%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP270_1 : TPTP v9.0.0. Released v8.0.0.
% 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 05:12:29 AM UTC 2025
% Result : Theorem 76.86s 77.19s
% Output : Proof 77.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 126 ( 53 ~; 49 |; 1 &)
% ( 12 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 10 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(pp_type,type,
pp: bool > $o ).
tff(aa_nat_bool_type,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(aa_nat_nat_type,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(deg_type,type,
deg: nat ).
tff(aa_nat_fun_nat_nat_type,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(aa_num_nat_type,type,
aa_num_nat: ( fun_num_nat * num ) > nat ).
tff(aa_num_num_type,type,
aa_num_num: ( fun_num_num * num ) > num ).
tff(one_type,type,
one: num ).
tff(bit0_type,type,
bit0: fun_num_num ).
tff(numeral_numeral_nat_type,type,
numeral_numeral_nat: fun_num_nat ).
tff(power_power_nat_type,type,
power_power_nat: fun_nat_fun_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(x_type,type,
x: nat ).
tff(ord_less_nat_type,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(ord_less_eq_nat_type,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(ma_type,type,
ma: nat ).
tff(mi_type,type,
mi: nat ).
tff(1,plain,
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)))
<=> ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(3,plain,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: nat,Y: nat,Z: nat] :
refl(( ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) )
<=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) )
<=> ! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) )
<=> ! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [X: nat,Y: nat,Z: nat] :
trans(monotonicity(rewrite(( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z)) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) )),
( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z)) ) )
<=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) ) )),
rewrite(( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) )
<=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) )),
( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z)) ) )
<=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: nat,Y: nat,Z: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z)) ) )
<=> ! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X: nat,Y: nat,Z: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_order__le__less__trans) ).
tff(10,plain,
! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma))
<=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma))
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,mi),x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24__092_060open_062x_A_092_060le_062_Ama_A_092_060and_062_Ami_A_092_060le_062_Ax_092_060close_062) ).
tff(16,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma)),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma)),
inference(modus_ponens,[status(thm)],[16,14]) ).
tff(18,plain,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)))
<=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__C5_Ohyps_C_I8_J) ).
tff(20,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ ! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))) )
<=> ( ~ ! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [X: nat,Y: nat,Z: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Z))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,20,17,13,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP270_1 : TPTP v9.0.0. Released v8.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 19 18:39:50 EDT 2025
% 0.13/0.34 % CPUTime :
% 76.86/77.19 % SZS status Theorem
% 76.86/77.19 % SZS output start Proof
% See solution above
% 77.96/78.27 % E exiting
%------------------------------------------------------------------------------