%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG047+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:00 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 64 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 355 ( 140 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 460 ( 192 ~; 171 |; 41 &)
% ( 34 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 73 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
tff(xt_type,type,
xt: $i ).
tff(xs_type,type,
xs: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) )
<=> ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) ) )
=> ( ( aVector0(sziznziztdt0(xt))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) ) ) )
=> ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ) )
<=> ~ ( ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ ( aVector0(sziznziztdt0(xt))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) )
& ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) ) ) )
| ~ ( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) ) )
=> ( ( aVector0(sziznziztdt0(xt))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) )
& ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) ) ) )
=> ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ ( aVector0(sziznziztdt0(xt))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) )
& ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) ) ) )
| ~ ( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( aVector0(sziznziztdt0(xt))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) )
& ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) ) ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xt) )
<=> ( aDimensionOf0(xs) = aDimensionOf0(xt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
( ( aDimensionOf0(xs) = aDimensionOf0(xt) )
& ( aDimensionOf0(xt) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329_01) ).
tff(11,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(modus_ponens,[status(thm)],[11,9]) ).
tff(13,plain,
( ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
<=> ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
( aVector0(sziznziztdt0(xs))
& ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) )
& ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) ) ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(15,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))),
inference(transitivity,[status(thm)],[16,12,8]) ).
tff(18,plain,
( aVector0(sziznziztdt0(xs))
<=> aVector0(sziznziztdt0(xs)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
aVector0(sziznziztdt0(xs)),
inference(and_elim,[status(thm)],[14]) ).
tff(20,plain,
aVector0(sziznziztdt0(xs)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [W0: $i] :
refl(( ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [W0: $i] :
rewrite(( ( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) )
<=> ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [W0: $i] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
tff(27,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) )
<=> ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
( aVector0(sziznziztdt0(xt))
<=> aVector0(sziznziztdt0(xt)) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
aVector0(sziznziztdt0(xt)),
inference(and_elim,[status(thm)],[5]) ).
tff(37,plain,
aVector0(sziznziztdt0(xt)),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) )
<=> ( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [W0: $i] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) )
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aVector0(sziznziztdt0(xt)) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))),
inference(unit_resolution,[status(thm)],[40,30,37]) ).
tff(42,plain,
( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) )
<=> ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(or_elim,[status(thm)],[4]) ).
tff(44,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) )
<=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
tff(53,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[56,46]) ).
tff(58,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) )
<=> ( ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aNaturalNumber0(W1)
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aNaturalNumber0(W0) )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,57,44,41,34,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : RNG047+2 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n014.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 03:16:09 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% See solution above
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------