TSTP Solution File: NUM464+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM464+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Sun Sep 18 13:09:51 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 35
% Syntax : Number of formulae : 74 ( 16 unt; 7 typ; 0 def)
% Number of atoms : 587 ( 229 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 839 ( 351 ~; 375 |; 56 &)
% ( 46 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 66 !; 4 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz10_type,type,
sz10: $i ).
tff(xm_type,type,
xm: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(xn_type,type,
xn: $i ).
tff(1,plain,
( ~ sdtlseqdt0(sz10,xm)
<=> ~ sdtlseqdt0(sz10,xm) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ( ( xm != sz00 )
=> ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sz10,W0) = xm ) )
| sdtlseqdt0(sz10,xm) ) )
<=> ~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sz10,W0) = xm ) )
| ( xm = sz00 )
| sdtlseqdt0(sz10,xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( ( xm != sz00 )
=> ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sz10,W0) = xm ) )
| sdtlseqdt0(sz10,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sz10,W0) = xm ) )
| ( xm = sz00 )
| sdtlseqdt0(sz10,xm) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ sdtlseqdt0(sz10,xm),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
~ sdtlseqdt0(sz10,xm),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm )
| sdtlseqdt0(sz10,xm) ),
inference(tautology,[status(thm)],]) ).
tff(8,plain,
( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ),
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
( ( xm != sz00 )
<=> ( xm != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
xm != sz00,
inference(or_elim,[status(thm)],[4]) ).
tff(11,plain,
xm != sz00,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__987) ).
tff(14,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[14,12]) ).
tff(16,plain,
^ [W0: $i] :
refl(
( ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
<=> ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )),
( ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) ) )),
( ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) ) ) )),
( ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) ) ) )
<=> ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) ) ) ) )),
rewrite(
( ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) ) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) ) ) )
<=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
tff(24,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) )
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) ),
inference(modus_ponens,[status(thm)],[27,17]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ( xm = sz10 )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ( xm = sz10 )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ( xm = sz00 )
| ( xm = sz10 )
| ~ aNaturalNumber0(xm)
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) )
<=> ( ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ( xm = sz10 )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ ( ( sz10 = xm )
| ~ sdtlseqdt0(sz10,xm) )
<=> ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( ( xm = sz00 )
| ( xm = sz10 )
| ~ aNaturalNumber0(xm)
| ~ ( ( sz10 = xm )
| ~ sdtlseqdt0(sz10,xm) ) )
<=> ( ( xm = sz00 )
| ( xm = sz10 )
| ~ aNaturalNumber0(xm)
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( ( xm = sz00 )
| ( xm = sz10 )
| ~ aNaturalNumber0(xm)
| ~ ( ( sz10 = xm )
| ~ sdtlseqdt0(sz10,xm) ) )
<=> ( ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ( xm = sz10 )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
| ( xm = sz00 )
| ( xm = sz10 )
| ~ aNaturalNumber0(xm)
| ~ ( ( sz10 = xm )
| ~ sdtlseqdt0(sz10,xm) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ( xm = sz10 )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
| ( xm = sz00 )
| ( xm = sz10 )
| ~ aNaturalNumber0(xm)
| ~ ( ( sz10 = xm )
| ~ sdtlseqdt0(sz10,xm) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ( xm = sz10 )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) ) ),
inference(transitivity,[status(thm)],[34,29]) ).
tff(36,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
| ( xm = sz00 )
| ( xm = sz10 )
| ~ aNaturalNumber0(xm)
| ~ ( ( sz10 = xm )
| ~ sdtlseqdt0(sz10,xm) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ( W0 = sz10 )
| ~ aNaturalNumber0(W0)
| ~ ( ( sz10 = W0 )
| ~ sdtlseqdt0(sz10,W0) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ( xm = sz10 )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ( sz10 = xm ) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
xm = sz10,
inference(unit_resolution,[status(thm)],[37,28,15,11,8]) ).
tff(39,plain,
( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10)
| ( xm != sz10 ) ),
inference(tautology,[status(thm)],]) ).
tff(40,plain,
( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
^ [W0: $i,W1: $i] :
refl(
( ( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
<=> ( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
<=> ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )),
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) ) )),
( ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( sdtlseqdt0(W0,W1)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ( sdtlseqdt0(W0,W1)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) )),
( ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) )
<=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
tff(49,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[52,42]) ).
tff(54,plain,
( aNaturalNumber0(sz10)
<=> aNaturalNumber0(sz10) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
tff(56,plain,
aNaturalNumber0(sz10),
inference(and_elim,[status(thm)],[55]) ).
tff(57,plain,
aNaturalNumber0(sz10),
inference(modus_ponens,[status(thm)],[56,54]) ).
tff(58,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) )
<=> ( sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) )
<=> ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) )
<=> ( sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) )
<=> ( sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) ) ),
inference(transitivity,[status(thm)],[63,58]) ).
tff(65,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ ( ( xm = sz10 )
| ~ sdtlseqdt0(xm,sz10) ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
$false,
inference(unit_resolution,[status(thm)],[66,57,53,15,6,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM464+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 10:56:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------