%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM458+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:21:02 AM UTC 2025
% Result : Theorem 0.22s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 44 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 180 ( 97 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 267 ( 145 ~; 73 |; 27 &)
% ( 19 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 29 !; 8 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(1,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) )
<=> ~ ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) )
<=> ~ ~ ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) )
<=> ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) )
| sdtlseqdt0(xm,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(7,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(or_elim,[status(thm)],[6]) ).
tff(8,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(modus_ponens,[status(thm)],[10,5]) ).
tff(12,plain,
^ [W0: $i] :
refl($oeq(~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ))),
inference(bind,[status(th)],[]) ).
tff(13,plain,
! [W0: $i] :
~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(nnf-neg,[status(sab)],[11,12]) ).
tff(14,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ),
inference(modus_ponens,[status(thm)],[13,4]) ).
tff(15,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ),
inference(modus_ponens,[status(thm)],[14,2]) ).
tff(16,plain,
( aNaturalNumber0(sz00)
<=> aNaturalNumber0(sz00) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(18,plain,
aNaturalNumber0(sz00),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xm,sz00) != xm ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xm,sz00) != xm ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xm,sz00) != xm ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xm,sz00) != xm ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
sdtpldt0(xm,sz00) != xm,
inference(unit_resolution,[status(thm)],[21,18,15]) ).
tff(23,plain,
( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sz00) = xm ) ),
inference(tautology,[status(thm)],[]) ).
tff(24,plain,
( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
aNaturalNumber0(xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__718) ).
tff(27,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
tff(36,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[39,29]) ).
tff(41,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,40,27,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM458+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:14:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.22/0.39 % SZS status Theorem
% 0.22/0.39 % SZS output start Proof
% See solution above
% 0.22/0.40 % E exiting
%------------------------------------------------------------------------------