TSTP Solution File: RNG047+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG047+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 03:17:54 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 61
% Syntax : Number of formulae : 143 ( 35 unt; 10 typ; 0 def)
% Number of atoms : 2113 (1151 equ)
% Maximal formula atoms : 48 ( 15 avg)
% Number of connectives : 3932 (2033 ~;1611 |; 132 &)
% ( 120 <=>; 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 : 9 ( 7 >; 2 *; 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(xs) = aDimensionOf0(xt) )
<=> ( aDimensionOf0(xs) = aDimensionOf0(xt) ) ),
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(xs) = aDimensionOf0(xt),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( aDimensionOf0(xt) = sz00 )
<=> ( aDimensionOf0(xs) = sz00 ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ( aDimensionOf0(xs) = sz00 )
<=> ( aDimensionOf0(xt) = sz00 ) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( ( aDimensionOf0(xs) != sz00 )
<=> ( aDimensionOf0(xt) != sz00 ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ( aDimensionOf0(xt) != sz00 )
<=> ( aDimensionOf0(xs) != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ( aDimensionOf0(xt) != sz00 )
<=> ( aDimensionOf0(xt) != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
aDimensionOf0(xt) != sz00,
inference(and_elim,[status(thm)],[2]) ).
tff(12,plain,
aDimensionOf0(xt) != sz00,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
aDimensionOf0(xs) != sz00,
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
aDimensionOf0(xt) != sz00,
inference(modus_ponens,[status(thm)],[13,8]) ).
tff(15,plain,
( aVector0(xt)
<=> aVector0(xt) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1329) ).
tff(17,plain,
aVector0(xt),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
aVector0(xt),
inference(modus_ponens,[status(thm)],[17,15]) ).
tff(19,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(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) ) ) ) )
| ~ ( ( 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)],[19]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(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) ) ) ) )
| ~ ( ( 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)],[23]) ).
tff(25,plain,
( ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) )
| ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) ) )
<=> ! [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)],[24,22]) ).
tff(26,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(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)) ) ) ) ) )
<=> ! [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)],[26]) ).
tff(28,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(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)) ) ) ) ) )
<=> ! [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)],[28]) ).
tff(30,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(31,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(32,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)],[31]) ).
tff(33,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(34,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)],[33,32]) ).
tff(35,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)],[34,30]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36,29]) ).
tff(38,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)],[37,27]) ).
tff(39,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)],[38,25]) ).
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) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[39,20]) ).
tff(41,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)
| ( W1 = sziznziztdt0(xt) )
| ( 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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xt) )
| ( 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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(rewrite,[status(thm)],]) ).
tff(43,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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(bind,[status(th)],]) ).
tff(44,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)
| ( W1 = sziznziztdt0(xt) )
| ( 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_intro,[status(thm)],[43]) ).
tff(45,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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(monotonicity,[status(thm)],[44]) ).
tff(46,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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(transitivity,[status(thm)],[45,42]) ).
tff(47,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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(monotonicity,[status(thm)],[46]) ).
tff(48,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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(transitivity,[status(thm)],[47,41]) ).
tff(49,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(50,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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ( aDimensionOf0(xt) = sz00 )
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xt) )
| ( 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(unit_resolution,[status(thm)],[50,40,18]) ).
tff(52,plain,
! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xt) )
| ( 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(unit_resolution,[status(thm)],[51,14]) ).
tff(53,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xt) )
| ( 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(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xt) )
| ( 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(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ( ~ ( ~ aVector0(sziznziztdt0(xt))
| ( sziznziztdt0(xt) = sziznziztdt0(xt) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(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))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xt) )
| ( 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(sziznziztdt0(xt))
| ( sziznziztdt0(xt) = sziznziztdt0(xt) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xt) )
| ( 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(sziznziztdt0(xt))
| ( sziznziztdt0(xt) = sziznziztdt0(xt) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(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)
| ( W1 = sziznziztdt0(xt) )
| ( 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(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xt) )
| ( 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(sziznziztdt0(xt))
| ( sziznziztdt0(xt) = sziznziztdt0(xt) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(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(58,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xt) )
| ( 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(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
~ ( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) ) ),
inference(unit_resolution,[status(thm)],[58,52]) ).
