TSTP Solution File: RNG052+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG052+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 03:17:56 EDT 2022
% Result : Theorem 30.08s 19.16s
% Output : Proof 30.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 78
% Syntax : Number of formulae : 164 ( 43 unt; 19 typ; 0 def)
% Number of atoms : 1969 ( 959 equ)
% Maximal formula atoms : 48 ( 13 avg)
% Number of connectives : 3322 (1615 ~;1331 |; 175 &)
% ( 141 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 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 : 17 ( 11 >; 6 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 395 ( 368 !; 0 ?; 395 :)
% 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(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/sandbox/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/sandbox/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/sandbox/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)
| ( W1 = sziznziztdt0(xs) )
| ( 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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( 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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(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)
| ( W1 = sziznziztdt0(xs) )
| ( 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_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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( 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(unit_resolution,[status(thm)],[39,29,7,3]) ).
tff(41,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( 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(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( 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(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(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))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( 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(sziznziztdt0(xs))
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( 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(sziznziztdt0(xs))
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( 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(sziznziztdt0(xs))
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(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)
| ( W1 = sziznziztdt0(xs) )
| ( 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(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ),
inference(unit_resolution,[status(thm)],[46,40]) ).
tff(48,plain,
( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( 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,
( ( aDimensionOf0(xs) = aDimensionOf0(xt) )
<=> ( aDimensionOf0(xs) = aDimensionOf0(xt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
tff(55,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( aVector0(xt)
<=> aVector0(xt) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
aVector0(xt),
inference(and_elim,[status(thm)],[5]) ).
tff(59,plain,
aVector0(xt),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,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(61,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)],[60]) ).
tff(62,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(63,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)],[62]) ).
tff(64,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(65,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(66,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)],[65]) ).
tff(67,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) != sz00 ) )
=> ( aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEqInit) ).
tff(68,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)],[67,66]) ).
tff(69,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)],[68,64]) ).
tff(70,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)],[69]) ).
tff(71,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)],[70,63]) ).
tff(72,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)],[71,61]) ).
tff(73,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(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ( aDimensionOf0(xt) != aDimensionOf0(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(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,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(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,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(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,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(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,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(78,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(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)) )
| ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)),
inference(unit_resolution,[status(thm)],[78,72,7,59,3,56]) ).
tff(80,plain,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,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(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
<=> ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(84,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,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)],[84,81]) ).
tff(86,plain,
( aVector0(xq)
<=> aVector0(sziznziztdt0(xt)) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( aVector0(xq)
<=> aVector0(xq) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
( aVector0(xq)
& ( xq = sziznziztdt0(xt) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
tff(89,plain,
aVector0(xq),
inference(and_elim,[status(thm)],[88]) ).
tff(90,plain,
aVector0(xq),
inference(modus_ponens,[status(thm)],[89,87]) ).
tff(91,plain,
aVector0(sziznziztdt0(xt)),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( aVector0(xp)
<=> aVector0(sziznziztdt0(xs)) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( aVector0(xp)
<=> aVector0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
( aVector0(xp)
& ( xp = sziznziztdt0(xs) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).
tff(95,plain,
aVector0(xp),
inference(and_elim,[status(thm)],[94]) ).
tff(96,plain,
aVector0(xp),
inference(modus_ponens,[status(thm)],[95,93]) ).
tff(97,plain,
aVector0(sziznziztdt0(xs)),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,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(99,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)],[98]) ).
tff(100,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(101,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)],[100]) ).
tff(102,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(103,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(104,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)],[103]) ).
tff(105,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> ( iLess0(aDimensionOf0(W0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(W0,W1),sdtasasdt0(W0,W1)),sdtasdt0(sdtasasdt0(W0,W0),sdtasasdt0(W1,W1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1652) ).
tff(106,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)],[105,104]) ).
tff(107,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)],[106,102]) ).
tff(108,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)],[107]) ).
tff(109,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)],[108,101]) ).
tff(110,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)],[109,99]) ).
tff(111,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) )
| 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(rewrite,[status(thm)],]) ).
tff(112,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(113,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(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) )
| ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) ),
inference(unit_resolution,[status(thm)],[113,110,97,91,85]) ).
tff(115,plain,
~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)),
inference(unit_resolution,[status(thm)],[114,80]) ).
tff(116,plain,
~ iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))),
inference(modus_ponens,[status(thm)],[115,52]) ).
tff(117,plain,
^ [W0: $i] :
refl(
( ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(118,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
^ [W0: $i] :
rewrite(
( ( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,axiom,
! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
tff(123,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[125,118]) ).
tff(127,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(128,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[129,126,97]) ).
tff(131,plain,
^ [W0: $i] :
refl(
( ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
^ [W0: $i] :
rewrite(
( ( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) )
<=> ( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) )),
inference(bind,[status(th)],]) ).
tff(135,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> iLess0(W0,szszuzczcdt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
tff(137,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| iLess0(W0,szszuzczcdt0(W0)) ),
inference(modus_ponens,[status(thm)],[139,132]) ).
tff(141,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(142,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(143,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)],[142,141]) ).
tff(144,plain,
iLess0(aDimensionOf0(sziznziztdt0(xs)),szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))),
inference(unit_resolution,[status(thm)],[143,140,130]) ).
tff(145,plain,
$false,
inference(unit_resolution,[status(thm)],[144,116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.32 % Problem : RNG052+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.33 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.55 % Computer : n018.cluster.edu
% 0.12/0.55 % Model : x86_64 x86_64
% 0.12/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.55 % Memory : 8042.1875MB
% 0.12/0.55 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.55 % CPULimit : 300
% 0.12/0.55 % WCLimit : 300
% 0.12/0.55 % DateTime : Fri Sep 2 22:04:14 EDT 2022
% 0.12/0.55 % CPUTime :
% 0.12/0.55 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.55 Usage: tptp [options] [-file:]file
% 0.12/0.55 -h, -? prints this message.
% 0.12/0.55 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.55 -m, -model generate model.
% 0.12/0.55 -p, -proof generate proof.
% 0.12/0.55 -c, -core generate unsat core of named formulas.
% 0.12/0.55 -st, -statistics display statistics.
% 0.12/0.55 -t:timeout set timeout (in second).
% 0.12/0.55 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.55 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.55 -<param>:<value> configuration parameter and value.
% 0.12/0.55 -o:<output-file> file to place output in.
% 30.08/19.16 % SZS status Theorem
% 30.08/19.16 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------