%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV010-2 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:08:54 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 30 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 66 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 23 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 23 ( 21 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
tff(n0_type,type,
n0: $i ).
tff(fwork_DOTfifo_DOTrtl_DOTlevel__type,type,
fwork_DOTfifo_DOTrtl_DOTlevel_: $i > $i ).
tff(t_206_type,type,
t_206: $i ).
tff(fwork_DOTfifo_DOTrtl_DOTint__level__type,type,
fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i ).
tff(p__pred__type,type,
p__pred_: $i > $o ).
tff(fwork_DOTfifo_DOTrtl_DOTempty__type,type,
fwork_DOTfifo_DOTrtl_DOTempty_: $i > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n0 )
<=> ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0 ) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0 )
<=> ( fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n0 ) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206))
<=> p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).
tff(14,plain,
p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,axiom,
! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax',axiom_9) ).
tff(19,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)],[18,17]) ).
tff(20,plain,
! [T_4: $i] :
( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))
| ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0 ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,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)],[20,16]) ).
tff(22,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(23,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(24,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)],[23,22]) ).
tff(25,plain,
fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0,
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = n0,
inference(modus_ponens,[status(thm)],[25,11]) ).
tff(27,plain,
( ( fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) != n0 )
<=> ( fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) != n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) != n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_1) ).
tff(29,plain,
fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) != n0,
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
$false,
inference(unit_resolution,[status(thm)],[29,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : HWV010-2 : TPTP v9.0.0. Released v2.5.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.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 17:19:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.44 % SZS status Unsatisfiable
% 0.22/0.44 % SZS output start Proof
% See solution above
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------