TSTP Solution File: HWV023-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV023-2 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 02:10:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 64
% Syntax : Number of formulae : 139 ( 48 unt; 16 typ; 0 def)
% Number of atoms : 513 ( 191 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 573 ( 218 ~; 289 |; 0 &)
% ( 66 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 35 ( 35 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 12 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 147 ( 131 !; 0 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
tff(def_89_type,type,
def_89: ( $i * $i ) > $o ).
tff(f_ADD__type,type,
f_ADD_: ( $i * $i ) > $i ).
tff(fwork_DOTfifo_DOTrtl_DOTlevel__type,type,
fwork_DOTfifo_DOTrtl_DOTlevel_: $i > $i ).
tff(t_206_type,type,
t_206: $i ).
tff(f__length__type,type,
f__length_: $i > $i ).
tff(f__empty__type,type,
f__empty_: $i ).
tff(n1_type,type,
n1: $i ).
tff(n0_type,type,
n0: $i ).
tff(f_SUB__type,type,
f_SUB_: ( $i * $i ) > $i ).
tff(fwork_DOTfifo_DOTrtl_DOTint__level__type,type,
fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i ).
tff(p_LES_EQU__type,type,
p_LES_EQU_: ( $i * $i ) > $o ).
tff(p__pred__type,type,
p__pred_: $i > $o ).
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(fwork_DOTfifo_DOTrtl_DOTempty__type,type,
fwork_DOTfifo_DOTrtl_DOTempty_: $i > $i ).
tff(1,plain,
( ( n1 = f_ADD_(n0,n1) )
<=> ( fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( n1 = f_ADD_(n0,n1) )
<=> ( n1 = f_ADD_(n0,n1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
n1 = f_ADD_(n0,n1),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_78) ).
tff(4,plain,
n1 = f_ADD_(n0,n1),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
f_ADD_(f__length_(f__empty_),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,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(12,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ~ ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) )
| ( fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(unit_resolution,[status(thm)],[15,14]) ).
tff(17,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),
inference(transitivity,[status(thm)],[17,5]) ).
tff(19,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
<=> p_LES_EQU_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( p_LES_EQU_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_))
<=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_)) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ~ p_LES_EQU_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_))
<=> ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_)) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
^ [X_81: $i] :
refl(
( ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_))
<=> ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_))
<=> ! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
^ [X_81: $i] :
rewrite(
( ~ p_LES_EQU_(f_ADD_(X_81,n1),n0)
<=> ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,n1),n0)
<=> ! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,n1),n0)
<=> ! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,n1),n0) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,n1),n0),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_60) ).
tff(28,plain,
! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,n1),n0),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ~ ! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_))
| ~ p_LES_EQU_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
~ p_LES_EQU_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f__length_(f__empty_)),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_)),
inference(modus_ponens,[status(thm)],[33,21]) ).
tff(35,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_4) ).
tff(37,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_3) ).
tff(40,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).
tff(43,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ) )),
inference(bind,[status(th)],]) ).
tff(45,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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
^ [T_13: $i] :
rewrite(
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ) )),
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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) )
<=> ! [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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ) ),
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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) )
<=> ! [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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ) ),
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)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0) )
<=> ( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) )
<=> ( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) ) )),
rewrite(
( ( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) ) )),
rewrite(
( ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ~ 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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ~ 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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| 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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| 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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ) )),
( ( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ~ 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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [T_13: $i] :
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ~ 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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [T_13: $i] :
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) )
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ~ 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/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_43) ).
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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ),
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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ),
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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(modus_ponens,[status(thm)],[53,47]) ).
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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(skolemize,[status(sab)],[54]) ).
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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(modus_ponens,[status(thm)],[55,45]) ).
tff(57,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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTlevel_(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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTlevel_(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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(quant_inst,[status(thm)],]) ).
