%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV026-3 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:08:59 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 198 ( 59 ~; 123 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(p__pred__type,type,
p__pred_: $i > $o ).
tff(fwork_DOTfifo_DOTrtl_DOTwr__error__type,type,
fwork_DOTfifo_DOTrtl_DOTwr__error_: $i > $i ).
tff(t_206_type,type,
t_206: $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(1,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_4) ).
tff(3,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1)))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_3) ).
tff(6,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).
tff(9,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
<=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_1) ).
tff(12,plain,
~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [T_13: $i] :
refl(( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
<=> ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
<=> ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [T_13: $i] :
trans(monotonicity(rewrite(( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ) )),
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) )
<=> ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) ) )),
rewrite(( ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ) )),
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| 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__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| 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__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| 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_56) ).
tff(19,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1))) )
<=> ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206)) )
<=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206)) )
<=> ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1))) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206)) )
<=> ( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1))) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [T_13: $i] :
( p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_13,n1)))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(T_13)) )
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))
| p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(t_206))
| ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(t_206,n1))) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,22,12,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV026-3 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 17:20:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42 % SZS output start Proof
% See solution above
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------