdt0(xt),
inference(and_elim,[status(thm)],[59]) ).
tff(61,plain,
xq = sziznziztdt0(xt),
inference(modus_ponens,[status(thm)],[60,58]) ).
tff(62,plain,
sziznziztdt0(xt) = xq,
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)) = sdtasasdt0(xq,xq),
inference(monotonicity,[status(thm)],[62,62]) ).
tff(64,plain,
sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)) = xD,
inference(transitivity,[status(thm)],[63,57]) ).
tff(65,plain,
( ( xC = sdtasasdt0(xp,xp) )
<=> ( xC = sdtasasdt0(xp,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
( aScalar0(xC)
& ( xC = sdtasasdt0(xp,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
tff(67,plain,
xC = sdtasasdt0(xp,xp),
inference(and_elim,[status(thm)],[66]) ).
tff(68,plain,
xC = sdtasasdt0(xp,xp),
inference(modus_ponens,[status(thm)],[67,65]) ).
tff(69,plain,
sdtasasdt0(xp,xp) = xC,
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ( xp = sziznziztdt0(xs) )
<=> ( xp = sziznziztdt0(xs) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
( aVector0(xp)
& ( xp = sziznziztdt0(xs) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
tff(72,plain,
xp = sziznziztdt0(xs),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
xp = sziznziztdt0(xs),
inference(modus_ponens,[status(thm)],[72,70]) ).
tff(74,plain,
sziznziztdt0(xs) = xp,
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sdtasasdt0(xp,xp),
inference(monotonicity,[status(thm)],[74,74]) ).
tff(76,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = xC,
inference(transitivity,[status(thm)],[75,69]) ).
tff(77,plain,
sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt))) = sdtasdt0(xC,xD),
inference(monotonicity,[status(thm)],[76,64]) ).
tff(78,plain,
( ( xE = sdtasasdt0(xp,xq) )
<=> ( xE = sdtasasdt0(xp,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
tff(80,plain,
xE = sdtasasdt0(xp,xq),
inference(and_elim,[status(thm)],[79]) ).
tff(81,plain,
xE = sdtasasdt0(xp,xq),
inference(modus_ponens,[status(thm)],[80,78]) ).
tff(82,plain,
sdtasasdt0(xp,xq) = xE,
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)) = sdtasasdt0(xp,xq),
inference(monotonicity,[status(thm)],[74,62]) ).
tff(84,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)) = xE,
inference(transitivity,[status(thm)],[83,82]) ).
tff(85,plain,
sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))) = sdtasdt0(xE,xE),
inference(monotonicity,[status(thm)],[84,84]) ).
tff(86,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)],[85,77]) ).
tff(87,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)],[86]) ).
tff(88,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)],[87]) ).
tff(89,plain,
( ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
<=> ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(91,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,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)],[91,88]) ).
tff(93,plain,
( aVector0(sziznziztdt0(xs))
<=> aVector0(xp) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(94,plain,
( aVector0(xp)
<=> aVector0(sziznziztdt0(xs)) ),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( aVector0(xp)
<=> aVector0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
aVector0(xp),
inference(and_elim,[status(thm)],[71]) ).
tff(97,plain,
aVector0(xp),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
aVector0(sziznziztdt0(xs)),
inference(modus_ponens,[status(thm)],[97,94]) ).
tff(99,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xt) )
<=> ( aDimensionOf0(xs) = aDimensionOf0(xt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
tff(101,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( aVector0(xt)
<=> aVector0(xt) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
aVector0(xt),
inference(and_elim,[status(thm)],[5]) ).
tff(105,plain,
aVector0(xt),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,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(107,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)],[106]) ).
tff(108,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(109,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)],[108]) ).
tff(110,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(111,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(112,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)],[111]) ).
tff(113,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/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
tff(114,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)],[113,112]) ).
tff(115,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)],[114,110]) ).
tff(116,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)],[115]) ).
tff(117,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)],[116,109]) ).
tff(118,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)],[117,107]) ).
tff(119,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(120,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(121,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)],[120]) ).
tff(122,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)],[121,119]) ).
tff(123,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(124,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)],[123,122]) ).
tff(125,plain,
aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)),
inference(unit_resolution,[status(thm)],[124,118,7,105,3,102]) ).
tff(126,plain,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( aVector0(sziznziztdt0(xt))
<=> aVector0(xq) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(128,plain,
( aVector0(xq)
<=> aVector0(sziznziztdt0(xt)) ),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
( aVector0(xq)
<=> aVector0(xq) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
aVector0(xq),
inference(and_elim,[status(thm)],[59]) ).
tff(131,plain,
aVector0(xq),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
aVector0(sziznziztdt0(xt)),
inference(modus_ponens,[status(thm)],[131,128]) ).
tff(133,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(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) )
<=> ! [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)],[133]) ).
tff(135,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(136,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)],[135]) ).
tff(137,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(138,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(139,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)],[138]) ).
tff(140,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/sandbox2/benchmark/theBenchmark.p',m__1652) ).
tff(141,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)],[140,139]) ).
tff(142,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)],[141,137]) ).
tff(143,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)],[142]) ).
tff(144,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)],[143,136]) ).
tff(145,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)],[144,134]) ).
tff(146,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(147,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(148,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)],[147]) ).
tff(149,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)],[148,146]) ).
tff(150,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(151,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)],[150,149]) ).
tff(152,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)],[151,145]) ).
tff(153,plain,
~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)),
inference(unit_resolution,[status(thm)],[152,132,126,98,92]) ).
tff(154,plain,
~ iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))),
inference(modus_ponens,[status(thm)],[153,52]) ).
tff(155,plain,
^ [W0: $i] :
refl(( ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(156,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
^ [W0: $i] :
rewrite(( ( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(159,plain,
( ! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[158]) ).
tff(160,axiom,
! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
tff(161,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[161,157]) ).
tff(163,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(skolemize,[status(sab)],[162]) ).
tff(164,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[163,156]) ).
tff(165,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(166,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[167,164,98]) ).
tff(169,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(170,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) )
<=> ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(173,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
tff(175,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[175,171]) ).
tff(177,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(skolemize,[status(sab)],[176]) ).
tff(178,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[177,170]) ).
tff(179,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))),
inference(unit_resolution,[status(thm)],[181,178,168]) ).
tff(183,plain,
$false,
inference(unit_resolution,[status(thm)],[182,154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG052+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:16:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.30/1.47 % SZS status Theorem
% 1.30/1.47 % SZS output start Proof
% See solution above
% 1.30/1.50 % E exiting
%------------------------------------------------------------------------------