%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV020-3 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:08:57 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 55 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 320 ( 19 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 390 ( 147 ~; 211 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 40 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_LES_EQU__type,type,
p_LES_EQU_: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $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_DOTempty__type,type,
fwork_DOTfifo_DOTrtl_DOTempty_: $i > $i ).
tff(fwork_DOTfifo_DOTrtl_DOTrd__error__type,type,
fwork_DOTfifo_DOTrtl_DOTrd__error_: $i > $i ).
tff(f_ADD__type,type,
f_ADD_: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(fwork_DOTfifo_DOTrtl_DOTreset__type,type,
fwork_DOTfifo_DOTrtl_DOTreset_: $i > $i ).
tff(fwork_DOTfifo_DOTrtl_DOTwr__type,type,
fwork_DOTfifo_DOTrtl_DOTwr_: $i > $i ).
tff(fwork_DOTfifo_DOTrtl_DOTrd__type,type,
fwork_DOTfifo_DOTrtl_DOTrd_: $i > $i ).
tff(1,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_4) ).
tff(3,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_4: $i] :
refl(( ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) )
<=> ! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) )
<=> ! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax',axiom_9) ).
tff(8,plain,
! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0 ) )
<=> ( ~ ! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) )
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0 ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0,
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0)
<=> p_LES_EQU_(n0,n0) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0)
<=> ~ p_LES_EQU_(n0,n0) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1))) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_5) ).
tff(19,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1))),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_3) ).
tff(22,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).
tff(25,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_1) ).
tff(28,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
^ [T_13: $i] :
refl(( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
<=> ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
<=> ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [T_13: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0) ) )),
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(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__error_(f_ADD_(T_13,n1)))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) ) )),
rewrite(( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(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__error_(f_ADD_(T_13,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0) ) )),
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(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__error_(f_ADD_(T_13,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0) ) )),
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(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__error_(f_ADD_(T_13,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) ) )),
rewrite(( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13),n0)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ) )),
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(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__error_(f_ADD_(T_13,n1)))
| 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) ) )),
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(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_DOTrd__error_(f_ADD_(T_13,n1)))
| 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)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) ) )),
rewrite(( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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)
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ) )),
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(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_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(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_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(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/sandbox/benchmark/Axioms/HWV004-0.ax',axiom_49) ).
tff(35,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) )
<=> ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| 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) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| 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) )
<=> ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| 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) )
<=> ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| 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) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13,n1)))
| 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) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206,n1)))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))
| ~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),n0),
inference(unit_resolution,[status(thm)],[44,38,28,25,22,19]) ).
tff(46,plain,
~ p_LES_EQU_(n0,n0),
inference(modus_ponens,[status(thm)],[45,16]) ).
tff(47,plain,
^ [X_106: $i] :
refl(( p_LES_EQU_(X_106,X_106)
<=> p_LES_EQU_(X_106,X_106) )),
inference(bind,[status(th)],[]) ).
tff(48,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)],[47]) ).
tff(49,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(50,axiom,
! [X_106: $i] : p_LES_EQU_(X_106,X_106),
file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax',axiom_75) ).
tff(51,plain,
! [X_106: $i] : p_LES_EQU_(X_106,X_106),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X_106: $i] : p_LES_EQU_(X_106,X_106),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X_106: $i] : p_LES_EQU_(X_106,X_106),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [X_106: $i] : p_LES_EQU_(X_106,X_106)
| p_LES_EQU_(n0,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,53,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV020-3 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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 : Thu Jun 19 17:20:12 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% See solution above
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------