TSTP Solution File: NUM924+7 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 13:12:41 EDT 2022
% Result : Theorem 78.97s 51.61s
% Output : Proof 79.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 92
% Syntax : Number of formulae : 194 ( 74 unt; 26 typ; 0 def)
% Number of atoms : 486 ( 158 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 459 ( 158 ~; 181 |; 7 &)
% ( 99 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 18 >; 13 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 8 con; 0-4 aty)
% Number of variables : 207 ( 187 !; 0 ?; 207 :)
% Comments :
%------------------------------------------------------------------------------
tff(ti_type,type,
ti: ( $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(zero_zero_type,type,
zero_zero: $i > $i ).
tff(int_type,type,
int: $i ).
tff(times_times_type,type,
times_times: ( $i * $i ) > $i ).
tff(one_one_type,type,
one_one: $i > $i ).
tff(plus_plus_type,type,
plus_plus: ( $i * $i ) > $i ).
tff(m_type,type,
m: $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(t_type,type,
t: $i ).
tff(pls_type,type,
pls: $i ).
tff(mult_zero_type,type,
mult_zero: $i > $o ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(ord_less_type,type,
ord_less: $i > $i ).
tff(fun_type,type,
fun: ( $i * $i ) > $i ).
tff(bool_type,type,
bool: $i ).
tff(ord_less_eq_type,type,
ord_less_eq: $i > $i ).
tff(twoSqu1929807760sum2sq_type,type,
twoSqu1929807760sum2sq: $i > $i ).
tff(product_Pair_type,type,
product_Pair: ( $i * $i * $i * $i ) > $i ).
tff(s_type,type,
s: $i ).
tff(min_type,type,
min: $i ).
tff(minus_minus_type,type,
minus_minus: ( $i * $i ) > $i ).
tff(nat_type,type,
nat: $i ).
tff(power_power_type,type,
power_power: ( $i * $i ) > $i ).
tff(1,plain,
^ [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] :
refl(
( ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) )
<=> ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) )
<=> ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) )
<=> ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
tff(5,plain,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) )
| ( ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,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(12,plain,
( ( one_one(int) = number_number_of(int,bit1(pls)) )
<=> ( one_one(int) = number_number_of(int,bit1(pls)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_one__is__num__one) ).
tff(14,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
one_one(int) = number_number_of(int,bit1(zero_zero(int))),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),number_number_of(int,bit1(zero_zero(int)))),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),number_number_of(int,bit1(zero_zero(int)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int)),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),number_number_of(int,bit1(zero_zero(int))))) = times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int))),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int))) = times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),number_number_of(int,bit1(zero_zero(int))))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,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(zero_zero(int)))))),m)),one_one(int))),zero_zero(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(zero_zero(int)))))),m)),number_number_of(int,bit1(zero_zero(int))))),zero_zero(int)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,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(zero_zero(int)))))),m)),number_number_of(int,bit1(zero_zero(int))))),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( mult_zero(int)
<=> mult_zero(int) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
mult_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
tff(24,plain,
mult_zero(int),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
^ [X_a: $i] :
refl(
( ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [X_a: $i] :
rewrite(
( ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
^ [X_a: $i] :
rewrite(
( ( mult_zero(X_a)
=> ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [X_a: $i] :
( mult_zero(X_a)
=> ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
<=> ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [X_a: $i] :
( mult_zero(X_a)
=> ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_mult__zero__right) ).
tff(34,plain,
! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
| ~ mult_zero(int)
| ! [A_1: $i] : ( hAPP(int,int,times_times(int,A_1),zero_zero(int)) = zero_zero(int) ) )
<=> ( ~ ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
| ~ mult_zero(int)
| ! [A_1: $i] : ( hAPP(int,int,times_times(int,A_1),zero_zero(int)) = zero_zero(int) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
| ~ mult_zero(int)
| ! [A_1: $i] : ( hAPP(int,int,times_times(int,A_1),zero_zero(int)) = zero_zero(int) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X_a: $i] :
( ~ mult_zero(X_a)
| ! [A_1: $i] : ( hAPP(X_a,X_a,times_times(X_a,A_1),zero_zero(X_a)) = zero_zero(X_a) ) )
| ~ mult_zero(int)
| ! [A_1: $i] : ( hAPP(int,int,times_times(int,A_1),zero_zero(int)) = zero_zero(int) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [A_1: $i] : ( hAPP(int,int,times_times(int,A_1),zero_zero(int)) = zero_zero(int) ),
inference(unit_resolution,[status(thm)],[40,37,24]) ).
