%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP234_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:12:12 AM UTC 2025
% Result : Theorem 2.79s 3.06s
% Output : Proof 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(vEBT_vebt_insert_type,type,
vEBT_vebt_insert: ( vEBT_VEBT * nat ) > vEBT_VEBT ).
tff(aa_nat_nat_type,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(na_type,type,
na: nat ).
tff(aa_nat_fun_nat_nat_type,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(mi_type,type,
mi: nat ).
tff(vEBT_VEBT_low_type,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(nth_VEBT_VEBT_type,type,
nth_VEBT_VEBT: ( list_VEBT_VEBT * nat ) > vEBT_VEBT ).
tff(vEBT_VEBT_high_type,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(treeList_type,type,
treeList: list_VEBT_VEBT ).
tff(i_type,type,
i: nat ).
tff(list_u1324408373059187874T_VEBT_type,type,
list_u1324408373059187874T_VEBT: ( list_VEBT_VEBT * nat * vEBT_VEBT ) > list_VEBT_VEBT ).
tff(1,plain,
( ( nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)) = vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na)) )
<=> ( nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)) = vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)) = vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_insprop) ).
tff(3,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)) = vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( i = aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na) )
<=> ( i = aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
i = aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_True) ).
tff(6,plain,
i = aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),i) = nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),i) = vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na)),
inference(transitivity,[status(thm)],[7,3]) ).
tff(9,plain,
( ( nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),i) != vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na)) )
<=> ( nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),i) != vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),i) != vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(11,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na))),i) != vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,mi),na)),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.18 % Problem : ITP234_1 : TPTP v9.0.0. Released v8.0.0.
% 0.11/0.18 % Command : run_E %s %d THM
% 0.12/0.42 % Computer : n006.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8042.1875MB
% 0.12/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Thu Jun 19 18:32:50 EDT 2025
% 0.12/0.42 % CPUTime :
% 2.79/3.06 % SZS status Theorem
% 2.79/3.06 % SZS output start Proof
% See solution above
% 3.40/3.71 % E exiting
%------------------------------------------------------------------------------