TSTP Solution File: HWV009-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV009-2 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 Sep 17 02:10:32 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 48 ( 17 unt; 10 typ; 0 def)
% Number of atoms : 91 ( 54 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 89 ( 40 ~; 33 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 6 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 27 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(f__length__type,type,
f__length_: $i > $i ).
tff(f__empty__type,type,
f__empty_: $i ).
tff(fwork_DOTfifo_DOTrtl_DOTlevel__type,type,
fwork_DOTfifo_DOTrtl_DOTlevel_: $i > $i ).
tff(f_ADD__type,type,
f_ADD_: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(t_206_type,type,
t_206: $i ).
tff(fwork_DOTfifo_DOTrtl_DOTint__level__type,type,
fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i ).
tff(p__pred__type,type,
p__pred_: $i > $o ).
tff(fwork_DOTfifo_DOTrtl_DOTreset__type,type,
fwork_DOTfifo_DOTrtl_DOTreset_: $i > $i ).
tff(n0_type,type,
n0: $i ).
tff(1,plain,
^ [T_0: $i] :
refl(
( ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) )
<=> ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) )
<=> ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) )
<=> ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_5) ).
tff(5,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) )
| ( fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) = f__length_(f__empty_) )
<=> ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) )
<=> ( fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_1) ).
tff(14,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [T_5: $i] :
refl(
( ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
<=> ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [T_5: $i] :
rewrite(
( ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 ) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 ) )
<=> ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 ) )
<=> ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
^ [T_5: $i] :
rewrite(
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5)) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [T_5: $i] :
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5)) )
<=> ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [T_5: $i] :
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_12) ).
tff(23,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ),
inference(modus_ponens,[status(thm)],[24,18]) ).
tff(26,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
( ( ~ ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) )
<=> ( ~ ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_),
inference(unit_resolution,[status(thm)],[30,27,14]) ).
tff(32,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) = f__length_(f__empty_),
inference(modus_ponens,[status(thm)],[31,11]) ).
tff(33,plain,
( ( fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) != n0 )
<=> ( fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) != f__length_(f__empty_) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) != n0 )
<=> ( fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) != n0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) != n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).
tff(36,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) != n0,
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206,n1)) != f__length_(f__empty_),
inference(modus_ponens,[status(thm)],[36,33]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HWV009-2 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 22:22:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------