tff(42,plain,
( ~ ! [A_1: $i] : ( hAPP(int,int,times_times(int,A_1),zero_zero(int)) = zero_zero(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(zero_zero(int)))))),m)),number_number_of(int,bit1(zero_zero(int))))),zero_zero(int)) = zero_zero(int) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,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(zero_zero(int)))))),m)),number_number_of(int,bit1(zero_zero(int))))),zero_zero(int)) = zero_zero(int),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
zero_zero(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(zero_zero(int)))))),m)),number_number_of(int,bit1(zero_zero(int))))),zero_zero(int)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ( ti(int,pls) = pls )
<=> ( ti(int,zero_zero(int)) = zero_zero(int) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ti(int,pls) = pls )
<=> ( ti(int,pls) = pls ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
ti(int,pls) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
tff(48,plain,
ti(int,pls) = pls,
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
ti(int,zero_zero(int)) = zero_zero(int),
inference(modus_ponens,[status(thm)],[48,45]) ).
tff(50,plain,
^ [Z_2: $i] :
refl(
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [Z_2: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) )
<=> ! [Z_2: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [Z_2: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) )
<=> ! [Z_2: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [Z_2: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_int__one__le__iff__zero__less) ).
tff(54,plain,
! [Z_2: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [Z_2: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [Z_2: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [Z_2: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) )
| ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t)) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t))
<=> ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
tff(61,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t)) ),
inference(tautology,[status(thm)],]) ).
tff(63,plain,
( ~ ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t)) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t)) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t)),
inference(unit_resolution,[status(thm)],[63,58]) ).
tff(65,plain,
^ [B: $i,A_1: $i] :
refl(
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) )
<=> ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) )
<=> ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [B: $i,A_1: $i] :
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B)))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ) )),
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B)))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) ) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ) ) )),
rewrite(
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ) )),
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B)))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) ) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B)))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) ) )
<=> ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B)))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_pos__zmult__pos) ).
tff(71,plain,
! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int)))) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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)))) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_p0) ).
tff(78,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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)))),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int)))),
inference(modus_ponens,[status(thm)],[78,75]) ).
tff(80,plain,
( ( ~ ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) )
<=> ( ~ ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ~ ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [B: $i,A_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,times_times(int,A_1),B))) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(zero_zero(int)))))),m)),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),t))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ),
inference(unit_resolution,[status(thm)],[82,79,74]) ).
tff(84,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))),
inference(unit_resolution,[status(thm)],[83,64]) ).
tff(85,plain,
( ( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),one_one(int)) )
<=> ( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min)) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( 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)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) )
<=> ( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),one_one(int)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( 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)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(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)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
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)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
tff(89,plain,
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)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),one_one(int)),
inference(modus_ponens,[status(thm)],[89,86]) ).
tff(91,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min)) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(modus_ponens,[status(thm)],[90,85]) ).
tff(92,plain,
hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min))) = hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),zero_zero(int)),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min))),
inference(symmetry,[status(thm)],[92]) ).
tff(95,plain,
( ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),one_one(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(zero_zero(int)))))),m)),one_one(int))),t) )
<=> ( twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(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(zero_zero(int)))))),m)),one_one(int))),t) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(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,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),one_one(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(zero_zero(int)))))),m)),one_one(int))),t) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(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,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(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) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(99,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(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),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),one_one(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(zero_zero(int)))))),m)),one_one(int))),t),
inference(modus_ponens,[status(thm)],[99,96]) ).
tff(101,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(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(zero_zero(int)))))),m)),one_one(int))),t),
inference(modus_ponens,[status(thm)],[100,95]) ).
tff(102,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(zero_zero(int)))))),m)),one_one(int))),t) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)) = hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min))),
inference(transitivity,[status(thm)],[103,94]) ).
tff(105,plain,
hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min))),zero_zero(int)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),zero_zero(int)),
inference(transitivity,[status(thm)],[105,93]) ).
tff(107,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),zero_zero(int))) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int))) ),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),zero_zero(int)))
<=> ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int))) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min))),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),zero_zero(int))) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(111,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min))),zero_zero(int)))
<=> ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),zero_zero(int))) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),one_one(int))),zero_zero(int)))
<=> ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min))),zero_zero(int))) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),one_one(int))),zero_zero(int))) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,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(115,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(116,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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)],[115,114]) ).
tff(117,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),one_one(int))),zero_zero(int))),
inference(modus_ponens,[status(thm)],[116,113]) ).
tff(118,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(zero_zero(int)))))),number_number_of(int,min))),zero_zero(int))),
inference(modus_ponens,[status(thm)],[117,112]) ).
tff(119,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),zero_zero(int))),
inference(modus_ponens,[status(thm)],[118,111]) ).
tff(120,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int))),
inference(modus_ponens,[status(thm)],[119,109]) ).
tff(121,plain,
^ [X_1: $i,Y: $i] :
refl(
( ( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
<=> ( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
<=> ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
<=> ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
^ [X_1: $i,Y: $i] :
rewrite(
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
<=> ( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [X_1: $i,Y: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
<=> ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,axiom,
! [X_1: $i,Y: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_zless__linear) ).
