TSTP Solution File: NUM926+6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM926+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 13:12:48 EDT 2022
% Result : Theorem 0.94s 0.91s
% Output : Proof 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 57
% Syntax : Number of formulae : 112 ( 29 unt; 18 typ; 0 def)
% Number of atoms : 382 ( 147 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 427 ( 159 ~; 183 |; 0 &)
% ( 55 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 13 >; 12 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 186 ( 137 !; 40 ?; 186 :)
% Comments :
%------------------------------------------------------------------------------
tff(ord_less_eq_type,type,
ord_less_eq: ( $i * $i * $i ) > $o ).
tff(int_type,type,
int: $i ).
tff(ord_less_type,type,
ord_less: ( $i * $i * $i ) > $o ).
tff(ti_type,type,
ti: ( $i * $i ) > $i ).
tff(order_type,type,
order: $i > $o ).
tff(t_type,type,
t: $i ).
tff(number_number_of_type,type,
number_number_of: ( $i * $i ) > $i ).
tff(bit1_type,type,
bit1: $i > $i ).
tff(zero_zero_type,type,
zero_zero: $i > $i ).
tff(one_one_type,type,
one_one: $i > $i ).
tff(pls_type,type,
pls: $i ).
tff(number_type,type,
number: $i > $o ).
tff(plus_plus_type,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(times_times_type,type,
times_times: ( $i * $i * $i ) > $i ).
tff(m_type,type,
m: $i ).
tff(bit0_type,type,
bit0: $i > $i ).
tff(power_power_type,type,
power_power: ( $i * $i * $i ) > $i ).
tff(nat_type,type,
nat: $i ).
tff(1,plain,
( order(int)
<=> order(int) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
order(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
tff(3,plain,
order(int),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X_a: $i] :
refl(
( ( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
<=> ( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
<=> ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [X_a: $i] :
rewrite(
( ( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
<=> ( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
<=> ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
<=> ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) ),
inference(transitivity,[status(thm)],[7,5]) ).
tff(9,plain,
( ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
<=> ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [X_a: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [X_1: $i,Y_1: $i] :
trans(
monotonicity(
rewrite(
( ( ( ti(X_a,X_1) != ti(X_a,Y_1) )
=> ord_less(X_a,X_1,Y_1) )
<=> ( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1) ) )),
( ( ord_less_eq(X_a,X_1,Y_1)
=> ( ( ti(X_a,X_1) != ti(X_a,Y_1) )
=> ord_less(X_a,X_1,Y_1) ) )
<=> ( ord_less_eq(X_a,X_1,Y_1)
=> ( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1) ) ) )),
rewrite(
( ( ord_less_eq(X_a,X_1,Y_1)
=> ( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1) ) )
<=> ( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )),
( ( ord_less_eq(X_a,X_1,Y_1)
=> ( ( ti(X_a,X_1) != ti(X_a,Y_1) )
=> ord_less(X_a,X_1,Y_1) ) )
<=> ( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ))),
( ! [X_1: $i,Y_1: $i] :
( ord_less_eq(X_a,X_1,Y_1)
=> ( ( ti(X_a,X_1) != ti(X_a,Y_1) )
=> ord_less(X_a,X_1,Y_1) ) )
<=> ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )),
( ( order(X_a)
=> ! [X_1: $i,Y_1: $i] :
( ord_less_eq(X_a,X_1,Y_1)
=> ( ( ti(X_a,X_1) != ti(X_a,Y_1) )
=> ord_less(X_a,X_1,Y_1) ) ) )
<=> ( order(X_a)
=> ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) )),
rewrite(
( ( order(X_a)
=> ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
<=> ( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) )),
( ( order(X_a)
=> ! [X_1: $i,Y_1: $i] :
( ord_less_eq(X_a,X_1,Y_1)
=> ( ( ti(X_a,X_1) != ti(X_a,Y_1) )
=> ord_less(X_a,X_1,Y_1) ) ) )
<=> ( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X_a: $i] :
( order(X_a)
=> ! [X_1: $i,Y_1: $i] :
( ord_less_eq(X_a,X_1,Y_1)
=> ( ( ti(X_a,X_1) != ti(X_a,Y_1) )
=> ord_less(X_a,X_1,Y_1) ) ) )
<=> ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X_a: $i] :
( order(X_a)
=> ! [X_1: $i,Y_1: $i] :
( ord_less_eq(X_a,X_1,Y_1)
=> ( ( ti(X_a,X_1) != ti(X_a,Y_1) )
=> ord_less(X_a,X_1,Y_1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_order__le__neq__implies__less) ).
