%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP224_1 : TPTP v9.0.0. Released v8.0.0.
% 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 05:12:07 AM UTC 2025
% Result : Theorem 68.81s 69.02s
% Output : Proof 69.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 63 ( 28 ~; 24 |; 0 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-1 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(pp_type,type,
pp: bool > $o ).
tff(aa_nat_bool_type,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(zero_zero_nat_type,type,
zero_zero_nat: nat ).
tff(aa_nat_fun_nat_bool_type,type,
aa_nat_fun_nat_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(ord_less_nat_type,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(vEBT_invar_vebt_type,type,
vEBT_invar_vebt: vEBT_VEBT > fun_nat_bool ).
tff(vEBT_Node_type,type,
vEBT_Node: ( option4927543243414619207at_nat * nat * list_VEBT_VEBT * vEBT_VEBT ) > vEBT_VEBT ).
tff(summary_type,type,
summary: vEBT_VEBT ).
tff(treeList_type,type,
treeList: list_VEBT_VEBT ).
tff(deg_type,type,
deg: nat ).
tff(info_type,type,
info: option4927543243414619207at_nat ).
tff(1,plain,
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),zero_zero_nat))
<=> ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_less__numeral__extra_I3_J) ).
tff(3,plain,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),zero_zero_nat)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T2: vEBT_VEBT,N2: nat] :
refl(( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) )
<=> ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) )
<=> ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [T2: vEBT_VEBT,N2: nat] :
rewrite(( ( pp(aa_nat_bool(vEBT_invar_vebt(T2),N2))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2)) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(vEBT_invar_vebt(T2),N2))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2)) )
<=> ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(vEBT_invar_vebt(T2),N2))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_deg__not__0) ).
tff(10,plain,
! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( pp(aa_nat_bool(vEBT_invar_vebt(vEBT_Node(info,deg,treeList,summary)),zero_zero_nat))
<=> pp(aa_nat_bool(vEBT_invar_vebt(vEBT_Node(info,deg,treeList,summary)),zero_zero_nat)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
pp(aa_nat_bool(vEBT_invar_vebt(vEBT_Node(info,deg,treeList,summary)),zero_zero_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Node_Oprems) ).
tff(16,plain,
pp(aa_nat_bool(vEBT_invar_vebt(vEBT_Node(info,deg,treeList,summary)),zero_zero_nat)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) )
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),zero_zero_nat))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(vEBT_Node(info,deg,treeList,summary)),zero_zero_nat)) )
<=> ( ~ ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) )
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),zero_zero_nat))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(vEBT_Node(info,deg,treeList,summary)),zero_zero_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) )
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),zero_zero_nat))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(vEBT_Node(info,deg,treeList,summary)),zero_zero_nat)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [T2: vEBT_VEBT,N2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),N2))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(T2),N2)) )
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,zero_zero_nat),zero_zero_nat))
| ~ pp(aa_nat_bool(vEBT_invar_vebt(vEBT_Node(info,deg,treeList,summary)),zero_zero_nat)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,13,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16 % Problem : ITP224_1 : TPTP v9.0.0. Released v8.0.0.
% 0.11/0.16 % Command : run_E %s %d THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8042.1875MB
% 0.12/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Jun 19 18:32:12 EDT 2025
% 0.12/0.37 % CPUTime :
% 68.81/69.02 % SZS status Theorem
% 68.81/69.02 % SZS output start Proof
% See solution above
% 69.83/70.02 % E exiting
%------------------------------------------------------------------------------