%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV023-2 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 Jun 21 05:08:58 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.45s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 46
% Syntax : Number of formulae : 116 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 445 ( 154 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 440 ( 143 ~; 239 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 134 ( 123 !; 0 ?; 134 :)
% Comments :
%------------------------------------------------------------------------------
tff(def_89_type,type,
def_89: ( $i * $i ) > $o ).
tff(f_ADD__type,type,
f_ADD_: ( $i * $i ) > $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(t_206_type,type,
t_206: $i ).
tff(fwork_DOTfifo_DOTrtl_DOTlevel__type,type,
fwork_DOTfifo_DOTrtl_DOTlevel_: $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) )
<=> ( n1 = f_ADD_(n0,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
n1 = f_ADD_(n0,n1),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_78) ).
tff(3,plain,
n1 = f_ADD_(n0,n1),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
f_ADD_(n0,n1) = n1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
f_ADD_(n0,f_ADD_(n0,n1)) = f_ADD_(n0,n1),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
f_ADD_(n0,n1) = f_ADD_(n0,f_ADD_(n0,n1)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( def_89(f_ADD_(n0,n1),f_ADD_(n0,n1))
<=> def_89(f_ADD_(n0,n1),f_ADD_(n0,f_ADD_(n0,n1))) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( def_89(f_ADD_(n0,n1),f_ADD_(n0,f_ADD_(n0,n1)))
<=> def_89(f_ADD_(n0,n1),f_ADD_(n0,n1)) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,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(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(quant_intro,[status(thm)],[9]) ).
tff(11,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(12,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(13,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,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(17,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
( ( fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n1 )
<=> ( fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_1) ).
tff(20,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n1,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
n1 = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
f_ADD_(n0,f_ADD_(n0,n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(transitivity,[status(thm)],[5,4,21,17]) ).
tff(23,plain,
f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n1),
inference(monotonicity,[status(thm)],[22,4]) ).
tff(24,plain,
f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n1) = f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206),
inference(symmetry,[status(thm)],[17]) ).
tff(26,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f_ADD_(n0,n1),
inference(transitivity,[status(thm)],[25,20,3]) ).
tff(27,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0)
<=> p_LES_EQU_(f_ADD_(n0,n1),n0) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( p_LES_EQU_(f_ADD_(n0,n1),n0)
<=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ~ p_LES_EQU_(f_ADD_(n0,n1),n0)
<=> ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
^ [X_81: $i] :
refl(( ~ p_LES_EQU_(f_ADD_(X_81,n1),n0)
<=> ~ p_LES_EQU_(f_ADD_(X_81,n1),n0) )),
inference(bind,[status(th)],[]) ).
tff(31,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(quant_intro,[status(thm)],[30]) ).
tff(32,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(33,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(34,plain,
! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,n1),n0),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,n1),n0),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,n1),n0),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [X_81: $i] : ~ p_LES_EQU_(f_ADD_(X_81,n1),n0)
| ~ p_LES_EQU_(f_ADD_(n0,n1),n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
~ p_LES_EQU_(f_ADD_(n0,n1),n0),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0),
inference(modus_ponens,[status(thm)],[38,29]) ).
tff(40,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_4) ).
tff(42,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_3) ).
tff(45,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).
tff(48,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,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(50,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),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),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(51,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(quant_intro,[status(thm)],[50]) ).
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) ) )
<=> ! [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(53,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(54,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)],[53]) ).
tff(55,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(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),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)],[55,54]) ).
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),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)],[56,52]) ).
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),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n1) ) ),
inference(skolemize,[status(sab)],[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))
| 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)],[58,51]) ).
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))
| 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)],[59,49]) ).
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))
| 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_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),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),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) ) )
| 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),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,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) ) )
| 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),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,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) ) )
| 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),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n1) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0)
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n1) ) ),
inference(unit_resolution,[status(thm)],[63,60,48,45,42]) ).
tff(65,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n1),
inference(unit_resolution,[status(thm)],[64,39]) ).
tff(66,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)),
inference(transitivity,[status(thm)],[65,24]) ).
tff(67,plain,
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) = n0 )
<=> ( f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)) = n0 ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != n0 )
<=> ( f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)) != n0 ) ),
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,n1))) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_5) ).
tff(71,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1))),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
^ [T_3: $i] :
refl(( ( 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) != n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,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(quant_intro,[status(thm)],[72]) ).
tff(74,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(75,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(76,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)],[75,74]) ).
tff(77,plain,
! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,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)],[77,73]) ).
