%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG047+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:00 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 50
% Syntax : Number of formulae : 130 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 2109 (1147 equ)
% Maximal formula atoms : 48 ( 16 avg)
% Number of connectives : 3928 (2030 ~;1611 |; 132 &)
% ( 119 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 81 ( 81 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 433 ( 413 !; 0 ?; 433 :)
% Comments :
%------------------------------------------------------------------------------
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(xt_type,type,
xt: $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(1,plain,
( ( aDimensionOf0(xt) != sz00 )
<=> ( aDimensionOf0(xt) != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( ( aDimensionOf0(xs) = aDimensionOf0(xt) )
& ( aDimensionOf0(xt) != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1329_01) ).
tff(3,plain,
aDimensionOf0(xt) != sz00,
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aDimensionOf0(xt) != sz00,
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aVector0(xt)
<=> aVector0(xt) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1329) ).
tff(7,plain,
aVector0(xt),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aVector0(xt),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,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(10,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)],[9]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(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(quant_intro,[status(thm)],[13]) ).
tff(15,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)],[14,12]) ).
tff(16,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(17,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)],[16]) ).
tff(18,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(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) ) ) ) )
& ( ( 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)],[18]) ).
tff(20,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(21,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(22,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)],[21]) ).
tff(23,axiom,
! [W0: $i] :
( aVector0(W0)
=> ( ( aDimensionOf0(W0) != sz00 )
=> ! [W1: $i] :
( ( W1 = sziznziztdt0(W0) )
<=> ( aVector0(W1)
& ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) )
& ! [W2: $i] :
( aNaturalNumber0(W2)
=> ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
tff(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)],[23,22]) ).
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) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
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(skolemize,[status(sab)],[25]) ).
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)],[26,19]) ).
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)],[27,17]) ).
tff(29,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)],[28,15]) ).
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) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[29,10]) ).
tff(31,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(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,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(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [W1: $i] :
rewrite(( ~ ( ~ ( ( W1 = sziznziztdt0(xt) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
<=> ~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xt) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
<=> ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ( ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xt) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xt) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[35,32]) ).
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(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xt) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,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(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
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(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xt) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,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(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[37,31]) ).
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(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xt) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,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(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[40,30,8,4]) ).
tff(42,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xt))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xt))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ( ~ ( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ( sziznziztdt0(xt) = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xt),xt))
| ( sdtlbdtrb0(sziznziztdt0(xt),tptp_fun_W2_1(sziznziztdt0(xt),xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(sziznziztdt0(xt),xt)) ) ) )
| ~ ( ( sziznziztdt0(xt) != sziznziztdt0(xt) )
| ~ ( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
<=> ~ ( ~ aVector0(sziznziztdt0(xt))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ( sziznziztdt0(xt) = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xt),xt))
| ( sdtlbdtrb0(sziznziztdt0(xt),tptp_fun_W2_1(sziznziztdt0(xt),xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(sziznziztdt0(xt),xt)) ) ) )
| ~ ( ( sziznziztdt0(xt) != sziznziztdt0(xt) )
| ~ ( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xt))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) ) ) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ( sziznziztdt0(xt) = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xt),xt))
| ( sdtlbdtrb0(sziznziztdt0(xt),tptp_fun_W2_1(sziznziztdt0(xt),xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(sziznziztdt0(xt),xt)) ) ) )
| ~ ( ( sziznziztdt0(xt) != sziznziztdt0(xt) )
| ~ ( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xt))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) ) ) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ( sziznziztdt0(xt) = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xt),xt))
| ( sdtlbdtrb0(sziznziztdt0(xt),tptp_fun_W2_1(sziznziztdt0(xt),xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(sziznziztdt0(xt),xt)) ) ) )
| ~ ( ( sziznziztdt0(xt) != sziznziztdt0(xt) )
| ~ ( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ( W1 = sziznziztdt0(xt) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xt))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xt)) = sdtlbdtrb0(xt,tptp_fun_W2_1(W1,xt)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xt) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xt))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) ) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ ( ~ aVector0(sziznziztdt0(xt))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) ) ),
inference(unit_resolution,[status(thm)],[47,41]) ).
tff(49,plain,
( ~ aVector0(sziznziztdt0(xt))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) ) ),
inference(tautology,[status(thm)],[]) ).
tff(50,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xt) )
<=> ( aDimensionOf0(xs) = aDimensionOf0(xt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(and_elim,[status(thm)],[2]) ).
tff(54,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ( aDimensionOf0(xs) = sz00 )
<=> ( aDimensionOf0(xt) = sz00 ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( aDimensionOf0(xt) = sz00 )
<=> ( aDimensionOf0(xs) = sz00 ) ),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( ( aDimensionOf0(xt) != sz00 )
<=> ( aDimensionOf0(xs) != sz00 ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
aDimensionOf0(xs) != sz00,
inference(modus_ponens,[status(thm)],[4,57]) ).
tff(59,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
aVector0(xs),
inference(and_elim,[status(thm)],[6]) ).
tff(61,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,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) ) ) ) ) ) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) = sz00 )
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) = sz00 )
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ aVector0(xs)
| ( aDimensionOf0(xs) = sz00 )
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
^ [W1: $i] :
rewrite(( ~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
<=> ~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
<=> ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,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) ) ) ) ) ) )
<=> ( ~ aVector0(xs)
| ( aDimensionOf0(xs) = sz00 )
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[66,63]) ).
tff(68,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) ) ) ) ) ) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) = sz00 )
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,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) ) ) ) ) ) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) = sz00 )
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[68,62]) ).
tff(70,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(71,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) ) ) ) ) ) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) = sz00 )
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ( aDimensionOf0(xs) = sz00 )
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[71,30,61]) ).
tff(73,plain,
! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[72,58]) ).
tff(74,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
<=> ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ) ),
inference(transitivity,[status(thm)],[76,74]) ).
tff(78,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ( W1 = sziznziztdt0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
~ ( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ),
inference(unit_resolution,[status(thm)],[79,73]) ).
tff(81,plain,
( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ) ),
inference(tautology,[status(thm)],[]) ).
tff(82,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))),
inference(transitivity,[status(thm)],[82,54,51]) ).
tff(84,plain,
( ~ aVector0(sziznziztdt0(xt))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| aVector0(sziznziztdt0(xt)) ),
inference(tautology,[status(thm)],[]) ).
tff(85,plain,
aVector0(sziznziztdt0(xt)),
inference(unit_resolution,[status(thm)],[84,48]) ).
tff(86,plain,
^ [W0: $i] :
refl(( ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
^ [W0: $i] :
rewrite(( ( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,axiom,
! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
tff(92,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[94,87]) ).
tff(96,plain,
( ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) )
<=> ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ),
inference(unit_resolution,[status(thm)],[98,95]) ).
tff(100,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))),
inference(unit_resolution,[status(thm)],[99,85]) ).
tff(101,plain,
( ~ aVector0(sziznziztdt0(xs))
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| aVector0(sziznziztdt0(xs)) ),
inference(tautology,[status(thm)],[]) ).
tff(102,plain,
aVector0(sziznziztdt0(xs)),
inference(unit_resolution,[status(thm)],[101,80]) ).
tff(103,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(104,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(unit_resolution,[status(thm)],[105,95]) ).
tff(107,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[106,102]) ).
tff(108,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) )
<=> ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(110,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) )
<=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
tff(119,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[122,112]) ).
tff(124,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ( ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) )
<=> ( ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(transitivity,[status(thm)],[126,124]) ).
tff(128,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
$false,
inference(unit_resolution,[status(thm)],[129,123,110,107,100,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG047+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:16:17 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% See solution above
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------