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))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),f__length_(f__empty_))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(unit_resolution,[status(thm)],[59,56,43,40,37]) ).
tff(61,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),
inference(unit_resolution,[status(thm)],[60,34]) ).
tff(62,plain,
f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(transitivity,[status(thm)],[6,16]) ).
tff(64,plain,
f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),
inference(monotonicity,[status(thm)],[63,6]) ).
tff(65,plain,
f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ( f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f__length_(f__empty_) )
<=> ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f__length_(f__empty_) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f__length_(f__empty_) )
<=> ( f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f__length_(f__empty_) ) ),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f__length_(f__empty_) )
<=> ( f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f__length_(f__empty_) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1)))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)))) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1)))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1))) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_5) ).
tff(72,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1))),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)))),
inference(modus_ponens,[status(thm)],[72,69]) ).
tff(74,plain,
^ [T_3: $i] :
refl(
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) )
<=> ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
^ [T_3: $i] :
rewrite(
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) )
<=> ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) )
<=> ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_8) ).
tff(80,plain,
! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) ),
inference(modus_ponens,[status(thm)],[80,77]) ).
tff(82,plain,
! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ( ~ ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f__length_(f__empty_) ) )
<=> ( ~ ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f__length_(f__empty_) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ~ ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f__length_(f__empty_) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != f__length_(f__empty_) ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f__length_(f__empty_) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f__length_(f__empty_),
inference(unit_resolution,[status(thm)],[86,83,73]) ).
tff(88,plain,
f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f__length_(f__empty_),
inference(modus_ponens,[status(thm)],[87,68]) ).
tff(89,plain,
^ [Y_84: $i,Z_85: $i,X_83: $i] :
refl(
( ( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) )
<=> ( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) )
<=> ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) )
<=> ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [Y_84: $i,Z_85: $i,X_83: $i] :
trans(
monotonicity(
rewrite(
( ( def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) )
<=> ( def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ) )),
( ( def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 )
| ( f_SUB_(X_83,Y_84) = Z_85 ) )
<=> ( def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 )
| ( f_SUB_(X_83,Y_84) = Z_85 ) ) )),
rewrite(
( ( def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 )
| ( f_SUB_(X_83,Y_84) = Z_85 ) )
<=> ( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ) )),
( ( def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 )
| ( f_SUB_(X_83,Y_84) = Z_85 ) )
<=> ( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [Y_84: $i,Z_85: $i,X_83: $i] :
( def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 )
| ( f_SUB_(X_83,Y_84) = Z_85 ) )
<=> ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [Y_84: $i,Z_85: $i,X_83: $i] :
( def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 )
| ( f_SUB_(X_83,Y_84) = Z_85 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_63) ).
tff(95,plain,
! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) )
| ( f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f__length_(f__empty_) )
| def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)))
| ( f_ADD_(f__length_(f__empty_),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) )
<=> ( ~ ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) )
| ( f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f__length_(f__empty_) )
| def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)))
| ( f_ADD_(f__length_(f__empty_),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) )
| ( f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f__length_(f__empty_) )
| def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)))
| ( f_ADD_(f__length_(f__empty_),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(X_83,Y_84) = Z_85 )
| def_89(Y_84,X_83)
| ( f_ADD_(Z_85,Y_84) != X_83 ) )
| ( f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f__length_(f__empty_) )
| def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)))
| ( f_ADD_(f__length_(f__empty_),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ( f_SUB_(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) = f__length_(f__empty_) )
| def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)))
| ( f_ADD_(f__length_(f__empty_),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) ) ),
inference(unit_resolution,[status(thm)],[101,98]) ).
tff(103,plain,
def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))),
inference(unit_resolution,[status(thm)],[102,88,7]) ).
tff(104,plain,
^ [Y_84: $i,X_83: $i] :
refl(
( ( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
<=> ( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
<=> ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
<=> ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_64) ).
tff(108,plain,
! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
( ( ~ ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) )
<=> ( ~ ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ( $false
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) )
<=> ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ( f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) = f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ( f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ( f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) )
<=> $false ),
inference(transitivity,[status(thm)],[115,113]) ).
tff(117,plain,
( ( ( f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) )
<=> ( $false
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) ) ),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ( ( f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) )
<=> ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) ),
inference(transitivity,[status(thm)],[117,112]) ).
tff(119,plain,
( ( ~ ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
| ( f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) )
<=> ( ~ ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) ) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ( ~ ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
| ( f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) )
<=> ( ~ ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) ) ),
inference(transitivity,[status(thm)],[119,111]) ).
tff(121,plain,
( ~ ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
| ( f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) != f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
| ~ def_89(f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),f_ADD_(f__length_(f__empty_),fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
$false,
inference(unit_resolution,[status(thm)],[122,110,103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HWV023-2 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 22:08:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------