tff(60,plain,
( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) ) ),
inference(tautology,[status(thm)],]) ).
tff(61,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
aVector0(xs),
inference(and_elim,[status(thm)],[16]) ).
tff(65,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [W1: $i] :
rewrite(
( ~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
<=> ~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
<=> ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[70,67]) ).
tff(72,plain,
( ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(xs) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[72,66]) ).
tff(74,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(75,plain,
( ~ ! [W0: $i] :
( ( aDimensionOf0(W0) = sz00 )
| ~ aVector0(W0)
| ! [W1: $i] :
~ ( ~ ( ( W1 = sziznziztdt0(W0) )
| ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,W0)) = sdtlbdtrb0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( ( W1 != sziznziztdt0(W0) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ) )
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs)
| ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[75,40,65,13]) ).
tff(77,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
<=> ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ ( ~ aVector0(sziznziztdt0(xs))
| ( sziznziztdt0(xs) = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(sziznziztdt0(xs),xs))
| ( sdtlbdtrb0(sziznziztdt0(xs),tptp_fun_W2_1(sziznziztdt0(xs),xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(sziznziztdt0(xs),xs)) ) ) )
| ~ ( ( sziznziztdt0(xs) != sziznziztdt0(xs) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aVector0(W1)
| ( W1 = sziznziztdt0(xs) )
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,xs))
| ( sdtlbdtrb0(W1,tptp_fun_W2_1(W1,xs)) = sdtlbdtrb0(xs,tptp_fun_W2_1(W1,xs)) ) ) )
| ~ ( ( W1 != sziznziztdt0(xs) )
| ~ ( ~ aVector0(W1)
| ( szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xs,W2) ) ) ) ) )
| ~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ ( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) ) ),
inference(unit_resolution,[status(thm)],[82,76]) ).
tff(84,plain,
( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))),
inference(transitivity,[status(thm)],[85,4,62]) ).
tff(87,plain,
( ~ aVector0(sziznziztdt0(xt))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xt) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xt),W2) = sdtlbdtrb0(xt,W2) ) )
| aVector0(sziznziztdt0(xt)) ),
inference(tautology,[status(thm)],]) ).
tff(88,plain,
aVector0(sziznziztdt0(xt)),
inference(unit_resolution,[status(thm)],[87,59]) ).
tff(89,plain,
^ [W0: $i] :
refl(
( ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [W0: $i] :
rewrite(
( ( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
tff(95,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,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(100,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ),
inference(unit_resolution,[status(thm)],[101,98]) ).
tff(103,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))),
inference(unit_resolution,[status(thm)],[102,88]) ).
tff(104,plain,
( ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) )
| ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtlbdtrb0(sziznziztdt0(xs),W2) = sdtlbdtrb0(xs,W2) ) )
| aVector0(sziznziztdt0(xs)) ),
inference(tautology,[status(thm)],]) ).
tff(105,plain,
aVector0(sziznziztdt0(xs)),
inference(unit_resolution,[status(thm)],[104,83]) ).
tff(106,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(107,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(unit_resolution,[status(thm)],[108,98]) ).
tff(110,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[109,105]) ).
tff(111,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) )
<=> ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,axiom,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(113,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,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(115,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)],[114]) ).
tff(116,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(117,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)],[116]) ).
tff(118,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(119,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(120,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)],[119]) ).
tff(121,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
tff(122,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[125,115]) ).
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(xs)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( 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(xs)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,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(xs)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(rewrite,[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)))
| ( 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(xs)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,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(xs)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(transitivity,[status(thm)],[129,127]) ).
tff(131,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(132,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
$false,
inference(unit_resolution,[status(thm)],[132,126,113,110,103,86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG047+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 21:56:28 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------