%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM925+3 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:22:24 AM UTC 2025
% Result : Theorem 0.73s 0.92s
% Output : Proof 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 40
% Syntax : Number of formulae : 94 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 488 ( 126 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 641 ( 285 ~; 224 |; 16 &)
% ( 93 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 38 ( 38 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 171 ( 153 !; 0 ?; 171 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_zero_int_type,type,
zero_zero_int: $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(one_one_int_type,type,
one_one_int: $i ).
tff(is_int_type,type,
is_int: $i > $o ).
tff(number_number_of_nat_type,type,
number_number_of_nat: $i > $i ).
tff(bit0_type,type,
bit0: $i > $i ).
tff(bit1_type,type,
bit1: $i > $i ).
tff(pls_type,type,
pls: $i ).
tff(power_power_int_type,type,
power_power_int: $i > $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_int_bool_type,type,
hAPP_int_bool: ( $i * $i ) > $i ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( $i * $i ) > $i ).
tff(ord_less_int_type,type,
ord_less_int: $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,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)],[4,3]) ).
tff(6,plain,
! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,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)],[6,2]) ).
tff(8,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(9,plain,
is_int(hAPP_nat_int(semiri1621563631at_int,n)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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(16,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)],[15]) ).
tff(17,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(18,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)],[17,16]) ).
tff(19,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)],[18,14]) ).
tff(20,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)],[19]) ).
tff(21,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)],[20,13]) ).
tff(22,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)],[21,11]) ).
tff(23,plain,
( is_int(one_one_int)
<=> is_int(one_one_int) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
is_int(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
tff(25,plain,
is_int(one_one_int),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,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(one_one_int)
| is_int(plus_plus_int(one_one_int,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(one_one_int)
| is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(one_one_int) )
<=> ( ~ is_int(one_one_int)
| is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,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(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(one_one_int) )
<=> ( ~ ! [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(one_one_int)
| is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,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(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(one_one_int) )
<=> ( ~ ! [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(one_one_int)
| is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,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(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(one_one_int) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,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(one_one_int)
| is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(unit_resolution,[status(thm)],[31,25,22]) ).
tff(33,plain,
is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),
inference(unit_resolution,[status(thm)],[32,9]) ).
tff(34,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(35,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(36,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(37,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)],[36,35]) ).
tff(38,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)],[37,34]) ).
tff(39,plain,
^ [N_20: $i,A_94: $i] :
refl(( ( ( 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) ) )),
inference(bind,[status(th)],[]) ).
tff(40,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(quant_intro,[status(thm)],[39]) ).
tff(41,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(42,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(43,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)],[42]) ).
tff(44,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(45,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)],[44,43]) ).
tff(46,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)],[45,41]) ).
tff(47,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(skolemize,[status(sab)],[46]) ).
tff(48,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)],[47,40]) ).
tff(49,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) )
| ( 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = 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) )
| ( 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) )
<=> ( ( 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,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) )
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) )
<=> ( ~ ! [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) )
| ( 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,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) )
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) )
<=> ( ~ ! [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) )
| ( 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,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) )
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,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) )
| ( 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 )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[54,48,38]) ).
tff(56,plain,
plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(unit_resolution,[status(thm)],[55,33]) ).
tff(57,plain,
^ [A_1: $i] :
refl(( ( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) )
<=> ( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
^ [A_1: $i] :
trans(monotonicity(trans(rewrite(( ( 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 = zero_zero_int )
<=> 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)))))) ) )),
rewrite(( ~ ( ( A_1 = zero_zero_int )
<=> 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 )
<=> 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)))))) ) )),
( ( 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 = zero_zero_int )
<=> 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)))))) ) )),
( ( 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)
=> ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ) )),
rewrite(( ( is_int(A_1)
=> ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) )
<=> ( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ) )),
( ( 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)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(61,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)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,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(63,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ ( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) ) )
<=> ( ~ ! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ ( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ ( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [A_1: $i] :
( ~ is_int(A_1)
| ~ ( ( A_1 = zero_zero_int )
<=> 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)))))) ) )
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ ( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ ( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) ) ),
inference(unit_resolution,[status(thm)],[69,66]) ).
tff(71,plain,
~ ( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) ),
inference(unit_resolution,[status(thm)],[70,33]) ).
tff(72,plain,
^ [N_14: $i,A_92: $i] :
refl(( ( 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,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(73,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(quant_intro,[status(thm)],[72]) ).
tff(74,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(75,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(76,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)],[75]) ).
tff(77,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(78,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)],[77,76]) ).
tff(79,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)],[78,74]) ).
tff(80,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(skolemize,[status(sab)],[79]) ).
tff(81,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)],[80,73]) ).
tff(82,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(83,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(84,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)],[83,82]) ).
tff(85,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)) )
| ~ 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),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)))))) )
<=> ( ~ ! [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)) )
| ~ 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),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)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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))))))
| ~ 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))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,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)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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))))))
| ~ 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)))) )
<=> ( ~ ! [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)) )
| ~ 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),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)))))) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,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)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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))))))
| ~ 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)))) )
<=> ( ~ ! [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)) )
| ~ 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),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)))))) ) ),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,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)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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))))))
| ~ 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(quant_inst,[status(thm)],[]) ).
tff(90,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)) )
| ~ 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),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)))))) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))),
inference(unit_resolution,[status(thm)],[90,84,81]) ).
tff(92,plain,
( ( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) )
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) != zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) ),
inference(tautology,[status(thm)],[]) ).
tff(93,plain,
( ( ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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)))))) )
| ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) != zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
$false,
inference(unit_resolution,[status(thm)],[93,71,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM925+3 : TPTP v9.0.0. Released v5.3.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 02:04:10 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.73/0.92 % SZS status Theorem
% 0.73/0.92 % SZS output start Proof
% See solution above
% 0.77/0.98 % E exiting
%------------------------------------------------------------------------------