tff(127,plain,
! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) ),
inference(modus_ponens,[status(thm)],[129,122]) ).
tff(131,plain,
( ( ~ ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)))
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) )
<=> ( ~ ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)))
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
( ( ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int))) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)))
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ( ~ ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int))) )
<=> ( ~ ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)))
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ) ),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( ( ~ ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int))) )
<=> ( ~ ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)))
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ) ),
inference(transitivity,[status(thm)],[133,131]) ).
tff(135,plain,
( ~ ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int))) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
( ~ ! [X_1: $i,Y: $i] :
( ( ti(int,X_1) = ti(int,Y) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X_1)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)))
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),m)),one_one(int))),t)),zero_zero(int)))
| ( ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)) )
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(zero_zero(int)))))),m)),one_one(int))),t))) ),
inference(unit_resolution,[status(thm)],[136,130]) ).
tff(138,plain,
ti(int,zero_zero(int)) = ti(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(zero_zero(int)))))),m)),one_one(int))),t)),
inference(unit_resolution,[status(thm)],[137,120,84]) ).
tff(139,plain,
ti(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(zero_zero(int)))))),m)),one_one(int))),t)) = ti(int,zero_zero(int)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
ti(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(zero_zero(int)))))),m)),one_one(int))),t)) = ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))),
inference(transitivity,[status(thm)],[139,49,44,21,10]) ).
tff(141,plain,
^ [Z_2: $i,W_1: $i] :
refl(
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
| ( ti(int,Z_2) = ti(int,W_1) ) ) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
| ( ti(int,Z_2) = ti(int,W_1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(142,plain,
( ! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
| ( ti(int,Z_2) = ti(int,W_1) ) ) )
<=> ! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
| ( ti(int,Z_2) = ti(int,W_1) ) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
^ [Z_2: $i,W_1: $i] :
rewrite(
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
& ( ti(int,Z_2) != ti(int,W_1) ) ) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
| ( ti(int,Z_2) = ti(int,W_1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(144,plain,
( ! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
& ( ti(int,Z_2) != ti(int,W_1) ) ) )
<=> ! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
| ( ti(int,Z_2) = ti(int,W_1) ) ) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
( ! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
& ( ti(int,Z_2) != ti(int,W_1) ) ) )
<=> ! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
& ( ti(int,Z_2) != ti(int,W_1) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,axiom,
! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
& ( ti(int,Z_2) != ti(int,W_1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zless__le) ).
tff(147,plain,
! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
& ( ti(int,Z_2) != ti(int,W_1) ) ) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
& ( ti(int,Z_2) != ti(int,W_1) ) ) ),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
| ( ti(int,Z_2) = ti(int,W_1) ) ) ),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
| ( ti(int,Z_2) = ti(int,W_1) ) ) ),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
( ~ ! [Z_2: $i,W_1: $i] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1))
| ( ti(int,Z_2) = ti(int,W_1) ) ) )
| ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
| ( ti(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(zero_zero(int)))))),m)),one_one(int))),t)) = ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
| ( ti(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(zero_zero(int)))))),m)),one_one(int))),t)) = ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))) ) ) ),
inference(unit_resolution,[status(thm)],[151,150]) ).
tff(153,plain,
hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))),
inference(monotonicity,[status(thm)],[103]) ).
tff(154,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)))) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)))) ),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)))) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)))) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,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(159,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(160,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,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)],[159,158]) ).
tff(161,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)))),
inference(modus_ponens,[status(thm)],[160,157]) ).
tff(162,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)))),
inference(modus_ponens,[status(thm)],[161,156]) ).
tff(163,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int)))),
inference(modus_ponens,[status(thm)],[162,155]) ).
tff(164,plain,
( ~ ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
<=> ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
| ( ti(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(zero_zero(int)))))),m)),one_one(int))),t)) = ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))) ) ) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
| ~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
| ( ti(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(zero_zero(int)))))),m)),one_one(int))),t)) = ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(165,plain,
~ ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
| ( ti(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(zero_zero(int)))))),m)),one_one(int))),t)) = ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))) ) ),
inference(unit_resolution,[status(thm)],[164,163,152]) ).
tff(166,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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(zero_zero(int)))))),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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))))
| ( ti(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(zero_zero(int)))))),m)),one_one(int))),t)) = ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))) )
| ( ti(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(zero_zero(int)))))),m)),one_one(int))),t)) != ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))) ) ),
inference(tautology,[status(thm)],]) ).
tff(167,plain,
ti(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(zero_zero(int)))))),m)),one_one(int))),t)) != ti(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(zero_zero(int)))))),m)),one_one(int))),zero_zero(int))),
inference(unit_resolution,[status(thm)],[166,165]) ).
tff(168,plain,
$false,
inference(unit_resolution,[status(thm)],[167,140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.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 15:49:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 78.97/51.61 % SZS status Theorem
% 78.97/51.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------