%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG050+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.23s 0.41s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 60 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 387 ( 176 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 519 ( 223 ~; 193 |; 42 &)
% ( 43 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 31 ( 31 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 59 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(xs_type,type,
xs: $i ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
tff(aVector0_type,type,
aVector0: $i > $o ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(1,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
<=> ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ( ( aDimensionOf0(xs) != sz00 )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
<=> ~ ( ~ ( ( aDimensionOf0(xs) = sz00 )
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ( ( aDimensionOf0(xs) != sz00 )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ~ ( ( aDimensionOf0(xs) = sz00 )
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ( ( aDimensionOf0(xs) = sz00 )
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
<=> ( ( aDimensionOf0(xs) = sz00 )
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
( ( aDimensionOf0(xs) = sz00 )
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(or_elim,[status(thm)],[4]) ).
tff(9,plain,
( ( aDimensionOf0(xs) = sz00 )
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
aDimensionOf0(xs) = sz00,
inference(unit_resolution,[status(thm)],[9,6]) ).
tff(11,plain,
( aVector0(xs)
<=> aVector0(xs) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
aVector0(xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542) ).
tff(13,plain,
aVector0(xs),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,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) ) )),
trans(monotonicity(rewrite(( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
<=> ~ ( ( aDimensionOf0(W1) != sz00 )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
<=> ~ ~ ( ( aDimensionOf0(W1) != sz00 )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
rewrite(( ~ ~ ( ( aDimensionOf0(W1) != sz00 )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ( ( aDimensionOf0(W1) != sz00 )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
<=> ( ( aDimensionOf0(W1) != sz00 )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W1) != sz00 )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
rewrite(( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ~ aVector0(W0)
| ( aDimensionOf0(W1) != sz00 )
| ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
<=> ( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
( ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) )
<=> ( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) )
<=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
| ( sdtasasdt0(W0,W1) = sz0z00 ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
<=> ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
| ( sdtasasdt0(W0,W1) = sz0z00 ) ) ) )),
rewrite(( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
| ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ) )),
( ( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
<=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [W0: $i,W1: $i] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) )
=> ( sdtasasdt0(W0,W1) = sz0z00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
tff(22,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ ( aVector0(W0)
& aVector0(W1) )
| ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
& ( aDimensionOf0(W1) = sz00 ) ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) ),
inference(modus_ponens,[status(thm)],[25,15]) ).
tff(27,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) != sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sz0z00 ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) != sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sz0z00 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ( aDimensionOf0(xs) != sz00 )
| ( sdtasasdt0(xs,xs) = sz0z00 )
| ~ aVector0(xs)
| $false
| ~ aVector0(xs) )
<=> ( ( aDimensionOf0(xs) != sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sz0z00 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xs) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
<=> $false ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ( ( aDimensionOf0(xs) != sz00 )
| ( sdtasasdt0(xs,xs) = sz0z00 )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ( aDimensionOf0(xs) != sz00 )
| ( sdtasasdt0(xs,xs) = sz0z00 )
| ~ aVector0(xs)
| $false
| ~ aVector0(xs) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ( aDimensionOf0(xs) != sz00 )
| ( sdtasasdt0(xs,xs) = sz0z00 )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ( aDimensionOf0(xs) != sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sz0z00 ) ) ),
inference(transitivity,[status(thm)],[33,28]) ).
tff(35,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) != sz00 )
| ( sdtasasdt0(xs,xs) = sz0z00 )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) != sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sz0z00 ) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) != sz00 )
| ( sdtasasdt0(xs,xs) = sz0z00 )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) != sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sz0z00 ) ) ),
inference(transitivity,[status(thm)],[35,27]) ).
tff(37,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) != sz00 )
| ( sdtasasdt0(xs,xs) = sz0z00 )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) )
| ~ aVector0(xs) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [W0: $i,W1: $i] :
( ( aDimensionOf0(W1) != sz00 )
| ( sdtasasdt0(W0,W1) = sz0z00 )
| ~ aVector0(W1)
| ( aDimensionOf0(W0) != aDimensionOf0(W1) )
| ~ aVector0(W0) )
| ( aDimensionOf0(xs) != sz00 )
| ~ aVector0(xs)
| ( sdtasasdt0(xs,xs) = sz0z00 ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
sdtasasdt0(xs,xs) = sz0z00,
inference(unit_resolution,[status(thm)],[38,26,13,10]) ).
tff(40,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
<=> sdtlseqdt0(sz0z00,sz0z00) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( sdtlseqdt0(sz0z00,sz0z00)
<=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [W0: $i] :
refl(( ( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
^ [W0: $i] :
rewrite(( ( aScalar0(W0)
=> sdtlseqdt0(W0,W0) )
<=> ( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) )
<=> ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [W0: $i] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
tff(48,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
( aScalar0(sz0z00)
<=> aScalar0(sz0z00) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
tff(54,plain,
aScalar0(sz0z00),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
| ~ aScalar0(sz0z00)
| sdtlseqdt0(sz0z00,sz0z00) )
<=> ( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
| ~ aScalar0(sz0z00)
| sdtlseqdt0(sz0z00,sz0z00) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
| ~ aScalar0(sz0z00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [W0: $i] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) )
| ~ aScalar0(sz0z00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(unit_resolution,[status(thm)],[57,54,51]) ).
tff(59,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(modus_ponens,[status(thm)],[58,41]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[6,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : RNG050+1 : TPTP v9.0.0. Released v4.0.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 03:16:10 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.23/0.41 % SZS status Theorem
% 0.23/0.41 % SZS output start Proof
% See solution above
% 0.23/0.43 % E exiting
%------------------------------------------------------------------------------