TSTP Solution File: HWV018-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV018-2 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 02:10:38 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 42
% Syntax : Number of formulae : 85 ( 27 unt; 11 typ; 0 def)
% Number of atoms : 371 ( 98 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 442 ( 168 ~; 234 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 8 >; 2 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 52 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_LES_EQU__type,type,
p_LES_EQU_: ( $i * $i ) > $o ).
tff(fwork_DOTfifo_DOTrtl_DOTfifo__length__type,type,
fwork_DOTfifo_DOTrtl_DOTfifo__length_: $i ).
tff(fwork_DOTfifo_DOTrtl_DOTint__level__type,type,
fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i ).
tff(t_206_type,type,
t_206: $i ).
tff(p__pred__type,type,
p__pred_: $i > $o ).
tff(fwork_DOTfifo_DOTrtl_DOTfull__type,type,
fwork_DOTfifo_DOTrtl_DOTfull_: $i > $i ).
tff(f_ADD__type,type,
f_ADD_: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(fwork_DOTfifo_DOTrtl_DOTwr__type,type,
fwork_DOTfifo_DOTrtl_DOTwr_: $i > $i ).
tff(fwork_DOTfifo_DOTrtl_DOTreset__type,type,
fwork_DOTfifo_DOTrtl_DOTreset_: $i > $i ).
tff(fwork_DOTfifo_DOTrtl_DOTrd__type,type,
fwork_DOTfifo_DOTrtl_DOTrd_: $i > $i ).
tff(1,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).
tff(3,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_2: $i] :
refl(
( ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
<=> ! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
<=> ! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax',axiom_7) ).
tff(8,plain,
! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
<=> ( ~ ! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [T_2: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_2) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_,
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
fwork_DOTfifo_DOTrtl_DOTfifo__length_ = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTfifo__length_)
<=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
<=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTfifo__length_) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
<=> ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTfifo__length_) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) )
<=> ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(20,plain,
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_ )
<=> ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ )
<=> ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(f_ADD_(t_206,n1)))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(f_ADD_(t_206,n1))) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(f_ADD_(t_206,n1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_5) ).
tff(24,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(f_ADD_(t_206,n1))),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
^ [T_1: $i] :
refl(
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
<=> ! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
<=> ! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax',axiom_6) ).
tff(29,plain,
! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ( ~ ! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(f_ADD_(t_206,n1)))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
<=> ( ~ ! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(f_ADD_(t_206,n1)))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ ! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(f_ADD_(t_206,n1)))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [T_1: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(f_ADD_(t_206,n1)))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != fwork_DOTfifo_DOTrtl_DOTfifo__length_,
inference(unit_resolution,[status(thm)],[34,31,24]) ).
tff(36,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(modus_ponens,[status(thm)],[35,21]) ).
tff(37,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_4) ).
tff(39,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_3) ).
tff(42,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_1) ).
tff(45,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
^ [T_13: $i] :
refl(
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
<=> ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
<=> ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
^ [T_13: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
<=> ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) )
<=> ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) ) )),
rewrite(
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) ) )),
rewrite(
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) ) )),
rewrite(
( ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [T_13: $i] :
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) )
<=> ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [T_13: $i] :
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax',axiom_23) ).
tff(52,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) )
<=> ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) )
<=> ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) )
<=> ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13) )
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ),
inference(unit_resolution,[status(thm)],[61,55,45,42,39]) ).
tff(63,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
inference(unit_resolution,[status(thm)],[62,36]) ).
tff(64,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTfifo__length_),
inference(modus_ponens,[status(thm)],[63,18]) ).
tff(65,plain,
^ [X_106: $i] :
refl(
( p_LES_EQU_(X_106,X_106)
<=> p_LES_EQU_(X_106,X_106) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [X_106: $i] : p_LES_EQU_(X_106,X_106)
<=> ! [X_106: $i] : p_LES_EQU_(X_106,X_106) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [X_106: $i] : p_LES_EQU_(X_106,X_106)
<=> ! [X_106: $i] : p_LES_EQU_(X_106,X_106) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
! [X_106: $i] : p_LES_EQU_(X_106,X_106),
file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax',axiom_75) ).
tff(69,plain,
! [X_106: $i] : p_LES_EQU_(X_106,X_106),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [X_106: $i] : p_LES_EQU_(X_106,X_106),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [X_106: $i] : p_LES_EQU_(X_106,X_106),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [X_106: $i] : p_LES_EQU_(X_106,X_106)
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTfifo__length_) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_,fwork_DOTfifo_DOTrtl_DOTfifo__length_),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV018-2 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n029.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 22:12:43 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.
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------