TSTP Solution File: NUM925+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM925+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 13:12:43 EDT 2022
% Result : Theorem 0.98s 0.94s
% Output : Proof 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 80
% Syntax : Number of formulae : 169 ( 53 unt; 20 typ; 0 def)
% Number of atoms : 661 ( 201 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 810 ( 359 ~; 283 |; 16 &)
% ( 132 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 61 ( 61 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 12 >; 4 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 223 ( 190 !; 0 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_int_bool_type,type,
hAPP_int_bool: ( $i * $i ) > $i ).
tff(plus_plus_int_type,type,
plus_plus_int: ( $i * $i ) > $i ).
tff(hAPP_nat_int_type,type,
hAPP_nat_int: ( $i * $i ) > $i ).
tff(n_type,type,
n: $i ).
tff(semiri1621563631at_int_type,type,
semiri1621563631at_int: $i ).
tff(number_number_of_int_type,type,
number_number_of_int: $i > $i ).
tff(bit1_type,type,
bit1: $i > $i ).
tff(succ_type,type,
succ: $i > $i ).
tff(min_type,type,
min: $i ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( $i * $i ) > $i ).
tff(ord_less_int_type,type,
ord_less_int: $i ).
tff(number_number_of_nat_type,type,
number_number_of_nat: $i > $i ).
tff(pls_type,type,
pls: $i ).
tff(zero_zero_nat_type,type,
zero_zero_nat: $i ).
tff(zero_zero_int_type,type,
zero_zero_int: $i ).
tff(one_one_int_type,type,
one_one_int: $i ).
tff(bit0_type,type,
bit0: $i > $i ).
tff(power_power_int_type,type,
power_power_int: $i > $i ).
tff(is_int_type,type,
is_int: $i > $o ).
tff(1,plain,
( ( number_number_of_int(succ(min)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(succ(min))) )
<=> ( succ(min) = number_number_of_int(succ(min)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( number_number_of_int(pls) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)) )
<=> ( number_number_of_int(succ(min)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(succ(min))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) )
<=> ( number_number_of_int(pls) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) )
<=> ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_transfer__int__nat__numerals_I1_J) ).
tff(6,plain,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
number_number_of_int(pls) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
number_number_of_int(succ(min)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(succ(min))),
inference(modus_ponens,[status(thm)],[7,2]) ).
tff(9,plain,
succ(min) = number_number_of_int(succ(min)),
inference(modus_ponens,[status(thm)],[8,1]) ).
tff(10,plain,
number_number_of_int(succ(min)) = succ(min),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))) = hAPP_i1948725293t_bool(ord_less_int,succ(min)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
hAPP_i1948725293t_bool(ord_less_int,succ(min)) = hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(20,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[21,16]) ).
tff(23,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
^ [B_1_1: $i,B_2_1: $i] :
refl(
( is_int(hAPP_nat_int(B_1_1,B_2_1))
<=> is_int(hAPP_nat_int(B_1_1,B_2_1)) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1))
<=> ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1))
<=> ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
tff(28,plain,
! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1))
| is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
is_int(hAPP_nat_int(semiri1621563631at_int,n)),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
^ [B_1_1: $i,B_2_1: $i] :
refl(
( ( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
<=> ( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
^ [B_1_1: $i,B_2_1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( is_int(B_1_1)
& is_int(B_2_1) )
<=> ~ ( ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) )),
( ~ ( is_int(B_1_1)
& is_int(B_2_1) )
<=> ~ ~ ( ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) )),
rewrite(
( ~ ~ ( ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
<=> ( ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) )),
( ~ ( is_int(B_1_1)
& is_int(B_2_1) )
<=> ( ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) )),
( ( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) )
<=> ( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) )),
rewrite(
( ( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
<=> ( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) )),
( ( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) )
<=> ( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
^ [B_1_1: $i,B_2_1: $i] :
rewrite(
( ( ( is_int(B_1_1)
& is_int(B_2_1) )
=> is_int(plus_plus_int(B_1_1,B_2_1)) )
<=> ( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( ( is_int(B_1_1)
& is_int(B_2_1) )
=> is_int(plus_plus_int(B_1_1,B_2_1)) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( is_int(B_1_1)
& is_int(B_2_1) )
=> is_int(plus_plus_int(B_1_1,B_2_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint) ).
tff(41,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ ( is_int(B_1_1)
& is_int(B_2_1) ) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(modus_ponens,[status(thm)],[44,34]) ).
tff(46,plain,
( is_int(number_number_of_int(bit1(pls)))
<=> is_int(number_number_of_int(bit1(succ(min)))) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( is_int(one_one_int)
<=> is_int(number_number_of_int(bit1(pls))) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( is_int(one_one_int)
<=> is_int(one_one_int) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
is_int(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
tff(50,plain,
is_int(one_one_int),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
is_int(number_number_of_int(bit1(pls))),
inference(modus_ponens,[status(thm)],[50,47]) ).
