TSTP Solution File: NUM925_3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM925_3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:12:43 EDT 2022
% Result : Theorem 0.94s 0.90s
% Output : Proof 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 48
% Syntax : Number of formulae : 85 ( 30 unt; 20 typ; 0 def)
% Number of atoms : 131 ( 96 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 86 ( 24 ~; 4 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 17 ( 12 >; 5 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 18 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_int_bool_type,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(plus_plus_int_type,type,
plus_plus_int: ( int * int ) > int ).
tff(hAPP_nat_int_type,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(n_type,type,
n: nat ).
tff(semiri1621563631at_int_type,type,
semiri1621563631at_int: fun_nat_int ).
tff(number_number_of_int_type,type,
number_number_of_int: int > int ).
tff(bit1_type,type,
bit1: int > int ).
tff(succ_type,type,
succ: int > int ).
tff(min_type,type,
min: int ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(ord_less_int_type,type,
ord_less_int: fun_int_fun_int_bool ).
tff(plus_plus_nat_type,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
tff(power_power_int_type,type,
power_power_int: int > fun_nat_int ).
tff(bit0_type,type,
bit0: int > int ).
tff(pls_type,type,
pls: int ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(zero_zero_nat_type,type,
zero_zero_nat: nat ).
tff(1,plain,
^ [A_1: int] :
refl(
( ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) )
<=> ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) )
<=> ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [A_1: int] :
rewrite(
( ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
<=> ( A_1 = number_number_of_int(succ(min)) ) )
<=> ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
<=> ( A_1 = number_number_of_int(succ(min)) ) )
<=> ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [A_1: int] :
rewrite(
( ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
<=> ( A_1 = number_number_of_int(pls) ) )
<=> ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
<=> ( A_1 = number_number_of_int(succ(min)) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
<=> ( A_1 = number_number_of_int(pls) ) )
<=> ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
<=> ( A_1 = number_number_of_int(succ(min)) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [A_1: int] :
rewrite(
( ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) )
<=> ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
<=> ( A_1 = number_number_of_int(pls) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) )
<=> ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
<=> ( A_1 = number_number_of_int(pls) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) )
<=> ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,axiom,
! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_zero__eq__power2) ).
tff(11,plain,
! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
<=> ( A_1 = number_number_of_int(pls) ) ),
inference(modus_ponens,[status(thm)],[11,8]) ).
tff(13,plain,
! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
<=> ( A_1 = number_number_of_int(succ(min)) ) ),
inference(modus_ponens,[status(thm)],[12,6]) ).
tff(14,plain,
! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) ),
inference(modus_ponens,[status(thm)],[13,4]) ).
tff(15,plain,
! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) ),
inference(modus_ponens,[status(thm)],[15,2]) ).
tff(17,plain,
( ~ ! [A_1: int] :
( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( A_1 = succ(min) ) )
| ( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) ),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
<=> ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
<=> ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,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(23,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(24,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(25,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)],[24,23]) ).
tff(26,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)],[25,22]) ).
tff(27,plain,
hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls),
inference(modus_ponens,[status(thm)],[26,21]) ).
tff(28,plain,
hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min),
inference(modus_ponens,[status(thm)],[28,19]) ).
tff(30,plain,
( ~ ( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) )
| ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) != succ(min) )
| ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
( ~ ( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
<=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) )
| ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min),
inference(unit_resolution,[status(thm)],[31,18]) ).
tff(33,plain,
( ( number_number_of_int(succ(min)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(succ(min))) )
<=> ( succ(min) = number_number_of_int(succ(min)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( number_number_of_int(pls) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)) )
<=> ( number_number_of_int(succ(min)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(succ(min))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) )
<=> ( number_number_of_int(pls) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) )
<=> ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_transfer__int__nat__numerals_I1_J) ).
tff(38,plain,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
number_number_of_int(pls) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)),
inference(modus_ponens,[status(thm)],[38,35]) ).
tff(40,plain,
number_number_of_int(succ(min)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(succ(min))),
inference(modus_ponens,[status(thm)],[39,34]) ).
tff(41,plain,
succ(min) = number_number_of_int(succ(min)),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
number_number_of_int(succ(min)) = succ(min),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))) = hAPP_i1948725293t_bool(ord_less_int,succ(min)),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min)),
inference(monotonicity,[status(thm)],[43,32]) ).
tff(45,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min))) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min)))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),number_number_of_int(succ(min))))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min))) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(pls)))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),number_number_of_int(succ(min)))) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(pls))) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_bin__less__0__simps_I1_J) ).
tff(53,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(pls))),
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),number_number_of_int(succ(min)))),
inference(modus_ponens,[status(thm)],[54,49]) ).
tff(56,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min))),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[56,47]) ).
tff(58,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(rewrite,[status(thm)],]) ).
tff(60,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(61,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/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(62,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)],[61,60]) ).
tff(63,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[62,59]) ).
tff(64,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[63,58]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925_3 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 15:51:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.94/0.90 % SZS status Theorem
% 0.94/0.90 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------