TSTP Solution File: HWV030-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV030-2 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 02:10:46 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 44 ( 13 unt; 11 typ; 0 def)
% Number of atoms : 83 ( 29 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 89 ( 42 ~; 32 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 6 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 18 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_LES_EQU__type,type,
p_LES_EQU_: ( $i * $i ) > $o ).
tff(fwork_DOTfifo_DOTrtl_DOTwr__level__type,type,
fwork_DOTfifo_DOTrtl_DOTwr__level_: $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_DOTfifo__length__type,type,
fwork_DOTfifo_DOTrtl_DOTfifo__length_: $i ).
tff(f__length__type,type,
f__length_: $i > $i ).
tff(f__empty__type,type,
f__empty_: $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,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_1) ).
tff(3,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_5: $i] :
refl(
( ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
<=> ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [T_5: $i] :
rewrite(
( ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = n0 ) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = n0 ) )
<=> ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = n0 ) )
<=> ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = n0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
^ [T_5: $i] :
rewrite(
( ( ( fwork_DOTfifo_DOTrtl_DOTwr__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_DOTwr__level_(f_ADD_(T_5,n1)) = n0 ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [T_5: $i] :
( ( fwork_DOTfifo_DOTrtl_DOTwr__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_DOTwr__level_(f_ADD_(T_5,n1)) = n0 ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [T_5: $i] :
( ( fwork_DOTfifo_DOTrtl_DOTwr__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_11) ).
tff(12,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ),
inference(modus_ponens,[status(thm)],[13,7]) ).
tff(15,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) ),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
( ( ~ ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) )
<=> ( ~ ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [T_5: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5,n1)) = f__length_(f__empty_) ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)) = f__length_(f__empty_),
inference(unit_resolution,[status(thm)],[19,16,3]) ).
tff(21,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)))
<=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,f__length_(f__empty_)) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,f__length_(f__empty_))
<=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1))) ),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,f__length_(f__empty_))
<=> ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1))) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n0)
<=> ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,f__length_(f__empty_)) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n0)
<=> ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_3) ).
tff(27,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,n0),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,f__length_(f__empty_)),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1))),
inference(modus_ponens,[status(thm)],[28,23]) ).
tff(30,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1)))
<=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1))) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).
tff(32,plain,
p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206,n1))),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
$false,
inference(unit_resolution,[status(thm)],[32,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : HWV030-2 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 22:04:05 EDT 2022
% 0.13/0.33 % 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.
% 0.18/0.43 % SZS status Unsatisfiable
% 0.18/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------