tff(52,plain,
is_int(number_number_of_int(bit1(succ(min)))),
inference(modus_ponens,[status(thm)],[51,46]) ).
tff(53,plain,
( ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
| ~ is_int(number_number_of_int(bit1(succ(min))))
| is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) )
<=> ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
| ~ is_int(number_number_of_int(bit1(succ(min))))
| is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(number_number_of_int(bit1(succ(min)))) )
<=> ( ~ is_int(number_number_of_int(bit1(succ(min))))
| is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
| is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(number_number_of_int(bit1(succ(min)))) )
<=> ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
| ~ is_int(number_number_of_int(bit1(succ(min))))
| is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
| is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(number_number_of_int(bit1(succ(min)))) )
<=> ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
| ~ is_int(number_number_of_int(bit1(succ(min))))
| is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
| is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(number_number_of_int(bit1(succ(min)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) )
| ~ is_int(number_number_of_int(bit1(succ(min))))
| is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(unit_resolution,[status(thm)],[58,52,45]) ).
tff(60,plain,
is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),
inference(unit_resolution,[status(thm)],[59,32]) ).
tff(61,plain,
^ [A_1: $i] :
refl(
( ( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) )
<=> ( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) )
<=> ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
^ [A_1: $i] :
rewrite(
( ( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != number_number_of_int(succ(min)) ) ) )
<=> ( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != number_number_of_int(succ(min)) ) ) )
<=> ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
^ [A_1: $i] :
rewrite(
( ( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != number_number_of_int(pls) ) ) )
<=> ( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != number_number_of_int(succ(min)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != number_number_of_int(pls) ) ) )
<=> ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != number_number_of_int(succ(min)) ) ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
^ [A_1: $i] :
rewrite(
( ( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) )
<=> ( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != number_number_of_int(pls) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) )
<=> ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != number_number_of_int(pls) ) ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) )
<=> ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
^ [A_1: $i] :
rewrite(
( ( is_int(A_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) )
<=> ( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [A_1: $i] :
( is_int(A_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) )
<=> ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,axiom,
! [A_1: $i] :
( is_int(A_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_zero__less__power2) ).
tff(73,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_1 != number_number_of_int(pls) ) ) ),
inference(modus_ponens,[status(thm)],[74,68]) ).
tff(76,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != number_number_of_int(succ(min)) ) ) ),
inference(modus_ponens,[status(thm)],[75,66]) ).
tff(77,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) ),
inference(modus_ponens,[status(thm)],[76,64]) ).
tff(78,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) ),
inference(modus_ponens,[status(thm)],[78,62]) ).
tff(80,plain,
( ( ~ ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) )
| ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) != succ(min) ) ) )
<=> ( ~ ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) )
| ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) != succ(min) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ~ ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) )
| ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) != succ(min) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [A_1: $i] :
( ~ is_int(A_1)
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( A_1 != succ(min) ) ) )
| ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) != succ(min) ) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) != succ(min) ) ) ),
inference(unit_resolution,[status(thm)],[82,79]) ).
tff(84,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) != succ(min) ) ),
inference(unit_resolution,[status(thm)],[83,60]) ).
tff(85,plain,
( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
<=> ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = succ(min) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
<=> ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ( ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
<=> ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
~ ( ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(91,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[91,88]) ).
tff(93,plain,
hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls),
inference(modus_ponens,[status(thm)],[92,87]) ).
tff(94,plain,
hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = succ(min),
inference(modus_ponens,[status(thm)],[94,85]) ).
tff(96,plain,
^ [N_20: $i,A_94: $i] :
refl(
( ( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) )
<=> ( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) )
<=> ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
^ [N_20: $i,A_94: $i] :
trans(
monotonicity(
rewrite(
( ( A_94 = number_number_of_int(succ(min)) )
<=> ( A_94 = succ(min) ) )),
rewrite(
( ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) )
<=> ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) )),
( ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(succ(min)) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) )
<=> ( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) ) )),
rewrite(
( ( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) )
<=> ( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) ) )),
( ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(succ(min)) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) )
<=> ( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = number_number_of_int(succ(min)) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) )
<=> ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
^ [N_20: $i,A_94: $i] :
trans(
monotonicity(
rewrite(
( ( A_94 = number_number_of_int(pls) )
<=> ( A_94 = number_number_of_int(succ(min)) ) )),
rewrite(
( ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) )
<=> ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) )),
( ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(pls) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) ) )
<=> ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(succ(min)) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) ) )),
rewrite(
( ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(succ(min)) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) )
<=> ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(succ(min)) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) ) )),
( ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(pls) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) ) )
<=> ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(succ(min)) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = number_number_of_int(pls) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) ) )
<=> ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = number_number_of_int(succ(min)) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
^ [N_20: $i,A_94: $i] :
trans(
monotonicity(
rewrite(
( ( A_94 = zero_zero_int )
<=> ( A_94 = number_number_of_int(pls) ) )),
rewrite(
( ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