tff(79,plain,
( ( ~ ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1)))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != n0 ) )
<=> ( ~ ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1)))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1)))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [T_3: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) != n0 ) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206,n1)))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != n0 ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206,n1)) != n0,
inference(unit_resolution,[status(thm)],[81,78,71]) ).
tff(83,plain,
f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)) != n0,
inference(modus_ponens,[status(thm)],[82,68]) ).
tff(84,plain,
^ [Y_84: $i,Z_85: $i] :
refl(( ( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) )
<=> ( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) )
<=> ! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) )
<=> ! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ! [Y_84: $i,Z_85: $i,X_83: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) )
<=> ! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(88,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_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(89,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] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ) ),
inference(transitivity,[status(thm)],[88,87]) ).
tff(90,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(91,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)],[90]) ).
tff(92,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] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ) ),
inference(transitivity,[status(thm)],[91,89]) ).
tff(93,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(94,plain,
! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ),
inference(modus_ponens,[status(thm)],[94,86]) ).
tff(96,plain,
! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) ),
inference(modus_ponens,[status(thm)],[96,85]) ).
tff(98,plain,
( ( ~ ! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) )
| ( f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)) = n0 )
| def_89(f_ADD_(n0,n1),f_ADD_(n0,f_ADD_(n0,n1))) )
<=> ( ~ ! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) )
| ( f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)) = n0 )
| def_89(f_ADD_(n0,n1),f_ADD_(n0,f_ADD_(n0,n1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) )
| ( f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)) = n0 )
| def_89(f_ADD_(n0,n1),f_ADD_(n0,f_ADD_(n0,n1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [Y_84: $i,Z_85: $i] :
( ( f_SUB_(f_ADD_(Z_85,Y_84),Y_84) = Z_85 )
| def_89(Y_84,f_ADD_(Z_85,Y_84)) )
| ( f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)) = n0 )
| def_89(f_ADD_(n0,n1),f_ADD_(n0,f_ADD_(n0,n1))) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
( ( f_SUB_(f_ADD_(n0,f_ADD_(n0,n1)),f_ADD_(n0,n1)) = n0 )
| def_89(f_ADD_(n0,n1),f_ADD_(n0,f_ADD_(n0,n1))) ),
inference(unit_resolution,[status(thm)],[100,97]) ).
tff(102,plain,
def_89(f_ADD_(n0,n1),f_ADD_(n0,f_ADD_(n0,n1))),
inference(unit_resolution,[status(thm)],[101,83]) ).
tff(103,plain,
def_89(f_ADD_(n0,n1),f_ADD_(n0,n1)),
inference(modus_ponens,[status(thm)],[102,8]) ).
tff(104,plain,
^ [Y_84: $i] :
refl(( ~ def_89(Y_84,Y_84)
<=> ~ def_89(Y_84,Y_84) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [Y_84: $i] : ~ def_89(Y_84,Y_84)
<=> ! [Y_84: $i] : ~ def_89(Y_84,Y_84) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [Y_84: $i] : ~ def_89(Y_84,Y_84)
<=> ! [Y_84: $i] : ~ def_89(Y_84,Y_84) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ! [Y_84: $i,X_83: $i] : ~ def_89(Y_84,Y_84)
<=> ! [Y_84: $i] : ~ def_89(Y_84,Y_84) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(108,plain,
( ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
<=> ! [Y_84: $i,X_83: $i] : ~ def_89(Y_84,Y_84) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(109,plain,
( ! [Y_84: $i,X_83: $i] :
( ( X_83 != Y_84 )
| ~ def_89(Y_84,X_83) )
<=> ! [Y_84: $i] : ~ def_89(Y_84,Y_84) ),
inference(transitivity,[status(thm)],[108,107]) ).
tff(110,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(111,plain,
! [Y_84: $i] : ~ def_89(Y_84,Y_84),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [Y_84: $i] : ~ def_89(Y_84,Y_84),
inference(modus_ponens,[status(thm)],[111,106]) ).
tff(113,plain,
! [Y_84: $i] : ~ def_89(Y_84,Y_84),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [Y_84: $i] : ~ def_89(Y_84,Y_84),
inference(modus_ponens,[status(thm)],[113,105]) ).
tff(115,plain,
( ~ ! [Y_84: $i] : ~ def_89(Y_84,Y_84)
| ~ def_89(f_ADD_(n0,n1),f_ADD_(n0,n1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
$false,
inference(unit_resolution,[status(thm)],[115,114,103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : HWV023-2 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 17:20:10 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.45 % SZS status Unsatisfiable
% 0.23/0.45 % SZS output start Proof
% See solution above
% 0.23/0.47 % E exiting
%------------------------------------------------------------------------------