TSTP Solution File: NUM489+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM489+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 13:10:01 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 61 ( 16 unt; 8 typ; 0 def)
% Number of atoms : 460 ( 166 equ)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 735 ( 355 ~; 214 |; 44 &)
% ( 111 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 117 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xn_type,type,
xn: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xm_type,type,
xm: $i ).
tff(xr_type,type,
xr: $i ).
tff(1,plain,
( sdtlseqdt0(xp,xn)
<=> sdtlseqdt0(xp,xn) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
tff(3,plain,
sdtlseqdt0(xp,xn),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(6,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[6,4]) ).
tff(8,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[5]) ).
tff(10,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i] :
rewrite(
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
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) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
tff(23,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) )
<=> ( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) ),
inference(unit_resolution,[status(thm)],[33,27,11,7,3]) ).
tff(35,plain,
( ( ~ ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) )
<=> ( ~ ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( $true
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) )
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) )
<=> ( $true
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) )
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ( ~ ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ( ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) )
<=> ( ~ ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ( ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) )
<=> ( ~ ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) ),
inference(transitivity,[status(thm)],[40,35]) ).
tff(42,plain,
( ~ ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ( ( sdtmndt0(xn,xp) = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [W2: $i] :
( ( W2 = sdtmndt0(xn,xp) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xp,W2) != xn ) ) )
| ~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
~ ( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn ) ),
inference(unit_resolution,[status(thm)],[43,34]) ).
tff(45,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) != xn )
| ( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn ) ),
inference(tautology,[status(thm)],]) ).
tff(46,plain,
sdtpldt0(xp,sdtmndt0(xn,xp)) = xn,
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
xn = sdtpldt0(xp,sdtmndt0(xn,xp)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ( xn != sdtpldt0(xp,xr) )
<=> ( xn != sdtpldt0(xp,sdtmndt0(xn,xp)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( xn != sdtpldt0(xp,xr) )
<=> ( xn != sdtpldt0(xp,xr) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
xn != sdtpldt0(xp,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(51,plain,
xn != sdtpldt0(xp,xr),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
xn != sdtpldt0(xp,sdtmndt0(xn,xp)),
inference(modus_ponens,[status(thm)],[51,48]) ).
tff(53,plain,
$false,
inference(unit_resolution,[status(thm)],[52,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM489+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.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 11:11:52 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.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------