TSTP Solution File: NUM458+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM458+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 13:09:49 EDT 2022
% Result : Theorem 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 52 ( 12 unt; 5 typ; 0 def)
% Number of atoms : 186 ( 100 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 273 ( 148 ~; 73 |; 30 &)
% ( 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 : 5 ( 3 >; 2 *; 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 : 46 ( 29 !; 11 ?; 46 :)
% 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/sandbox2/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] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(modus_ponens,[status(thm)],[11,5]) ).
tff(13,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(modus_ponens,[status(thm)],[13,5]) ).
tff(15,plain,
^ [W0: $i] :
refl(
$oeq(
~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ))),
inference(bind,[status(th)],]) ).
tff(16,plain,
! [W0: $i] :
~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xm ) ),
inference(nnf-neg,[status(sab)],[14,15]) ).
tff(17,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ),
inference(modus_ponens,[status(thm)],[16,4]) ).
tff(18,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) ),
inference(modus_ponens,[status(thm)],[17,2]) ).
tff(19,plain,
( aNaturalNumber0(sz00)
<=> aNaturalNumber0(sz00) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
tff(21,plain,
aNaturalNumber0(sz00),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,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(23,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xm,sz00) != xm ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != xm ) )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xm,sz00) != xm ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
sdtpldt0(xm,sz00) != xm,
inference(unit_resolution,[status(thm)],[24,21,18]) ).
tff(26,plain,
( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sz00) = xm ) ),
inference(tautology,[status(thm)],]) ).
tff(27,plain,
( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
aNaturalNumber0(xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__718) ).
tff(30,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,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(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(quant_intro,[status(thm)],[31]) ).
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,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(36,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(37,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)],[36]) ).
tff(38,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
tff(39,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[42,32]) ).
tff(44,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(45,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(46,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)],[45,44]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[46,43,30,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.10 % Problem : NUM458+2 : TPTP v8.1.0. Released v4.0.0.
% 0.01/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n020.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Sep 2 10:45:44 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.37 % SZS status Theorem
% 0.17/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------