TSTP Solution File: RNG049+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG049+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 03:17:55 EDT 2022
% Result : Theorem 0.17s 0.40s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 82
% Syntax : Number of formulae : 183 ( 41 unt; 15 typ; 0 def)
% Number of atoms : 2196 ( 796 equ)
% Maximal formula atoms : 48 ( 13 avg)
% Number of connectives : 3688 (1801 ~;1440 |; 225 &)
% ( 169 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 141 ( 141 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 12 >; 6 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 2 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 478 ( 441 !; 0 ?; 478 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(xs_type,type,
xs: $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
aVector0(xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542) ).
tff(3,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W0: $i] :
refl(
( ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [W0: $i] :
rewrite(
( ( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
tff(10,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
aNaturalNumber0(aDimensionOf0(xs)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aVector0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
( ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
rewrite(
( ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
( ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aVector0(W0)
& aNaturalNumber0(W1) )
=> aScalar0(sdtlbdtrb0(W0,W1)) )
<=> ( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aNaturalNumber0(W1) )
=> aScalar0(sdtlbdtrb0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aNaturalNumber0(W1) )
=> aScalar0(sdtlbdtrb0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ ( aVector0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[29,19]) ).
tff(31,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) )
<=> ( aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtlbdtrb0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aVector0(W0) )
| aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(unit_resolution,[status(thm)],[36,30,3,17]) ).
tff(38,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
tff(46,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[49,39]) ).
tff(51,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) )
<=> ( aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(unit_resolution,[status(thm)],[56,50]) ).
tff(58,plain,
aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(unit_resolution,[status(thm)],[57,37]) ).
tff(59,plain,
( ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
<=> ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1568) ).
tff(61,plain,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
<=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
<=> sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) ),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
<=> ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
<=> ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(68,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))),
inference(modus_ponens,[status(thm)],[68,65]) ).
tff(70,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) ),
inference(tautology,[status(thm)],]) ).
tff(71,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) ),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
<=> sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
& sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1590) ).
tff(74,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(and_elim,[status(thm)],[73]) ).
tff(75,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(modus_ponens,[status(thm)],[74,72]) ).
tff(76,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
<=> sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(and_elim,[status(thm)],[73]) ).
tff(78,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
<=> ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
<=> ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) )),
trans(
monotonicity(
rewrite(
( ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
<=> ~ ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
<=> ~ ~ ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
rewrite(
( ~ ~ ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) )
<=> ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
<=> ( ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
( ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) )
<=> ( ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) ) )),
rewrite(
( ( ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) )),
( ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) )
<=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
| ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
| ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ) )),
rewrite(
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
| ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
<=> ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
<=> ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
tff(87,plain,
! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [W0: $i,W1: $i] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
& sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ ( aScalar0(W0)
& aScalar0(W1) )
| ~ ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1) ) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) ),
inference(modus_ponens,[status(thm)],[90,80]) ).
tff(92,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
| ~ sdtlseqdt0(sz0z00,W1) )
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) )
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))) ) ),
inference(unit_resolution,[status(thm)],[94,91,78,75]) ).
tff(96,plain,
~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[95,71,58]) ).
tff(97,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aVector0(W0)
& aVector0(W1) )
<=> ~ ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aVector0(W1) )
<=> ~ ~ ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
rewrite(
( ~ ~ ( ~ aVector0(W1)
| ~ aVector0(W0) )
<=> ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ~ ( aVector0(W0)
& aVector0(W1) )
<=> ( ~ aVector0(W1)
| ~ aVector0(W0) ) )),
( ( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
rewrite(
( ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
( ( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) ) )
<=> ( ( aVector0(W0)
& aVector0(W1) )
=> ( aScalar0(sdtasasdt0(W0,W1))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) ) )),
rewrite(
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( aScalar0(sdtasasdt0(W0,W1))
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) ) )
<=> ( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
=> aScalar0(sdtasasdt0(W0,W1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
tff(105,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ ( aVector0(W0)
& aVector0(W1) )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[108,98]) ).
tff(110,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| $false
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xs)) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
<=> $false ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,plain,
( ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| $false
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
( ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(transitivity,[status(thm)],[116,111]) ).
tff(118,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(transitivity,[status(thm)],[118,110]) ).
tff(120,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasasdt0(W0,W1))
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(unit_resolution,[status(thm)],[121,109]) ).
tff(123,plain,
~ aVector0(sziznziztdt0(xs)),
inference(unit_resolution,[status(thm)],[122,96]) ).
tff(124,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(125,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)],[124,123]) ).
tff(126,plain,
( ( aDimensionOf0(xs) != sz00 )
<=> ( aDimensionOf0(xs) != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,axiom,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542_01) ).
tff(128,plain,
aDimensionOf0(xs) != sz00,
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,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(130,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)],[129]) ).
tff(131,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(132,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)],[131]) ).
tff(133,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(134,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)],[133]) ).
tff(135,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)],[134,132]) ).
tff(136,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(137,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)],[136]) ).
tff(138,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(139,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)],[138]) ).
tff(140,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(141,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(142,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)],[141]) ).
tff(143,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(144,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)],[143,142]) ).
tff(145,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)],[144,140]) ).
tff(146,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)],[145]) ).
tff(147,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)],[146,139]) ).
tff(148,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)],[147,137]) ).
tff(149,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)],[148,135]) ).
tff(150,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)],[149,130]) ).
tff(151,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(152,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(153,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(154,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)],[153]) ).
tff(155,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)],[154]) ).
tff(156,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)],[155,152]) ).
tff(157,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)],[156]) ).
tff(158,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)],[157,151]) ).
tff(159,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(160,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)],[159,158]) ).
tff(161,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)],[160,150,3,128]) ).
tff(162,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(163,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(164,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)],[163]) ).
tff(165,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)],[164,162]) ).
tff(166,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(167,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)],[166,165]) ).
tff(168,plain,
$false,
inference(unit_resolution,[status(thm)],[167,161,125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : RNG049+1 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n018.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Sep 2 22:03:29 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.17/0.40 % SZS status Theorem
% 0.17/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------