tff(13,plain,
! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
| ~ order(int)
| ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) ) )
<=> ( ~ ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
| ~ order(int)
| ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
| ~ order(int)
| ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X_a: $i] :
( ~ order(X_a)
| ! [X_1: $i,Y_1: $i] :
( ( ti(X_a,X_1) = ti(X_a,Y_1) )
| ord_less(X_a,X_1,Y_1)
| ~ ord_less_eq(X_a,X_1,Y_1) ) )
| ~ order(int)
| ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) ),
inference(unit_resolution,[status(thm)],[19,16,3]) ).
tff(21,plain,
( ( one_one(int) = number_number_of(int,bit1(pls)) )
<=> ( one_one(int) = number_number_of(int,bit1(zero_zero(int))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( one_one(int) = number_number_of(int,bit1(pls)) )
<=> ( one_one(int) = number_number_of(int,bit1(pls)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_one__is__num__one) ).
tff(24,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
one_one(int) = number_number_of(int,bit1(zero_zero(int))),
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
number_number_of(int,bit1(zero_zero(int))) = one_one(int),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t)
<=> ord_less_eq(int,one_one(int),t) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ord_less_eq(int,one_one(int),t)
<=> ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) ),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ord_less_eq(int,one_one(int),t)
<=> ord_less_eq(int,one_one(int),t) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
tff(31,plain,
ord_less_eq(int,one_one(int),t),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t),
inference(modus_ponens,[status(thm)],[31,28]) ).
tff(33,plain,
( ( one_one(int) = t )
<=> ( t = one_one(int) ) ),
inference(commutativity,[status(thm)],]) ).
tff(34,plain,
( ( ti(int,t) = t )
<=> ( ti(int,t) = t ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
ti(int,t) = t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_t_____res) ).
tff(36,plain,
ti(int,t) = t,
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( number(int)
<=> number(int) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(39,plain,
number(int),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
^ [B_1_1: $i,X_a: $i] :
refl(
( ( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) )
<=> ( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) )
<=> ! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) )
<=> ! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
^ [B_1_1: $i,X_a: $i] :
rewrite(
( ( number(X_a)
=> ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) )
<=> ( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [B_1_1: $i,X_a: $i] :
( number(X_a)
=> ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) )
<=> ! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [B_1_1: $i,X_a: $i] :
( number(X_a)
=> ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
tff(46,plain,
! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) )
| ~ number(int)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = number_number_of(int,bit1(zero_zero(int))) ) )
<=> ( ~ ! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) )
| ~ number(int)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = number_number_of(int,bit1(zero_zero(int))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) )
| ~ number(int)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = number_number_of(int,bit1(zero_zero(int))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [B_1_1: $i,X_a: $i] :
( ~ number(X_a)
| ( ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1) ) )
| ~ number(int)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = number_number_of(int,bit1(zero_zero(int))) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
ti(int,number_number_of(int,bit1(zero_zero(int)))) = number_number_of(int,bit1(zero_zero(int))),
inference(unit_resolution,[status(thm)],[52,49,39]) ).
tff(54,plain,
ti(int,number_number_of(int,bit1(zero_zero(int)))) = one_one(int),
inference(transitivity,[status(thm)],[53,26]) ).
tff(55,plain,
( ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
<=> ( one_one(int) = t ) ),
inference(monotonicity,[status(thm)],[54,36]) ).
tff(56,plain,
( ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
<=> ( t = one_one(int) ) ),
inference(transitivity,[status(thm)],[55,33]) ).
