TSTP Solution File: NUM924_3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM924_3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 13:12:39 EDT 2022
% Result : Theorem 0.83s 0.91s
% Output : Proof 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 43
% Syntax : Number of formulae : 74 ( 17 unt; 23 typ; 0 def)
% Number of atoms : 174 ( 132 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 143 ( 24 ~; 50 |; 0 &)
% ( 69 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 13 ( 4 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 20 ( 15 >; 5 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-2 aty)
% Number of variables : 58 ( 50 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_int_bool_type,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(hAPP_int_int_type,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(pls_type,type,
pls: int ).
tff(times_times_int_type,type,
times_times_int: int > fun_int_int ).
tff(number_number_of_int_type,type,
number_number_of_int: int > int ).
tff(bit1_type,type,
bit1: int > int ).
tff(plus_plus_int_type,type,
plus_plus_int: int > fun_int_int ).
tff(m_type,type,
m: int ).
tff(bit0_type,type,
bit0: int > int ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(twoSqu949963151sum2sq_type,type,
twoSqu949963151sum2sq: product_prod_int_int > int ).
tff(product_Pair_int_int_type,type,
product_Pair_int_int: ( int * int ) > product_prod_int_int ).
tff(s_type,type,
s: int ).
tff(ord_less_int_type,type,
ord_less_int: fun_int_fun_int_bool ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(min_type,type,
min: int ).
tff(minus_minus_int_type,type,
minus_minus_int: int > fun_int_int ).
tff(hAPP_nat_int_type,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
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(one_one_int_type,type,
one_one_int: int ).
tff(t_type,type,
t: int ).
tff(1,plain,
^ [A_2: int,B_2: int] :
refl(
( ( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
<=> ( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
<=> ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [A_2: int,B_2: int] :
rewrite(
( ( ( hAPP_int_int(times_times_int(A_2),B_2) = number_number_of_int(pls) )
<=> ( ( B_2 = number_number_of_int(pls) )
| ( A_2 = number_number_of_int(pls) ) ) )
<=> ( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = number_number_of_int(pls) )
<=> ( ( B_2 = number_number_of_int(pls) )
| ( A_2 = number_number_of_int(pls) ) ) )
<=> ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [A_2: int,B_2: int] :
rewrite(
( ( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( B_2 = zero_zero_int )
| ( A_2 = zero_zero_int ) ) )
<=> ( ( hAPP_int_int(times_times_int(A_2),B_2) = number_number_of_int(pls) )
<=> ( ( B_2 = number_number_of_int(pls) )
| ( A_2 = number_number_of_int(pls) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( B_2 = zero_zero_int )
| ( A_2 = zero_zero_int ) ) )
<=> ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = number_number_of_int(pls) )
<=> ( ( B_2 = number_number_of_int(pls) )
| ( A_2 = number_number_of_int(pls) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( B_2 = zero_zero_int )
| ( A_2 = zero_zero_int ) ) )
<=> ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( B_2 = zero_zero_int )
| ( A_2 = zero_zero_int ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
^ [A_2: int,B_2: int] :
rewrite(
( ( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( A_2 = zero_zero_int )
| ( B_2 = zero_zero_int ) ) )
<=> ( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( B_2 = zero_zero_int )
| ( A_2 = zero_zero_int ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( A_2 = zero_zero_int )
| ( B_2 = zero_zero_int ) ) )
<=> ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( B_2 = zero_zero_int )
| ( A_2 = zero_zero_int ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,axiom,
! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( A_2 = zero_zero_int )
| ( B_2 = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_mult__eq__0__iff) ).
tff(11,plain,
! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( B_2 = zero_zero_int )
| ( A_2 = zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int )
<=> ( ( B_2 = zero_zero_int )
| ( A_2 = zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = number_number_of_int(pls) )
<=> ( ( B_2 = number_number_of_int(pls) )
| ( A_2 = number_number_of_int(pls) ) ) ),
inference(modus_ponens,[status(thm)],[12,6]) ).
tff(14,plain,
! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) ),
inference(modus_ponens,[status(thm)],[13,4]) ).
tff(15,plain,
! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) ),
inference(modus_ponens,[status(thm)],[15,2]) ).
tff(17,plain,
( ( ~ ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
| ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls ) )
<=> ( ~ ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
| ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls )
<=> $true )
<=> ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( $true
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls))) = pls ) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( pls = pls )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( ( pls = pls )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls))) = pls ) )
<=> ( $true
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls))) = pls ) ) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ( ( pls = pls )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls))) = pls ) )
<=> $true ),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,plain,
( ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls )
<=> ( ( pls = pls )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls))) = pls ) ) )
<=> ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls )
<=> $true ) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls )
<=> ( ( pls = pls )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls))) = pls ) ) )
<=> ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls ) ),
inference(transitivity,[status(thm)],[23,18]) ).
tff(25,plain,
( ( ~ ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
| ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls )
<=> ( ( pls = pls )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls))) = pls ) ) ) )
<=> ( ~ ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
| ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
| ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls )
<=> ( ( pls = pls )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls))) = pls ) ) ) )
<=> ( ~ ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
| ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls ) ) ),
inference(transitivity,[status(thm)],[25,17]) ).
tff(27,plain,
( ~ ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
| ( ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls )
<=> ( ( pls = pls )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls))) = pls ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [A_2: int,B_2: int] :
( ( hAPP_int_int(times_times_int(A_2),B_2) = pls )
<=> ( ( B_2 = pls )
| ( A_2 = pls ) ) )
| ( hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls) = pls,
inference(unit_resolution,[status(thm)],[28,16]) ).
tff(30,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls)) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),pls),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),pls)) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls))) ),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),pls))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls))) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(min))),pls))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),pls)) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(bit1(pls)))),number_number_of_int(pls)))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(min))),pls)) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(bit1(pls)))),number_number_of_int(pls))) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(39,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(bit1(pls)))),number_number_of_int(pls))),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(min))),pls)),
inference(modus_ponens,[status(thm)],[40,35]) ).
tff(42,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),pls)),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls))),
inference(modus_ponens,[status(thm)],[42,33]) ).
tff(44,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),number_number_of_int(pls))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls))) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),number_number_of_int(pls)))) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(48,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),number_number_of_int(pls)))),
inference(modus_ponens,[status(thm)],[48,45]) ).
tff(50,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu949963151sum2sq(product_Pair_int_int(s,number_number_of_int(bit1(pls))))),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),number_number_of_int(bit1(pls)))),pls))),
inference(modus_ponens,[status(thm)],[49,44]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM924_3 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 15:40:47 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.83/0.91 % SZS status Theorem
% 0.83/0.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------