TSTP Solution File: NUM926_4 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM926_4 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 : Sun Sep 18 13:12:47 EDT 2022
% Result : Theorem 4.33s 3.39s
% Output : Proof 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 48
% Syntax : Number of formulae : 80 ( 19 unt; 22 typ; 0 def)
% Number of atoms : 201 ( 84 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 222 ( 87 ~; 88 |; 0 &)
% ( 32 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 14 con; 0-2 aty)
% Number of variables : 82 ( 38 !; 40 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_int_int_type,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(pls_type,type,
pls: int ).
tff(fact_fact_int_type,type,
fact_fact_int: fun_int_int ).
tff(t_type,type,
t: int ).
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_int_bool_type,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(ord_less_eq_int_type,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(ord_less_int_type,type,
ord_less_int: fun_int_fun_int_bool ).
tff(bit1_type,type,
bit1: fun_int_int ).
tff(number_number_of_int_type,type,
number_number_of_int: fun_int_int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(hAPP_int_fun_int_int_type,type,
hAPP_int_fun_int_int: ( fun_int_fun_int_int * int ) > fun_int_int ).
tff(m_type,type,
m: int ).
tff(bit0_type,type,
bit0: fun_int_int ).
tff(times_times_int_type,type,
times_times_int: fun_int_fun_int_int ).
tff(plus_plus_int_type,type,
plus_plus_int: fun_int_fun_int_int ).
tff(hAPP_nat_int_type,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(hAPP_int_nat_type,type,
hAPP_int_nat: ( fun_int_nat * int ) > nat ).
tff(number_number_of_nat_type,type,
number_number_of_nat: fun_int_nat ).
tff(hAPP_int_fun_nat_int_type,type,
hAPP_int_fun_nat_int: ( fun_int_fun_nat_int * int ) > fun_nat_int ).
tff(power_power_int_type,type,
power_power_int: fun_int_fun_nat_int ).
tff(1,plain,
^ [X_29: int,Y_23: int] :
refl(
( ( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
<=> ( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
<=> ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
<=> ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [X_29: int,Y_23: int] :
trans(
monotonicity(
rewrite(
( ( ( X_29 != Y_23 )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23)) )
<=> ( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23))
=> ( ( X_29 != Y_23 )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23)) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23))
=> ( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23)) ) ) )),
rewrite(
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23))
=> ( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23)) ) )
<=> ( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23))
=> ( ( X_29 != Y_23 )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23)) ) )
<=> ( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X_29: int,Y_23: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23))
=> ( ( X_29 != Y_23 )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23)) ) )
<=> ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X_29: int,Y_23: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23))
=> ( ( X_29 != Y_23 )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1011_order__le__neq__implies__less) ).
tff(7,plain,
! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),t))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| $false )
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) )
<=> ~ ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
~ ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(17,plain,
~ ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) )
<=> $false ),
inference(iff_false,[status(thm)],[17]) ).
tff(19,plain,
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| $false ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) )
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(transitivity,[status(thm)],[19,14]) ).
tff(21,plain,
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
=> ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
=> ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(23,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
inference(modus_ponens,[status(thm)],[24,13]) ).
tff(26,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),t)),
inference(modus_ponens,[status(thm)],[25,12]) ).
tff(27,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t)),
inference(modus_ponens,[status(thm)],[26,11]) ).
tff(28,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),t))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
tff(32,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),t)),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t)),
inference(modus_ponens,[status(thm)],[33,28]) ).
tff(35,plain,
( ( ~ ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
| ( hAPP_int_int(fact_fact_int,pls) = t ) )
<=> ( ~ ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
| ( hAPP_int_int(fact_fact_int,pls) = t ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ( hAPP_int_int(fact_fact_int,pls) = t )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
| ( hAPP_int_int(fact_fact_int,pls) = t ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
| ( hAPP_int_int(fact_fact_int,pls) = t )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t)) )
<=> ( ~ ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
| ( hAPP_int_int(fact_fact_int,pls) = t ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
| ( hAPP_int_int(fact_fact_int,pls) = t )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t)) )
<=> ( ~ ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
| ( hAPP_int_int(fact_fact_int,pls) = t ) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
| ( hAPP_int_int(fact_fact_int,pls) = t )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t)) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X_29: int,Y_23: int] :
( ( X_29 = Y_23 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),Y_23))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_23)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
| ( hAPP_int_int(fact_fact_int,pls) = t ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
hAPP_int_int(fact_fact_int,pls) = t,
inference(unit_resolution,[status(thm)],[40,34,27,10]) ).
tff(42,plain,
t = hAPP_int_int(fact_fact_int,pls),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ( t != hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) )
<=> ( t != hAPP_int_int(fact_fact_int,pls) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( t != one_one_int )
<=> ( t != hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( t != one_one_int )
<=> ( t != one_one_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ( t != one_one_int )
| $false )
<=> ( t != one_one_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ( ( t != one_one_int )
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) )
<=> ( ( t != one_one_int )
| $false ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(48,plain,
( ( ( t != one_one_int )
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) )
<=> ( t != one_one_int ) ),
inference(transitivity,[status(thm)],[47,46]) ).
tff(49,plain,
( ( ( t != one_one_int )
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) )
<=> ( ( t != one_one_int )
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( ( t = one_one_int )
=> ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) )
<=> ( ( t != one_one_int )
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
( ( t = one_one_int )
=> ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(52,plain,
( ( t != one_one_int )
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ( t != one_one_int )
| ? [X: int,Y: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int) ) ),
inference(modus_ponens,[status(thm)],[52,49]) ).
tff(54,plain,
t != one_one_int,
inference(modus_ponens,[status(thm)],[53,48]) ).
tff(55,plain,
t != one_one_int,
inference(modus_ponens,[status(thm)],[54,45]) ).
tff(56,plain,
t != hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
inference(modus_ponens,[status(thm)],[55,44]) ).
tff(57,plain,
t != hAPP_int_int(fact_fact_int,pls),
inference(modus_ponens,[status(thm)],[56,43]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM926_4 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.37 % Computer : n021.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Sep 2 15:47:29 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 4.33/3.39 % SZS status Theorem
% 4.33/3.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------