%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM925+4 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 4.50s 4.75s
% Output : Proof 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 58
% Syntax : Number of formulae : 128 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 1096 ( 372 equ)
% Maximal formula atoms : 28 ( 8 avg)
% Number of connectives : 1589 ( 705 ~; 578 |; 69 &)
% ( 163 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 84 ( 84 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-2 aty)
% Number of variables : 223 ( 197 !; 0 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
tff(is_int_type,type,
is_int: $i > $o ).
tff(hAPP_int_int_type,type,
hAPP_int_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(hAPP_int_fun_int_int_type,type,
hAPP_int_fun_int_int: ( $i * $i ) > $i ).
tff(one_one_int_type,type,
one_one_int: $i ).
tff(plus_plus_int_type,type,
plus_plus_int: $i ).
tff(zero_zero_int_type,type,
zero_zero_int: $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_eq_int_type,type,
ord_less_eq_int: $i ).
tff(hAPP_int_nat_type,type,
hAPP_int_nat: ( $i * $i ) > $i ).
tff(pls_type,type,
pls: $i ).
tff(bit1_type,type,
bit1: $i ).
tff(bit0_type,type,
bit0: $i ).
tff(number_number_of_nat_type,type,
number_number_of_nat: $i ).
tff(hAPP_int_fun_nat_int_type,type,
hAPP_int_fun_nat_int: ( $i * $i ) > $i ).
tff(power_power_int_type,type,
power_power_int: $i ).
tff(ord_less_int_type,type,
ord_less_int: $i ).
tff(hAPP_nat_bool_type,type,
hAPP_nat_bool: ( $i * $i ) > $i ).
tff(hAPP_n1699378549t_bool_type,type,
hAPP_n1699378549t_bool: ( $i * $i ) > $i ).
tff(zero_zero_nat_type,type,
zero_zero_nat: $i ).
tff(ord_less_nat_type,type,
ord_less_nat: $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/sandbox/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(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
<=> ( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [B_1_1: $i,B_2_1: $i] :
rewrite(( ( is_int(B_2_1)
=> is_int(hAPP_int_int(B_1_1,B_2_1)) )
<=> ( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_int(B_2_1)
=> is_int(hAPP_int_int(B_1_1,B_2_1)) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [B_1_1: $i,B_2_1: $i] :
( is_int(B_2_1)
=> is_int(hAPP_int_int(B_1_1,B_2_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint) ).
tff(16,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
| is_int(hAPP_int_int(hAPP_int_fun_int_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(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
| is_int(hAPP_int_int(hAPP_int_fun_int_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(21,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
| is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
| is_int(hAPP_int_int(hAPP_int_fun_int_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)],[21,20]) ).
tff(23,plain,
( is_int(hAPP_int_int(hAPP_int_fun_int_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)],[22,19]) ).
tff(24,plain,
is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),
inference(unit_resolution,[status(thm)],[23,9]) ).
tff(25,plain,
^ [Z_1: $i] :
refl(( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_736_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
tff(29,plain,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n))),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_zero__le__one) ).
tff(36,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
^ [Ya: $i,Xa: $i] :
refl(( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
<=> ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [Ya: $i,Xa: $i] :
trans(monotonicity(trans(trans(monotonicity(rewrite(( ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) )
<=> ~ ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) ) )),
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
<=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ~ ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) ) ) )),
rewrite(( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ~ ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) ) )
<=> ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )),
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
<=> ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )),
rewrite(( ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) )
<=> ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )),
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
<=> ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )),
trans(monotonicity(rewrite(( ( is_int(Ya)
& is_int(Xa) )
<=> ~ ( ~ is_int(Xa)
| ~ is_int(Ya) ) )),
( ~ ( is_int(Ya)
& is_int(Xa) )
<=> ~ ~ ( ~ is_int(Xa)
| ~ is_int(Ya) ) )),
rewrite(( ~ ~ ( ~ is_int(Xa)
| ~ is_int(Ya) )
<=> ( ~ is_int(Xa)
| ~ is_int(Ya) ) )),
( ~ ( is_int(Ya)
& is_int(Xa) )
<=> ( ~ is_int(Xa)
| ~ is_int(Ya) ) )),
( ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) )
<=> ( ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya) ) )),
rewrite(( ( ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ) )),
( ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) )
<=> ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) )
<=> ! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [Ya: $i,Xa: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) )),
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) )
<=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) )
<=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya)) ) )),
( ( ( is_int(Ya)
& is_int(Xa) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) )
<=> ( ( is_int(Ya)
& is_int(Xa) )
=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya)) ) ) )),
rewrite(( ( ( is_int(Ya)
& is_int(Xa) )
=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya)) ) )
<=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ) )),
( ( ( is_int(Ya)
& is_int(Xa) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) )
<=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [Ya: $i,Xa: $i] :
( ( is_int(Ya)
& is_int(Xa) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) )
<=> ! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [Ya: $i,Xa: $i] :
( ( is_int(Ya)
& is_int(Xa) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_add__nonneg__eq__0__iff) ).
tff(45,plain,
! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[48,38]) ).