<=> ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) ) )),
( ( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) )
<=> ( ( A_94 = number_number_of_int(pls) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) )
| ~ is_int(A_94) ) )),
rewrite(
( ( ( A_94 = number_number_of_int(pls) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) )
| ~ is_int(A_94) )
<=> ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(pls) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) ) ) )),
( ( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) )
<=> ( ~ is_int(A_94)
| ( A_94 = number_number_of_int(pls) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) ) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [N_20: $i,A_94: $i] :
( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) )
<=> ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = number_number_of_int(pls) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [N_20: $i,A_94: $i] :
( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) )
<=> ! [N_20: $i,A_94: $i] :
( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
^ [N_20: $i,A_94: $i] :
trans(
monotonicity(
rewrite(
( ( ( A_94 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int ) )
<=> ( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int ) ) )),
( ( is_int(A_94)
=> ( ( A_94 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int ) ) )
<=> ( is_int(A_94)
=> ( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int ) ) ) )),
rewrite(
( ( is_int(A_94)
=> ( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int ) ) )
<=> ( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) ) )),
( ( is_int(A_94)
=> ( ( A_94 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int ) ) )
<=> ( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [N_20: $i,A_94: $i] :
( is_int(A_94)
=> ( ( A_94 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int ) ) )
<=> ! [N_20: $i,A_94: $i] :
( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,axiom,
! [N_20: $i,A_94: $i] :
( is_int(A_94)
=> ( ( A_94 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
tff(108,plain,
! [N_20: $i,A_94: $i] :
( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [N_20: $i,A_94: $i] :
( ( A_94 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != zero_zero_int )
| ~ is_int(A_94) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = number_number_of_int(pls) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(pls) ) ),
inference(modus_ponens,[status(thm)],[109,103]) ).
tff(111,plain,
! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = number_number_of_int(succ(min)) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != number_number_of_int(succ(min)) ) ),
inference(modus_ponens,[status(thm)],[110,101]) ).
tff(112,plain,
! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) ),
inference(modus_ponens,[status(thm)],[111,99]) ).
tff(113,plain,
! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) ),
inference(modus_ponens,[status(thm)],[113,97]) ).
tff(115,plain,
( ( ~ ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) )
| ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) )
| ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) != succ(min) ) )
<=> ( ~ ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) )
| ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) )
| ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) != succ(min) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ~ ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) )
| ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) )
| ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) != succ(min) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
( ~ ! [N_20: $i,A_94: $i] :
( ~ is_int(A_94)
| ( A_94 = succ(min) )
| ( hAPP_nat_int(power_power_int(A_94),N_20) != succ(min) ) )
| ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) )
| ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) != succ(min) ) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
( ~ is_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) ),
inference(unit_resolution,[status(thm)],[117,114,95]) ).
tff(119,plain,
plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min),
inference(unit_resolution,[status(thm)],[118,60]) ).
tff(120,plain,
( ~ ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) != succ(min) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
| ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) != succ(min) ) ),
inference(tautology,[status(thm)],]) ).
tff(121,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))))),
inference(unit_resolution,[status(thm)],[120,119,84]) ).
tff(122,plain,
^ [N_14: $i,A_92: $i] :
refl(
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
<=> ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
^ [N_14: $i,A_92: $i] :
rewrite(
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),A_92)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),A_92)) )
<=> ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
^ [N_14: $i,A_92: $i] :
rewrite(
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),A_92)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),A_92)) ) )),
inference(bind,[status(th)],]) ).
tff(127,plain,
( ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),A_92)) )
<=> ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),A_92)) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
^ [N_14: $i,A_92: $i] :
rewrite(
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),A_92)) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92)) )
<=> ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),A_92)) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92)) )
<=> ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
^ [N_14: $i,A_92: $i] :
rewrite(
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14))) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92)) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14))) )
<=> ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92)) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,axiom,
! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_zero__less__power) ).
tff(134,plain,
! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92)) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_92)) ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),A_92)) ),
inference(modus_ponens,[status(thm)],[135,129]) ).
tff(137,plain,
! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),A_92)) ),
inference(modus_ponens,[status(thm)],[136,127]) ).
tff(138,plain,
! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) ),
inference(modus_ponens,[status(thm)],[137,125]) ).
tff(139,plain,
! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) ),
inference(modus_ponens,[status(thm)],[139,123]) ).
tff(141,plain,
( ( ~ ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))))) )
<=> ( ~ ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ( ~ ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) )
<=> ( ~ ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))))) ) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ( ~ ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) )
<=> ( ~ ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))))) ) ),
inference(transitivity,[status(thm)],[143,141]) ).
tff(145,plain,
( ~ ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min)))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
( ~ ! [N_14: $i,A_92: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(A_92),N_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),A_92)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))))) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))))) ),
inference(unit_resolution,[status(thm)],[146,140]) ).
tff(148,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(unit_resolution,[status(thm)],[147,121]) ).
tff(149,plain,
$false,
inference(unit_resolution,[status(thm)],[148,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM925+3 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 16:09:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.98/0.94 % SZS status Theorem
% 0.98/0.94 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------