TSTP Solution File: NUM521+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM521+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 13:10:14 EDT 2022
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 39
% Syntax : Number of formulae : 82 ( 18 unt; 5 typ; 0 def)
% Number of atoms : 572 ( 134 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 905 ( 427 ~; 371 |; 63 &)
% ( 41 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 82 ( 76 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xp_type,type,
xp: $i ).
tff(xm_type,type,
xm: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(xn_type,type,
xn: $i ).
tff(1,plain,
( ~ sdtlseqdt0(xp,xm)
<=> ~ sdtlseqdt0(xp,xm) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
tff(3,plain,
~ sdtlseqdt0(xp,xm),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ~ sdtlseqdt0(xp,xm)
| ( xp = xm )
| sdtlseqdt0(xp,xm) ),
inference(tautology,[status(thm)],]) ).
tff(5,plain,
( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ),
inference(unit_resolution,[status(thm)],[4,3]) ).
tff(6,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(8,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[7]) ).
tff(12,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(17,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)],[16]) ).
tff(18,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(19,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(20,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)],[19]) ).
tff(21,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
tff(22,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[25,15]) ).
tff(27,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) )
<=> ( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ( ( xp = xm )
| ~ sdtlseqdt0(xp,xm) )
<=> ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ ( ( xp = xm )
| ~ sdtlseqdt0(xp,xm) ) )
<=> ( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ ( ( xp = xm )
| ~ sdtlseqdt0(xp,xm) ) )
<=> ( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ ( ( xp = xm )
| ~ sdtlseqdt0(xp,xm) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ ( ( xp = xm )
| ~ sdtlseqdt0(xp,xm) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) ) ),
inference(transitivity,[status(thm)],[32,27]) ).
tff(34,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ ( ( xp = xm )
| ~ sdtlseqdt0(xp,xm) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xm)
| ( xp = xm ) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
sdtlseqdt0(xm,xp),
inference(unit_resolution,[status(thm)],[35,26,13,9,5]) ).
tff(37,plain,
( ~ sdtlseqdt0(xp,xn)
<=> ~ sdtlseqdt0(xp,xn) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
tff(39,plain,
~ sdtlseqdt0(xp,xn),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ sdtlseqdt0(xp,xn)
| ( xp = xn )
| sdtlseqdt0(xp,xn) ),
inference(tautology,[status(thm)],]) ).
tff(41,plain,
( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[11]) ).
tff(44,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) )
<=> ( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ( ( xp = xn )
| ~ sdtlseqdt0(xp,xn) )
<=> ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ ( ( xp = xn )
| ~ sdtlseqdt0(xp,xn) ) )
<=> ( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ ( ( xp = xn )
| ~ sdtlseqdt0(xp,xn) ) )
<=> ( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ ( ( xp = xn )
| ~ sdtlseqdt0(xp,xn) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ ( ( xp = xn )
| ~ sdtlseqdt0(xp,xn) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) ) ),
inference(transitivity,[status(thm)],[50,45]) ).
tff(52,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ ( ( xp = xn )
| ~ sdtlseqdt0(xp,xn) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ~ sdtlseqdt0(xp,xn)
| ( xp = xn ) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
sdtlseqdt0(xn,xp),
inference(unit_resolution,[status(thm)],[53,26,44,9,41]) ).
tff(55,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ( xn = xp )
| ~ sdtlseqdt0(xn,xp) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ( xn = xp )
| ~ sdtlseqdt0(xn,xp) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ( xn = xp )
| ~ sdtlseqdt0(xn,xp) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ ( ( xn = xp )
| ~ sdtlseqdt0(xn,xp) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
~ ( ( xn = xp )
| ~ sdtlseqdt0(xn,xp) ),
inference(unit_resolution,[status(thm)],[57,26,44,9,39]) ).
tff(59,plain,
( ( xn = xp )
| ~ sdtlseqdt0(xn,xp)
| ( xn != xp ) ),
inference(tautology,[status(thm)],]) ).
tff(60,plain,
xn != xp,
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ( xm = xp )
| ~ sdtlseqdt0(xm,xp) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ( xm = xp )
| ~ sdtlseqdt0(xm,xp) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ( xm = xp )
| ~ sdtlseqdt0(xm,xp) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 = W0 )
| ~ sdtlseqdt0(W1,W0) ) )
| sdtlseqdt0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ ( ( xm = xp )
| ~ sdtlseqdt0(xm,xp) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
~ ( ( xm = xp )
| ~ sdtlseqdt0(xm,xp) ),
inference(unit_resolution,[status(thm)],[63,26,13,9,3]) ).
tff(65,plain,
( ( xm = xp )
| ~ sdtlseqdt0(xm,xp)
| ( xm != xp ) ),
inference(tautology,[status(thm)],]) ).
tff(66,plain,
xm != xp,
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ ~ ( ( xn = xp )
| ( xm = xp )
| ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(xm,xp) )
<=> ( ( xn = xp )
| ( xm = xp )
| ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(xm,xp) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) )
<=> ~ ( ( xn = xp )
| ( xm = xp )
| ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(xm,xp) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) )
<=> ~ ~ ( ( xn = xp )
| ( xm = xp )
| ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(xm,xp) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) )
<=> ( ( xn = xp )
| ( xm = xp )
| ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(xm,xp) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) )
<=> ~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) )
<=> ~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
tff(74,plain,
~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) ),
inference(modus_ponens,[status(thm)],[74,71]) ).
tff(76,plain,
( ( xn = xp )
| ( xm = xp )
| ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(xm,xp) ),
inference(modus_ponens,[status(thm)],[75,70]) ).
tff(77,plain,
$false,
inference(unit_resolution,[status(thm)],[76,66,60,54,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM521+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Sep 2 11:25:18 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------