tff(57,plain,
( ( t = one_one(int) )
<=> ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) ) ),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ( t != one_one(int) )
<=> ( ti(int,number_number_of(int,bit1(zero_zero(int)))) != ti(int,t) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( t != one_one(int) )
<=> ( t != one_one(int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ( t != one_one(int) )
| $false )
<=> ( t != one_one(int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) )
<=> ~ ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
~ ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(63,plain,
~ ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) )
<=> $false ),
inference(iff_false,[status(thm)],[63]) ).
tff(65,plain,
( ( ( t != one_one(int) )
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) )
<=> ( ( t != one_one(int) )
| $false ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ( t != one_one(int) )
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) )
<=> ( t != one_one(int) ) ),
inference(transitivity,[status(thm)],[65,60]) ).
tff(67,plain,
( ( ( t != one_one(int) )
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) )
<=> ( ( t != one_one(int) )
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ( t = one_one(int) )
=> ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) )
<=> ( ( t != one_one(int) )
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
( ( t = one_one(int) )
=> ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(70,plain,
( ( t != one_one(int) )
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ( t != one_one(int) )
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
inference(modus_ponens,[status(thm)],[70,67]) ).
tff(72,plain,
t != one_one(int),
inference(modus_ponens,[status(thm)],[71,66]) ).
tff(73,plain,
t != one_one(int),
inference(modus_ponens,[status(thm)],[72,59]) ).
tff(74,plain,
ti(int,number_number_of(int,bit1(zero_zero(int)))) != ti(int,t),
inference(modus_ponens,[status(thm)],[73,58]) ).
tff(75,plain,
( ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
<=> ord_less(int,one_one(int),t) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(76,plain,
( ord_less(int,one_one(int),t)
<=> ord_less(int,number_number_of(int,bit1(zero_zero(int))),t) ),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ ord_less(int,one_one(int),t)
<=> ~ ord_less(int,number_number_of(int,bit1(zero_zero(int))),t) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ~ ord_less(int,one_one(int),t)
<=> ~ ord_less(int,one_one(int),t) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ~ ord_less(int,one_one(int),t)
| $false )
<=> ~ ord_less(int,one_one(int),t) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ ord_less(int,one_one(int),t)
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) )
<=> ( ~ ord_less(int,one_one(int),t)
| $false ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(81,plain,
( ( ~ ord_less(int,one_one(int),t)
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) )
<=> ~ ord_less(int,one_one(int),t) ),
inference(transitivity,[status(thm)],[80,79]) ).
tff(82,plain,
( ( ord_less(int,one_one(int),t)
=> ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) )
<=> ( ~ ord_less(int,one_one(int),t)
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
( ord_less(int,one_one(int),t)
=> ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(84,plain,
( ~ ord_less(int,one_one(int),t)
| ? [X: $i,Y: $i] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
~ ord_less(int,one_one(int),t),
inference(modus_ponens,[status(thm)],[84,81]) ).
tff(86,plain,
~ ord_less(int,one_one(int),t),
inference(modus_ponens,[status(thm)],[85,78]) ).
tff(87,plain,
~ ord_less(int,number_number_of(int,bit1(zero_zero(int))),t),
inference(modus_ponens,[status(thm)],[86,77]) ).
tff(88,plain,
( ( ~ ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) )
| ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) )
<=> ( ~ ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) )
| ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) )
<=> ( ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( ~ ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) )
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) )
<=> ( ~ ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) )
| ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) )
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) )
<=> ( ~ ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) )
| ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) )
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [X_1: $i,Y_1: $i] :
( ( ti(int,X_1) = ti(int,Y_1) )
| ord_less(int,X_1,Y_1)
| ~ ord_less_eq(int,X_1,Y_1) )
| ord_less(int,number_number_of(int,bit1(zero_zero(int))),t)
| ( ti(int,number_number_of(int,bit1(zero_zero(int)))) = ti(int,t) )
| ~ ord_less_eq(int,number_number_of(int,bit1(zero_zero(int))),t) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
$false,
inference(unit_resolution,[status(thm)],[93,87,74,32,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM926+6 : TPTP v8.1.0. Released v5.3.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Sep 2 15:36:48 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.94/0.91 % SZS status Theorem
% 0.94/0.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------