tff(50,plain,
( is_int(one_one_int)
<=> is_int(one_one_int) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
is_int(one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
tff(52,plain,
is_int(one_one_int),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ( ~ ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ is_int(one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) )
<=> ( ~ ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ is_int(one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(one_one_int)
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) )
<=> ( ~ is_int(one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) )
<=> ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(one_one_int)
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(one_one_int)
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(one_one_int)
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) )
<=> ( ~ is_int(one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ( ~ ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(one_one_int)
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) )
<=> ( ~ ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ is_int(one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(one_one_int)
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) )
<=> ( ~ ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ is_int(one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ) ),
inference(transitivity,[status(thm)],[58,53]) ).
tff(60,plain,
( ~ ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(one_one_int)
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [Ya: $i,Xa: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ is_int(Xa)
| ~ is_int(Ya)
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ is_int(one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(unit_resolution,[status(thm)],[61,52,49,36]) ).
tff(63,plain,
~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[62,9,33]) ).
tff(64,plain,
( ( one_one_int != zero_zero_int )
<=> ( one_one_int != zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_one__neq__zero) ).
tff(66,plain,
one_one_int != zero_zero_int,
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int )
| ( one_one_int = zero_zero_int ) ),
inference(tautology,[status(thm)],[]) ).
tff(68,plain,
( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) )
| ~ ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != zero_zero_int ) ),
inference(tautology,[status(thm)],[]) ).
tff(70,plain,
( ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != zero_zero_int,
inference(unit_resolution,[status(thm)],[70,63]) ).
tff(72,plain,
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int )
<=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_zero__power2) ).
tff(74,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
zero_zero_int = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int )
<=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_zero_int ) )
<=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
~ ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(79,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[79,76]) ).
tff(81,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(transitivity,[status(thm)],[80,75]) ).
tff(82,plain,
^ [X_20: $i,Y_16: $i] :
refl(( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [X_20: $i,Y_16: $i] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [X_20: $i,Y_16: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [X_20: $i,Y_16: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1979_order__less__imp__le) ).
tff(88,plain,
! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_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_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(94,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ( ~ ! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )
<=> ( ~ ! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [X_20: $i,Y_16: $i] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(unit_resolution,[status(thm)],[97,94,91]) ).
tff(99,plain,
^ [A_154: $i,N_32: $i,B_105: $i] :
refl(( ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
<=> ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
^ [A_154: $i,N_32: $i,B_105: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( is_int(A_154)
& is_int(B_105) )
<=> ~ ( ~ is_int(B_105)
| ~ is_int(A_154) ) )),
( ~ ( is_int(A_154)
& is_int(B_105) )
<=> ~ ~ ( ~ is_int(B_105)
| ~ is_int(A_154) ) )),
rewrite(( ~ ~ ( ~ is_int(B_105)
| ~ is_int(A_154) )
<=> ( ~ is_int(B_105)
| ~ is_int(A_154) ) )),
( ~ ( is_int(A_154)
& is_int(B_105) )
<=> ( ~ is_int(B_105)
| ~ is_int(A_154) ) )),
( ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ is_int(B_105)
| ~ is_int(A_154)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ) )),
rewrite(( ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ is_int(B_105)
| ~ is_int(A_154)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) ) )),
( ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) )
<=> ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) )
<=> ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
^ [A_154: $i,N_32: $i,B_105: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) )
<=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ( A_154 = B_105 ) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ( A_154 = B_105 ) ) ) )),
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ( A_154 = B_105 ) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32)) ) ) )),
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32)) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154)) ) )),
( ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) ) ) )
<=> ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154)) ) ) )),
rewrite(( ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154)) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ) )),
( ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) ) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ) )),
( ( ( is_int(A_154)
& is_int(B_105) )
=> ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) ) ) ) )
<=> ( ( is_int(A_154)
& is_int(B_105) )
=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ) ) )),
rewrite(( ( ( is_int(A_154)
& is_int(B_105) )
=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ) )),
( ( ( is_int(A_154)
& is_int(B_105) )
=> ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) ) ) ) )
<=> ( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [A_154: $i,N_32: $i,B_105: $i] :
( ( is_int(A_154)
& is_int(B_105) )
=> ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) ) ) ) )
<=> ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [A_154: $i,N_32: $i,B_105: $i] :
( ( is_int(A_154)
& is_int(B_105) )
=> ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> ( A_154 = B_105 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_power__eq__imp__eq__base) ).
tff(107,plain,
! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ~ ( is_int(A_154)
& is_int(B_105) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) ) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) ),
inference(modus_ponens,[status(thm)],[110,100]) ).
tff(112,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
tff(114,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_pos2) ).
tff(117,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
( is_int(zero_zero_int)
<=> is_int(zero_zero_int) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,axiom,
is_int(zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint) ).
tff(120,plain,
is_int(zero_zero_int),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
( ( ~ ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
<=> ( ~ ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) )
<=> ( ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,plain,
( ( ~ ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) )
<=> ( ~ ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( ( ~ ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) )
<=> ( ~ ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(transitivity,[status(thm)],[123,121]) ).
tff(125,plain,
( ~ ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [A_154: $i,N_32: $i,B_105: $i] :
( ( A_154 = B_105 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_105))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ is_int(B_105)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_154),N_32) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_105),N_32) )
| ~ is_int(A_154) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[126,120,117,114,111,98,81]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,71,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+4 : TPTP v9.0.0. Released v5.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:04:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.50/4.75 % SZS status Theorem
% 4.50/4.75 % SZS output start Proof
% See solution above
% 4.95/5.12 % E exiting
%------------------------------------------------------------------------------