TSTP Solution File: NUM925+7 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM925+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 13:12:45 EDT 2022
% Result : Theorem 124.25s 79.79s
% Output : Proof 124.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 51
% Syntax : Number of formulae : 91 ( 23 unt; 20 typ; 0 def)
% Number of atoms : 248 ( 148 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 267 ( 97 ~; 65 |; 7 &)
% ( 95 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 15 >; 9 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-4 aty)
% Number of variables : 99 ( 90 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_zero_type,type,
zero_zero: $i > $i ).
tff(int_type,type,
int: $i ).
tff(ti_type,type,
ti: ( $i * $i ) > $i ).
tff(plus_plus_type,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(n_type,type,
n: $i ).
tff(semiring_1_of_nat_type,type,
semiring_1_of_nat: $i > $i ).
tff(nat_type,type,
nat: $i ).
tff(one_one_type,type,
one_one: $i > $i ).
tff(power_power_type,type,
power_power: ( $i * $i ) > $i ).
tff(pls_type,type,
pls: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(ord_less_eq_type,type,
ord_less_eq: $i > $i ).
tff(fun_type,type,
fun: ( $i * $i ) > $i ).
tff(bool_type,type,
bool: $i ).
tff(ord_less_type,type,
ord_less: $i > $i ).
tff(number_number_of_type,type,
number_number_of: ( $i * $i ) > $i ).
tff(bit0_type,type,
bit0: $i > $i ).
tff(bit1_type,type,
bit1: $i > $i ).
tff(ring_11004092258visors_type,type,
ring_11004092258visors: $i > $o ).
tff(1,plain,
( ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = ti(int,zero_zero(int)) )
<=> ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( ti(int,pls) = pls )
<=> ( ti(int,zero_zero(int)) = zero_zero(int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( ti(int,pls) = pls )
<=> ( ti(int,pls) = pls ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
ti(int,pls) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
tff(5,plain,
ti(int,pls) = pls,
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
ti(int,zero_zero(int)) = zero_zero(int),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
zero_zero(int) = ti(int,zero_zero(int)),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) )
<=> ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = ti(int,zero_zero(int)) ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) )
<=> ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ),
inference(transitivity,[status(thm)],[8,1]) ).
tff(10,plain,
( ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) )
<=> ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) ) ),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ( ti(int,zero_zero(int)) != ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) )
<=> ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) != zero_zero(int) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
^ [Z_1: $i,Wa: $i] :
refl(
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
| ( ti(int,Z_1) = ti(int,Wa) ) ) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
| ( ti(int,Z_1) = ti(int,Wa) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
| ( ti(int,Z_1) = ti(int,Wa) ) ) )
<=> ! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
| ( ti(int,Z_1) = ti(int,Wa) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [Z_1: $i,Wa: $i] :
rewrite(
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
& ( ti(int,Z_1) != ti(int,Wa) ) ) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
| ( ti(int,Z_1) = ti(int,Wa) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
& ( ti(int,Z_1) != ti(int,Wa) ) ) )
<=> ! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
| ( ti(int,Z_1) = ti(int,Wa) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
& ( ti(int,Z_1) != ti(int,Wa) ) ) )
<=> ! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
& ( ti(int,Z_1) != ti(int,Wa) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
& ( ti(int,Z_1) != ti(int,Wa) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_zless__le) ).
tff(18,plain,
! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
& ( ti(int,Z_1) != ti(int,Wa) ) ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
& ( ti(int,Z_1) != ti(int,Wa) ) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
| ( ti(int,Z_1) = ti(int,Wa) ) ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
| ( ti(int,Z_1) = ti(int,Wa) ) ) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
( ~ ! [Z_1: $i,Wa: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),Wa))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),Wa))
| ( ti(int,Z_1) = ti(int,Wa) ) ) )
| ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ) ),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(26,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( ~ ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(28,plain,
( ~ ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ) )
| ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ) ),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ),
inference(unit_resolution,[status(thm)],[28,23]) ).
tff(30,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ( ti(int,zero_zero(int)) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) )
| ( ti(int,zero_zero(int)) != ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) ) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
ti(int,zero_zero(int)) != ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) != zero_zero(int),
inference(modus_ponens,[status(thm)],[31,11]) ).
tff(33,plain,
( ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(zero_zero(int))))) = zero_zero(int) )
<=> ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(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,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(zero_zero(int))))) = zero_zero(int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(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,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ( ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(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,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
~ ( ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(38,plain,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(modus_ponens,[status(thm)],[38,35]) ).
tff(40,plain,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(zero_zero(int))))) = zero_zero(int),
inference(modus_ponens,[status(thm)],[39,34]) ).
tff(41,plain,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ~ ( ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) )
<=> ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) ) )
| ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(nat,one_one(nat),one_one(nat))) != zero_zero(int) )
| ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) ) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
~ ( ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) )
<=> ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[42,41,32]) ).
tff(44,plain,
( ring_11004092258visors(int)
<=> ring_11004092258visors(int) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
tff(46,plain,
ring_11004092258visors(int),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
^ [X_a: $i] :
refl(
( ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
^ [X_a: $i] :
rewrite(
( ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
^ [X_a: $i] :
rewrite(
( ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(zero_zero(int))))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(zero_zero(int))))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [X_a: $i] :
rewrite(
( ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(zero_zero(int))))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(zero_zero(int))))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
^ [X_a: $i] :
rewrite(
( ( ring_11004092258visors(X_a)
=> ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [X_a: $i] :
( ring_11004092258visors(X_a)
=> ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [X_a: $i] :
( ring_11004092258visors(X_a)
=> ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_zero__eq__power2) ).
tff(60,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,bit0(bit1(zero_zero(int))))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[61,55]) ).
tff(63,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[62,53]) ).
tff(64,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[64,51]) ).
tff(66,plain,
( ( ~ ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
| ~ ring_11004092258visors(int)
| ! [A_2: $i] :
( ( hAPP(nat,int,power_power(int,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ) )
<=> ( ~ ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
| ~ ring_11004092258visors(int)
| ! [A_2: $i] :
( ( hAPP(nat,int,power_power(int,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
| ~ ring_11004092258visors(int)
| ! [A_2: $i] :
( ( hAPP(nat,int,power_power(int,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( hAPP(nat,X_a,power_power(X_a,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
| ~ ring_11004092258visors(int)
| ! [A_2: $i] :
( ( hAPP(nat,int,power_power(int,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [A_2: $i] :
( ( hAPP(nat,int,power_power(int,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[68,65,46]) ).
tff(70,plain,
( ~ ! [A_2: $i] :
( ( hAPP(nat,int,power_power(int,A_2),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) )
| ( ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int) )
<=> ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
$false,
inference(unit_resolution,[status(thm)],[70,69,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM925+7 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Sep 2 15:46:20 EDT 2022
% 0.14/0.35 % 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.
% 124.25/79.79 % SZS status Theorem
% 124.25/79.79 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------